LNNCHS Common Competency INFO-SHEET-1.2 PDF

LEARNING OUTCOME NO. 2 Carry Out Measurements and Calculations Contents: 1. Trade Mathematics/Mensuration a. Four Fundamental Operations b. Systems of Measurements c. Ratio and Proportion, Percentage d. Fractions and Decimals Assessment Criteria...

LEARNING OUTCOME NO. 2 Carry Out Measurements and Calculations Contents: 1. Trade Mathematics/Mensuration a. Four Fundamental Operations b. Systems of Measurements c. Ratio and Proportion, Percentage d. Fractions and Decimals Assessment Criteria 1. Calculations needed to complete work tasks are performed using the four basic processes of addition (+), subtraction (-), multiplication (x) and division (/) including but not limited to: trigonometric functions, algebraic computations. 2. Calculations involving fractions, percentages and mixed numbers are used to complete workplace tasks 3. Numerical computations are self-checked and corrected for accuracy. 4. Accurate measurements are obtained according to job requirements. 5. Identified and converted systems of measurement according to job requirements. 6. Measured work pieces according to job requirements. Conditions The student/trainee must be provided with the following: ▪ Classroom for discussion ▪ Workplace Location ▪ Problems to solve ▪ Measuring instruments ▪ Instructional materials relevant to the proposed activity. Assessment Method: 1. Oral questioning 2. Direct observation 3. Written test Document No. Date complied: Issued by: Perform mensuration June 2024 Page 1 of 26 and calculations Complied by: Kristine M. Capao Revision # Learning Experiences Learning Outcome 2: Carry Out Measurements and Calculations Learning Activities Special Instructions 1. Four Fundamental Operations a. Read Information Sheet 1.2-1 Read and understand the on Four Fundamental information sheet. If you feel you Operations. have already familiarized yourself with the Four Fundamental Operations, you can now answer self-check 1.2-1. b. Answer Self-Check 1.2-1. 2. Systems of Measurement a. Read Information Sheet 1.2-2 Read and understand the on Systems of Measurements. information sheet. If you feel you have already familiarized yourself with the Information sheet 1.2-2, b. Answer Self-Check 1.2-2. you can now answer self-check 1.2- c. Perform Task Sheet 1.2-1 on 2. Conversion of Measurements 3. Ratio, Proportion and Percentage Read and understand the a. Read Information Sheet 1.2-3 information sheet. If you feel you on Ratio Proportion and have already familiarized yourself Percentage. with the Information sheet 1.2-3, you can now answer self-check 1.2- 3. b. Answer Self-Check 1.2-3. 4. Fractions, Percentage and Decimals Read and understand the a. Read Information Sheet 1.2-4 information sheet. If you feel you on Fractions, Percentage and have already familiarized yourself Decimals. with the Information sheet 1.2-4, you can now answer self-check 1.2- 4. b. Answer Self-Check 1.2-4. c. Perform Task Sheet 1.2-2 on Conversion of Fractions to Decimals and Vice Versa Document No. Date complied: Issued by: Perform mensuration June 2024 Page 2 of 26 and calculations Complied by: Kristine M. Capao Revision #  INFORMATION SHEET 1-2.1 Four Fundamental Operations Learning Objectives: After reading this INFORMATION SHEET, YOU MUST be able to: 1. Understand the fundamental concepts and principles of addition, subtraction, multiplication, and division. 2. Apply and utilize addition, subtraction, multiplication and division operations effectively in solving simple and worded problems. Four Fundamental Operations The four basic mathematical operations – addition, subtraction, multiplication, and division – have applications even in the most advanced mathematical theories. Thus, mastering them is one of the keys to progressing in an understanding of mathematics. These operations are commonly called arithmetic operations. Arithmetic is the oldest and most elementary branch of mathematics. In this and other related lessons we will briefly explain basic math operations. Keep in mind that even though the operations and the examples shown here are simple, they provide the basis for even the most complex operations used in mathematics. Addition It is the act of adding two or more numbers. ( + ) Sign for addition Addends – refers to two or more things or numbers being added Sum – the result of addition or the total Example: 6+3=9 where, 6 and 3 is the addend 9 is the sum Subtraction It is taking away something from another. ( – ) Sign for subtraction Document No. Date complied: Issued by: Perform mensuration June 2024 Page 3 of 26 and calculations Complied by: Kristine M. Capao Revision #  Minuend is the first number where the second number is subtracted from. Subtrahend is the number being subtracted. Difference is the result of subtraction. Example: 9−3=6 where, 9 is the minuend 3 is the subtrahend 6 is the difference Take note that subtraction is the inverse of addition, as well as addition is the inverse of subtraction. Hence, by checking if your answer is correct, you will simply reverse the process. In the example above, 6 and 3 are being added to get the result which is 9. To check if we got the correct answer, we simply subtract 3 from 9 to get the result which is 6. Multiplication It is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number. Multiplication Formula The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where: Multiplicand: The first number (factor). Multiplier: The second number (factor). Product: The result after multiplying the multiplicand and multiplier. Multiplication symbol: '×' (which connects the entire expression) Let us understand the multiplication formula with the help of the following expression. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 4 of 26 and calculations Complied by: Kristine M. Capao Revision #  Example: 3 × 6 = 18 where, 3 and 6 are the factors 3 is the multiplicand 6 is the multiplier 18 is the product Properties of Multiplication ▪ Commutative Property: This property states that when we multiply two numbers, the order will not cause any change in the product. For example, 2×3=6. If we reverse the order, i.e., compute 3×2, the answer will still be 6. ▪ Associative Property: This property states that if we multiply three numbers or more, one after the other, the order does not matter. For example: if we have 2,3 and 4: (2×3)×4=24 2×(3×4)=24 If you jumble the order and multiply, the result will still not change. 3×(2×4)=24 ▪ Distributive Property: This property states that if you multiply a number by the sum of two numbers, the result will be equal to the sum of products you obtain by multiplying that number by those two numbers individually. For example, 3×8. You can write 8 as 6+2. Therefore 3×8=3×(6+2)=24 Now, 3×6=18. Also, 3×2=6. 18+6=24=3×8. Therefore, distributive property holds true. Tips and Tricks on Multiplication: Here is a few tips and tricks that can be used while performing multiplication. In multiplication, the order of numbers does not matter. So choose the order that you are more comfortable with. When using the multiplication tables, compared to 9 × 4, students may remember 4 × 9 more easily. When multiplying three numbers, choose the two numbers that can be multiplied easily. For example, multiplying 5 × 17 × 2 will be difficult if Document No. Date complied: Issued by: Perform mensuration June 2024 Page 5 of 26 and calculations Complied by: Kristine M. Capao Revision #  we try to multiply 5 × 17 first. Instead of this, multiplying 5 and 2 gives 10 which can be easily multiplied by 17 to get 170. When multiplying a 2-digit number with a one-digit number, it sometimes helps to break the two-digit number as per the place values. Then multiply each part and add. For example, 37 × 4 can be solved mentally by breaking 37 as 30 + 7. Then 30 × 4 = 120 and 7 × 4 = 28. So, the final answer is 120 + 28 = 148. While this may seem more tedious when written down, it is much easier to solve mentally. Even if you do not remember the multiplication fact, it can be easily mentally figured out. For example, 17 × 9 is difficult to remember. But this can be restructured mentally as 17 × (10 - 1). So, the answer will be 170 - 17 = 153. Division It is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken. Dividend is the number that is divided by another number in a division operation. Divisor is the number used to divide. Quotient is the result of the division. Remainder is the part that is left over after the division operation. ÷ Sign for division Example: 10 ÷ 3 = 3 𝑟𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟 1 or 10 ÷ 3 = 3 𝑟 1 where, 10 is the dividend The first 3 is the divisor The second 3 is the quotient 1 is the remainder Take note that division is the inverse of multiplication. Thus, to check if you get the correct answer, you simply reverse the process. In the example above from multiplication, we have 3 multiplied by 6 to get the product of 18. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 6 of 26 and calculations Complied by: Kristine M. Capao Revision # Now, to check if our answer is correct, we will divide 6 from 18 (18 ÷6) to get the result of 3 (the quotient). Properties of Division 1. If we divide a whole number (except zero) by itself, the quotient or the answer is always 1. For example: 7÷7=1 25 ÷ 25 = 1 2. If we divide a whole number by zero, the answer will be undefined. For example: 6 ÷ 0 = undefined 325 ÷ 0 = undefined 3. Zero divided by any number will give the answer zero. For example: 0÷5=0 0 ÷ 100 = 0 4. If we divide a whole number (other than zero) by 1, the answer will be the number itself. For example: 4÷1=4 11 ÷ 1 = 11 5. If a whole number is divided by another whole number, the quotient may not necessarily be a whole number. For example: 15 ÷ 2 = 7.5 20 ÷ 3 = 6.67 6. In the case of exact division (with no remainder), the divisor multiplied by the quotient is the dividend. This property holds true only if all three numbers are non-zero whole numbers. For example: If 30 ÷ 5 = 6 then 5 × 6 = 30 7. If there are three non-zero whole numbers a, b and c, and b × c = a, then, a ÷ b = c and a ÷ c = b For example: 5 × 10 = 50, then, 50 ÷ 5 = 10 50÷ 10 = 5 Long Division In math, long division is the mathematical method for dividing large numbers into smaller groups or parts. It helps in breaking down a problem into simple and easy steps. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 7 of 26 and calculations Complied by: Kristine M. Capao Revision # Long Division Steps: Example: Document No. Date complied: Issued by: Perform mensuration June 2024 Page 8 of 26 and calculations Complied by: Kristine M. Capao Revision #  INFORMATION SHEET 1-2.2 Systems of Measurements Learning Objectives: After reading this INFORMATION SHEET, YOU MUST be able to: 1. Identify and differentiate between metric and imperial measurement systems. 2. Understand the different systems of measurement used in technical drafting and mensuration. 3. Apply the appropriate system of measurement based on job requirements or international standards (ISO). 4. Convert measurements between different systems accurately. 5. Utilize systems of measurement effectively to ensure precision in technical measurements and calculations. Trade Mathematics/Measurement The word measurement comes from the Greek word “metron”, which means limited proportion. The metre (US: meter) was standardized as the unit for length after the French Revolution, and it has been adopted throughout the world. Metric scale is applied when the meter is used for linear measurement. Accurate measurement is essential in many fields, and since all measurements are necessary, a great deal of effort must be taken to make measurements as accurate as possible. Measuring accurately is a skill that should be developed. Inaccurate measurement would mean waste of time, effort and materials. The development of the skill in measuring starts with the ability to read measurements improving one’s numeracy skills that can be used in the trades, thus the term – trade mathematics. Systems of Measurement There are two systems of measurement: English and Metric System. The English system originated in England and the Metric system or Systems International (S.I.) originated in France. The basic unit in the System International measurement is called meter. The meter is divided into 100 centimeters. Each centimeter is divided into 10 millimeters. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 9 of 26 and calculations Complied by: Kristine M. Capao Revision #  Unit Name Abbreviation Millimeters mm Centimeters cm Decimeters dm Meters m In English system, each inch is divided into 16 graduations and the smallest graduation is read 1/16. To read measurements exceeding 1-inch, say 2 inches (2”) and for smaller graduations, it is read and written as: in or in. 1 foot + 2 inches + 3 smaller graduations is read and written as: in. In the S.I. measurement, the centimeter is divided into 10 millimeters. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 10 of 26 and calculations Complied by: Kristine M. Capao Revision # Metric System of Measurement (Linear equivalent) 10 millimeters (mm) = 1 centimeter (cm) 10 centimeters (cm) = 1 decimeter (dm) 10 decimeters (dm) = 1 meter (m) 10 meters (m) = 1 decameter (Dm) 10 decameters (Dm) = 1 hectometer (Hm) 10 hectometers (Hm) = 1 kilometer (km) 10 (km) = 1 myriameter (Mn) English System of Measurement (Linear equivalent) 12 inches (in) = 1 foot (ft) 3 feet (ft) = 1 yard (yd) Metric Conversion Table 1 millimeter = 0.03937 inches (in) 1 centimeter = 0.3937 inches (in) 1 meter = 39.37 inches (in) English Conversion Table 1 inch (in) = 0.0254 mm = 2.54 cm = 0.0254 m 1 foot (ft) = 304.8 mm = 30.48 cm = 0.3048 m 1 yard (yd) = 914.4 mm = 91.4 cm = 0.9144 m Conversion Formulas Length in inches  0.0254 = length in meters Length in inches  2.54 = length in centimeters Length in feet + 3.28 = length in meters Length in meters  39.37 = length in inches Length in inches + 39.37 = length in meters Length in feet  0.305 = length in meters Length in feet  30.5 = length in centimeters Document No. Date complied: Issued by: Perform mensuration June 2024 Page 11 of 26 and calculations Complied by: Kristine M. Capao Revision # Unit of Conversion System International (S.I.) to English 1 meter = 39.37 inches = 3.28083 feet = 1.094 yards 0.3048 meter 1 foot 1 centimeter 0.3937 inch 2.54 centimeters 1 inch 1 millimeter 0.03937 inch 25.4 millimeters 1 inch 1 kilometer 1093.61 yards Example1: If 10mm = 1cm, then 13mm = _____cm? Solution: 1 cm 13 cm 13mm  = = 1.3 cm 10 mm 10 Example1: If 1 in = 0.0254 m, then 2.5 in = _____m? Solution: 0.0252 m 0.0635 m 2.5 in  = = 0.0635 m 1 in 1 Document No. Date complied: Issued by: Perform mensuration June 2024 Page 12 of 26 and calculations Complied by: Kristine M. Capao Revision #  INFORMATION SHEET 1-2.3 Ratio, Proportion and Percentage Learning Objectives: After reading this INFORMATION SHEET, YOU MUST be able to: 1. Understand the concept of ratio, proportion and percentage, and its application in technical drafting and mensuration. 2. Apply ratios to compare quantities and sizes of objects accurately. 3. Solve problems involving proportions to determine dimensions and scaling factors. 4. Utilize ratios and proportions effectively in resizing or scaling technical drawings and measurements. 5. Interpret and apply ratio and proportion concepts in real-world scenarios related to technical drafting tasks. Ratio A ratio compares two values. It shows the relationship between different values. A ratio says how much of one thing there is compared to another thing. It is a comparison of two values a and b, written in the form a : b. Suppose we want to write the ratio of 3 and 1, we can write this as 3:1 or as fraction 3/1, and we say the ratio is eight to twelve. Here, there are 3 blue squares to 1 yellow square. In the ratio a : b, the first quantity is called an antecedent and the second quantity is called consequent. But ratios can be shown in different ways: Use the ":" to separate the values: 3:1 Or we can use the word "to": 3 to 1 or 3 is to 1 3 Or write it like a fraction: 1 A ratio can be scaled up. Look at the ratio below. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 13 of 26 and calculations Complied by: Kristine M. Capao Revision #  Here the ratio is also 3 blue squares to 1 yellow square, even though there are more squares. "Part-to-Part" and "Part-to-Whole" Ratios The examples so far have been "part-to-part" (comparing one part to another part). But a ratio can also show a part compared to the whole lot. For example, in a group of 30 people, 17 of them prefer to walk in the morning and 13 of them prefer to cycle. Part-to-Part: ▪ The ratio of people who prefer walking to the people who prefer cycling is 17:13 or 17/13. ▪ The ratio of people who prefer cycling to the people who prefer walking is 13:17 or 13/17. Part-to-Whole: ▪ The ratio of people who prefer walking to the group of people is 17:30 or 17/30. ▪ The ratio of people who prefer cycling to the group of people is 13:30 or 13/30. Note that ratios must be presented as two numbers in the lowest possible integer values. Scaling Two common uses of ratios in design & technology are to communicate the scale on drawings. A scale is a ratio of size in a map, model, plan, or drawing. The standard way to write the scale is scale model to actual object or scale:actual. Ratio is 1:2 Document No. Date complied: Issued by: Perform mensuration June 2024 Page 14 of 26 and calculations Complied by: Kristine M. Capao Revision #  Another example is the ratio between 500 mm and 125 mm is 4:1, as 500 is 4 times the value of 125. Ratios do not have units. Ratios in design are necessary to communicate the scale on drawings. On technical drawings, the size of the drawn item is typically either smaller or bigger than the actual item. The scale represents the size of the drawing compared to its actual size. A scale of 1:1 is the actual size. A scale of 1:2 implies that the drawing is half the size of the part; 2:1 implies that the drawing is twice the size of the part. Proportion Proportion says that two ratios (or fractions) are equal. We see that 1-out-of-3 is equal to 2-out-of-6. The ratios are the same, so they are in proportion. Example: A rope's length and weight are in proportion. When 20m of rope weighs 1kg, then: 40m of that rope weighs 2kg 200m of that rope weighs 10kg Etc. 20 40 So: = 1 2 Sizes When shapes are "in proportion" their relative sizes are the same. Here we see that the ratios of head length to body length are the same in both drawings. So, they are proportional. Making the head too long or short would look bad! Document No. Date complied: Issued by: Perform mensuration June 2024 Page 15 of 26 and calculations Complied by: Kristine M. Capao Revision # Interpreting Scale Drawing Example: The scale is 1in:5ft. Find the actual length of the canoe. 1in 3in What did you do to 1 5ft ? to get to 3? 1in 3in Cross multiply, you 5ft ? get 15 inft 1 in 15 inft = 15 ft 1 in Using Proportions to Solve Percents A percent is a ratio. Saying "25%" is the same as saying "25 per 100": 25 25% = 100 We can use proportions to solve questions involving percents. Part Percent The trick is to put what we know into this form: Whole = 100 Example: What is 25% of 160? Part 25 Solution: = 160 100 Multiply across the known corners, then divide by the third number: Part = (160 × 25) / 100 = 4000 / 100 = 40 Answer: 25% of 160 is 40. Note: we could have also solved this by doing the divide first, like this: Part = 160 × (25 / 100) = 160 × 0.25 = 40 Either method works fine. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 16 of 26 and calculations Complied by: Kristine M. Capao Revision # We can also find a Percent: What is 12cm as a percentage of 80cm? Fill in what we know: 12cm Percent = 80cm 100 Multiply across the known corners, then divide by the third number. This time the known corners are top left and bottom right: 12cm Percent = 80cm 100 Percent = (12 × 100) / 80 = 1200 / 80 = 15% Answer: 12cm is 15% of 80cm. Real World Example Ratios can have more than two numbers. For example, concrete is made by mixing cement, sand, stones and water. A typical mix of cement, sand and gravel is written as a ratio, such as 1:2:3. We can multiply all values by the same amount and still have the same ratio. 10:20:30 is the same as 1:2:3 So, when we use 10 sacks of cement, we should use 20 of sand and 30 of gravel. Example: You have just put 12 sacks of gravel into a mixer, how much cement and how much sand should you add to make a 1:2:3 mix? Let us lay it out in a table to make it clearer: Cement Sand Gravel Ratio Needed: 1 2 3 You Have: 12 You have 12 sacks of gravel, but the ratio says 3. That is alright, you simply have four times as many gravel as the number in the ratio... so you need four times more of everything to keep the ratio. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 17 of 26 and calculations Complied by: Kristine M. Capao Revision #  Here is the solution: Cement Sand Gravel Ratio Needed: 1 2 3 You Have: 4 8 12 And the ratio 4:8:12 is the same as 1:2:3 (because they show the same relative sizes) So, the answer is: add 4 sacks of cement and 8 sacks of sand. (You will also need water and a lot of stirring....). Why are they the same ratio? Well, the 1:2:3 ratio says to have: twice as much sand as cement (1:2:3) 3 times as much gravel as cement (1:2:3) In our mix we have: twice as much sand as cement (4:8:12) 3 times as much gravel as cement (4:8:12) So, it should be just right! Document No. Date complied: Issued by: Perform mensuration June 2024 Page 18 of 26 and calculations Complied by: Kristine M. Capao Revision #  INFORMATION SHEET 1-2.4 Fractions and Decimals Learning Objectives: After reading this INFORMATION SHEET, YOU MUST be able to: 1. Perform Basic Operations with Fractions. 2. Perform Basic Operations with Decimals. 3. Apply Fractions and Decimals in Workplace Contexts. Fraction Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator. It tells how many equal parts of the whole collection are taken. The number below the line is called the denominator. It shows the total number of equal parts the whole is divided into or the total number of the same objects in a collection. Fraction of a Whole When the whole is divided into equal parts, the number of parts we take makes up a fraction. If a cake is divided into eight equal pieces and one piece of the cake is placed on a plate, then each plate is said to have 18 of the cake. It is read as ‘one-eighth’ or ‘1 by 8’. Fraction of a Collection of Objects There are a total of 5 children. 3 3 out of 5 are girls. So, the fraction of girls is three-fifths ( ). 5 2 out of 5 are boys. So, the fraction of boys is two-fifths (2 ). 5 Equal and Unequal Parts To identify the fraction, the whole must be divided into equal parts. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 19 of 26 and calculations Complied by: Kristine M. Capao Revision # Representing a Fraction A fraction can be represented in 3 ways: as a fraction, as a percentage, or as a decimal. Let us see each of the three forms of representation. Fractional Representation a The first and most common form of representing a fraction is.bHere, a is the numerator, and b is the denominator. Both the numerator and denominator are separated by a horizontal bar. 3 Example: We can understand the fraction as follows. 4 Numerator: 3 Denominator: 4 The fraction represents three parts when a whole is divided into four equal parts. Decimal Representation In this format, the fraction is represented as a decimal number. 3 Example: The fraction 4 can be shown as a decimal by dividing the numerator (3) by the denominator (4). 3 = 0.75. 4 Thus, in decimal representation, 3 is written as 0.75. 4 Percentage Representation In this representation, a fraction is multiplied by 100 to convert it into a percentage. Example: If we want to represent as a percentage, we should 3 multiply sas by 100. 4 3 3 x 100 = 0.75 x 100 = 75. Thus, we can represent as 75%. 4 4 Types of Fractions The primary parts of a fraction are the numerator and the denominator. Based on these, different types of fractions can be defined. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 20 of 26 and calculations Complied by: Kristine M. Capao Revision # Mixed Fractions to Improper Fractions Mixed fractions can be converted to improper fractions by multiplying the whole number by the denominator and adding it to the numerator. It becomes the new numerator, and the denominator remains unchanged. 2 (83) + 2 26 Example: 8 3 = (8×3)+23 = 3 = 3 Examples on Fractions 14 1. Are the fractions and 7 equivalent? 20 10 Solution: 14 7 Simplest form of = 10 20 7 7 Simplest form of = 10 10 7 Since the simplest form of both fractions is , we can say that the two 10 fractions are equivalent. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 21 of 26 and calculations Complied by: Kristine M. Capao Revision #  2 2. Convert as a percentage. 5 Solution: 2 ×100 = 40% 5 Decimal A decimal is a number that consists of a whole and a fractional part. For example, in the given image, we have one whole pizza and a half of another pizza. This can be represented in two ways: Fractional form: In fraction form, we can write 1 that there is one and one-half 1 of a pizza. That is pizza. 2 Decimal Form: In decimal form, we will write this as 1.5 pizzas. Here, the dot represents the decimal point and the number before the dot, i.e., “1” represents one whole pizza and the number behind the decimal point represents the half pizza or the fractional part. We get decimals when we break a whole into smaller parts. A decimal number then has two components: a whole number part and a fractional part. The decimal place value system for the whole part of a decimal number is the same as the whole number value system. However, we get the fractional part of the decimal number as we move toward the right after the decimal point. The given image shows the decimal place value chart: Note that as we go from left to right in the decimal place value system, each value is 1 times smaller than the value to its left. 10 The first place after the decimal point is called the “tenths”, which 1 represents a place value of 10 of the whole or one-tenth of the whole. In decimal form, this fraction is written as “0.1”. Such fractions whose denominator is 10 or a positive power of 10 is called a decimal fraction. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 22 of 26 and calculations Complied by: Kristine M. Capao Revision #  The second place is called the “hundredths”, which represents a place 1 value of 100 of the whole or one-hundredth of the whole. In numerical form, this decimal fraction is written as “0.01”. And the 1 third place is called the “thousandths”, which represents a place value of 1000 of the whole or one-thousandth of the whole. In numerical form, this decimal fraction is written as “0.001”. Changing Fractions to Decimals Any rational number (numerator/denominator) can be changed from fractional form to decimal form. This is done by simply dividing the numerator by the denominator. Method 1: If the fraction has 10, 100 or 1000 as the denominator, we can reverse the process we used to convert decimals to fractions. You should already know that: To convert 37/100 to a decimal, we need to write 37 so that the last digit appears in the hundredths column, i.e. 0.37. From this we can see that: Method 2: If the fraction isn't like the one above, we may be able to change it to an equivalent fraction which does have 10, 100 or 1000 as the denominator. The fractions can then be converted in the same way as before. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 23 of 26 and calculations Complied by: Kristine M. Capao Revision # Method 3: Sometimes we are not able to find an equivalent fraction which has 10, 100 or 1000 as the denominator. In these cases, we need to divide the numerator by the denominator. For example, we saw before that 37/100 converts to 0.37. If we calculate 37 ÷ 100, we also get the answer 0.37. So, to write as a decimal, we need to calculate 5 ÷ 8: So, = 0.625 as a decimal. Rounding Off Decimals Metric measurements in decimals are often long numbers. They must often be rounded to a convenient number of digits. In this text most metric dimensions are either whole millimeter or two-places decimals that have been rounded off. Rules of Rounding Off 1. If the first number to be eliminated is less than 5, simply drop it (and the number to the right of it) and let the last significant digit stand. Example: Round off 25.4 mm to whole millimeter. Solution: Simply drop the.4 Answer: 25 Example : Round off 0.3125 (5/16) into two significant digits. Solution: The first number to be eliminated is 2: Simply drop it and all numbers to its right(5) Answer:0.31 2. If the number to be eliminated is 5 or more, drop the number, then add one to the last digit retained. Example: a. Round off 78.6 into its nearest ones. Solution: The number to be rounded off is 6 which is greater than 5, drop 6 and add one to the last digit retained. Answer: 79 Document No. Date complied: Issued by: Perform mensuration June 2024 Page 24 of 26 and calculations Complied by: Kristine M. Capao Revision #  b. Round off 92.65 into its nearest tenths. Solution: The number to be rounded off is 5, drop 5 and add one to 6 which is the last digit retained. Answer: 92.7 Conversion of Decimals to Fractions A decimal is changed to a fraction by using 10 or any power of 10 as denominator of the given decimal. Then change to lowest term when possible. Now think about the number 0.27: One tenth is the same as ten hundredths, so two tenths must be the same as twenty hundredths. This means that 0.27 can also be thought of as 27 hundredths or. In the same way, 0.127 is 127 thousandths or. The fractions you need to know in order to convert decimals to fractions are shown on the right: Examples: You can see that some fractions may be simplified (or cancelled down) after conversion. Also, if you convert a number which is larger than 1, you will get a vulgar or improper (top-heavy) fraction. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 25 of 26 and calculations Complied by: Kristine M. Capao Revision # References: Technical Drafting Training Regulation Technical Drafting Curriculum Based Curriculum https://www.scribd.com/document/493395893/techdraftmodule8 https://www.splashlearn.com https://www.cuemath.com Manaois, German (2004) Drafting Volume 2. Quezon City, Phoenix Publishing House, Inc., pp 1-22. Document No. Date complied: Issued by: Perform mensuration June 2024 Page 26 of 26 and calculations Complied by: Kristine M. Capao Revision #