8 Questions
What is a decimal number?
A way to represent numbers in base 10 using digits from 0 to 9
What type of decimal has an infinite number of random digits after the decimal point?
Non-Repeating Decimal
How do you add and subtract decimal numbers?
Align the decimal points, then add or subtract as with whole numbers
How do you convert a proper fraction to a decimal?
Divide the numerator by the denominator
How do you round a decimal number to a specific place value?
Look at the digit to the right of the desired place value
What is a common application of decimal numbers in real-world scenarios?
Science and engineering
How many decimal places are used to represent money?
Two decimal places
What type of decimal has an infinite number of digits that repeat in a cycle after the decimal point?
Repeating Decimal
Study Notes
Decimal Numbers
Definition
- A decimal number is a way to represent a number in base 10 using digits from 0 to 9.
- Decimal numbers are used to represent fractions, decimals, and percentages.
Types of Decimal Numbers
- Terminating Decimals: Decimals that have a finite number of digits after the decimal point.
- Repeating Decimals (Recurring Decimals): Decimals that have an infinite number of digits that repeat in a cycle after the decimal point.
- Non-Repeating Decimals (Irrational Decimals): Decimals that have an infinite number of random digits after the decimal point.
Operations with Decimal Numbers
- Addition and Subtraction: Same as with whole numbers, but align the decimal points.
- Multiplication: Multiply the numbers as if they were whole numbers, then place the decimal point in the product.
- Division: Divide the numbers as if they were whole numbers, then place the decimal point in the quotient.
Converting Fractions to Decimals
- Proper Fractions: Divide the numerator by the denominator to get a decimal equivalent.
- Improper Fractions: Divide the numerator by the denominator to get a decimal equivalent, then simplify if necessary.
Rounding Decimal Numbers
- Rounding to a Specific Place Value: Round to the nearest tenth, hundredth, etc. by looking at the digit to the right of the desired place value.
- Rounding to a Specific Number of Decimal Places: Round to the desired number of decimal places by looking at the digit to the right of the desired number of places.
Real-World Applications
- Money: Decimals are used to represent money, with two decimal places for dollars and cents.
- Measurement: Decimals are used to represent precise measurements, such as length, weight, and time.
- Science and Engineering: Decimals are used to represent precise calculations and measurements in scientific and engineering applications.
Decimal Numbers
Definition
- Decimal numbers represent numbers in base 10 using digits from 0 to 9.
- They are used to represent fractions, decimals, and percentages.
Types of Decimal Numbers
Types of Decimals
- Terminating Decimals: Finite number of digits after the decimal point.
- Repeating Decimals (Recurring Decimals): Infinite number of digits that repeat in a cycle after the decimal point.
- Non-Repeating Decimals (Irrational Decimals): Infinite number of random digits after the decimal point.
Operations with Decimal Numbers
Decimal Operations
- Addition and Subtraction: Align decimal points, then perform operations as with whole numbers.
- Multiplication: Multiply as with whole numbers, then place decimal point in product.
- Division: Divide as with whole numbers, then place decimal point in quotient.
Converting Fractions to Decimals
Fraction Conversion
- Proper Fractions: Divide numerator by denominator to get decimal equivalent.
- Improper Fractions: Divide numerator by denominator, then simplify if necessary.
Rounding Decimal Numbers
Rounding Decimals
- Rounding to a Specific Place Value: Round to nearest tenth, hundredth, etc. by looking at digit to the right of desired place value.
- Rounding to a Specific Number of Decimal Places: Round to desired number of decimal places by looking at digit to the right of desired number of places.
Real-World Applications
Real-World Uses
- Money: Decimals represent money with two decimal places for dollars and cents.
- Measurement: Decimals represent precise measurements, such as length, weight, and time.
- Science and Engineering: Decimals are used in precise calculations and measurements in scientific and engineering applications.
Learn about decimal numbers, including their definition, types such as terminating and repeating decimals, and their applications.
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