Chapter Nine: Decimals PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Nine Decimals Introduction The concept of decimals is new to you since it has not been taught or learnt...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Nine Decimals Introduction The concept of decimals is new to you since it has not been taught or learnt before. However, it is very closely connected to the concept of fractions that LY you have learnt in Chapter Eight. The competence of decimals will help you to deal with money accurately. For example, conversion of money. Also, it will provide you with the ability to measure mass, length, volume and other N quantities accurately. O Meaning of a decimal Study the following rectangle: _ 1 1 1 1 1 1 SE 1 1 1 1 ​   ​​ ​​ _ ​​ ​​ _ ​​ ​​ _ ​​ ​​ _ ​​ ​​ _ ​​ ​​ _ ​​ ​​ _ ​​ ​​ _ ​​ ​​ _ ​​ ​ 10 10 10 10 10 10 10 10 10 10 U E 0.1 N A rectangle sub divided into 10 equal parts. LI _ 1 A rectangle is subdivided into 10 equal parts. The shaded part is ​​   ​​ of the 1 10 _ N original rectangle. In decimal notation, the fraction ​​   ​​ is written as 0.1, which 10 O is obtained by dividing 1 by 10. It is one-tenth of the rectangle. Place value of decimals R You have already learnt how to determine the place values of digits in whole FO numbers. In decimals, the place values of digits to the left of the decimal point are determined as in whole numbers. The place values of the digits to the right of the decimal point are tenth, followed by hundredth, thousandth, and so on depending on the number of decimal places. 138 MATH std 5.indd 138 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example Write the place value of each of the digits in the following decimals: (a) 8.1 (b) 0.1 (c) 12.34 (d) 27.312 Solution (a) 8.1 (b) 0. 1 Tenth Tenth LY Ones Ones N (c) 1 2. 3 4 (d) 2 7. 3 1 2 Hundredth Thousandth O Tenth Hundredth Ones Tenth Tens SE Ones Tens U Exercise 1 E 1. Write down the place value of each of the digits in the following decimals: N (a) 32.03 (b) 0.05 (c) 1.37 (d) 146.02 LI (e) 48.22 (f) 1.16 N 2. Write down the following decimals in numerals: O (a) Four tens, zero ones, zero tenth, nine hundredth (b) Five ones, two tenth, three hundredth (c) One hundreds, zero tens, four ones, four tenth R FO 139 MATH std 5.indd 139 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE There are many types of decimals. The following are some decimals based on a number divided by 10: 2 _ 4 _ _ 9 (a) ​​   ​ = 0.2​ (b) ​​   ​  = 0.4​ (c) ​​  ​  = 0.9​ 10 10 10 In the decimals 0.2, 0.4 and 0.9, the point separates a whole number, which is 0, and a number, which is a fraction of 10. LY A decimal has two parts: (a) A whole number N (b) A decimal part (which represents a fraction). O These parts are separated by a dot (.) called a decimal point. For example; (a) (b) SE In 0.8, a whole number is 0 and a decimal part is 8. In 3.15, a whole number is 3 and a decimal part is 15. U Reading decimal numbers Reading numbers with one decimal place Decimal numbers are read from left to right as shown in the following example. E N Example LI Decimal number How the number is read 0.7 Zero point seven N 1.8 One point eight O 25.6 Twenty-five point six 250.1 Two hundred fifty point one R FO Reading decimal numbers with two decimal places Use the following table to study decimal numbers: 140 MATH std 5.indd 140 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 1 _ ​​   ​​ 100 LY N _1 The shaded area is ​​  ​​ of the whole drawing and it is written as 0.01. The O 100 number 0.01 is obtained by dividing 1 by 100. Using the drawing, you can get different decimal numbers. For example; _ 100 3 (a) ​​   ​  = 0.03​ 12 _ (b) ​​  SE  ​  = 0.12​ 100 (c) _ ​​  100 94  ​  = 0.94​ U The digits to the left of the point are read like whole numbers. The digits to the right of the point are read one after the other, starting from the tenth, followed by hundredth, thousandth and so on. For example: E N Decimal number How the number is read 0.05 Zero point zero five LI 0.13 Zero point one three 15.34 Fifteen point three four N 525.25 Five hundred twenty-five point two five O Exercise 2 R Read the following decimals: FO 1. (a) 0.4 (b) 1.7 (c) 18.9 (d) 28.2 141 MATH std 5.indd 141 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. (a) 43.5 (b) 132.5 (c) 631.8 (d) 0.1 3. (a) 0.01 (b) 1.23 (c) 2.07 (d) 0.25 4. (a) 18.15 (b) 84.72 (c) 24.99 (d) 72.75 5. (a) 113.04 (b) 583.94 (c) 716.88 (d) 2.04 LY Writing decimals in numerals and in words N Example 1 O Write the following decimals in words: Decimals in numerals SE Decimals in words 0.4 Zero point four U 2.1 Two point one 0.08 Zero point zero eight 13.26 Thirteen point two six E Example 2 N LI Write the following decimals in numerals: Decimals in words Decimal numbers in numerals N Zero point five 0.5 Eleven point six 11.6 O Zero point zero nine 0.09 Twenty-three point three 23.37 R seven FO 142 MATH std 5.indd 142 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 3 Answer the following questions: 1. Write the following decimals in words: (a) 0.6 (b) 0.1 (c) 0.3 (d) 2.4 (e) 6.7 (f) 12.8 (g) 0.02 (h) 0.29 (i) 48.65 (j) 93.07 (k) 68.31 LY 2. Write the following decimals in numerals: N (a) Zero point five three. (b) Eight point seven five. O (c) Ten point nine. (d) Zero point zero two. (e) (f) Eleven point eight two. Thirteen point zero one. SE (g) Fifty-six point two five. U (h) Twenty-eight point one eight. Changing a fraction into a decimal number E Decimals are obtained by dividing a numerator by a denominator. N Example 1 LI 6 _ Change ​​   ​​ into decimal. N 10 O Solution Steps: _ ⟌ ​​ 1. Divide the numerator 6 by the denominator 10. This is denoted by ​10​ 6 R The division is not sufficient. Write 0 in the answer’s position above FO the digit 6 followed by a decimal point as shown in Step 2. 2. Put a zero to the right of 6 to get 60. Divide 60 by 10 to get 6. Write 6 after the decimal point. 143 MATH std 5.indd 143 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 0.6 10 60 − 60 0 6 _ Therefore, ​​   ​   =  0.6​. LY 10 Example 2 N 1 _ Change ​​   ​​ into decimal. 2 O Solution Steps: SE 1. Divide 1 by 2. This is denoted by ​2​ 1 _ ⟌ ​. U The division is not sufficient. Write 0 in the 0. answer’s position followed by a decimal 2 1 point. E 2. Put a zero to the right of 1 to get 10. 0.5 N Divide 10 by 2 to get 5. Write 5 in the 2 10 LI answer’s position. Multiply 5 by 2 to get − 10 10. Subtract to get 0. 0 N O _ 1 Therefore, ​​   ​  = 0.5​. 2 R Example 3 FO 1 _ Change ​​   ​​ into decimal. 100 144 MATH std 5.indd 144 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Divide 1 by 100. 100 1 2. The division in step 1 is not sufficient. Write 0 above the digit 1 followed by a 0. 100 10 decimal point. Put a zero to the right of LY 1 to get 10. 3. Divide 10 by 100. The division is still not sufficient. Write 0 in the tenth position in N 0.0 the answer’s position, then put 0 to the 100 100 O right of 10 to get 100. 4. Divide 100 by 100 to get 1. Write 1 in 0.01 the hundredth position in the answer’s 100 100 position. SE − 100 0 U ​  1  ​ Therefore, _ ​ = 0.01​. 100 E Example 4 N _ 5 Convert ​​   ​​ into a decimal number. LI 2 N Solution 2.5 O 2 5 −4 R 10 − 10 FO 0 5 _ Therefore, ​​   ​  = 2.5​. 2 145 MATH std 5.indd 145 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 4 Change the following into decimals: 3 _ 8 _ _ 7 12 _ 1. (a) ​​   ​​ (b) ​​   ​​ (c) ​​   ​​ (d) ​​   ​​ 10 10 10 10 LY _ 1 _ 2 _ 3 _ 7 2. (a) ​​   ​​ (b) ​​   ​​ (c) ​​   ​​ (d) ​​   ​​ 5 5 2 5 N _ 3 _ 15 _ 76 _ 83 3. (a) ​ ​  ​​ (b) ​​  ​​ (c) ​​   ​​ (d) ​​  ​​ O 100 100 100 100 _ 1 _1 _ 3 _ 5 4. (a) ​​   ​​ 25 6 (b) ​​   ​​ 4 108 (c) SE ​​   ​​ 4 176 (d) ​​   ​​ 4 27 5. (a) _ ​​   ​​ (b) _ ​​  ​​ (c) _ ​​   ​​ _ (d) ​​   ​​ U 100 100 100 100 Addition of decimals E Addition of decimals with only one decimal place N Use the following figure to find the value of ​0.5 + 0.3.​ Key: One box represents zero point one. LI 0.8 N O R 0.5 0.3 FO Using the figure, we conclude that: ​0.5 + 0.3 = 0.8​. 146 MATH std 5.indd 146 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 1 0.5 + 0.2 = Solution Steps: 1. Arrange the two numbers in a vertical LY position in such a way that the zero digits 0.5 before the decimal points are in the same + 0.2 N vertical position. O 2. Add the tenth: 5 + 2 = 7. Write 7 in the decimal position. Add the ones: 0 + 0 = 0. 0.5 + 0.2 Write 0 in the ones position. SE 3. Put a decimal point after the ones digit to separate the tenth digit. 0.7 U Therefore, ​0.5 + 0.2 = 0.7​. E N Example 2 LI ​       1. 7 ‾ ​+    2. 6   ​ N ‾ ​                 ​​ O Solution Steps: 1. Add the tenth: ​7  +  6  =  13​. Write 3 in the tenth position and take 1 to R the ones digits. FO 2. Add the ones: ​1  +  2  +  1  =  4​. Write 4 in the ones position. 3. Put a decimal point after the ones digit to separate the tenth digit. 147 MATH std 5.indd 147 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 1.7 Therefore, + 2.6 4.3 Example 3 ​22.5 + 30.2 =​ LY Solution N In order to find the answer, arrange the numbers vertically as shown: O 22.5 + 30.2 5 2.7 SE Therefore, ​22.5 + 30.2 = 52.7​. U Exercise 5 E Answer the following questions: N ​1. 0.4 + 0.7 =​ ​2. 0.6 + 0.3 =​ ​3. 126.7 + 2.1 =​ LI ​4. 6.4 + 7.9 =​ ​5.  23.4 + 5.2 =​ ​6. 36.7 + 5.4 =​ N ​7. 34.9 + 98.5 =​ ​8. 86.5 + 12.2 =​ ​9. 137.1 + 28.7 =​ O ​10. 250.8 + 22.4 =​ ​11. 324.4 + 86.8 =​ ​12. 58 + 2.6 =​ R ​13. 224.2 + 4.5 =​ ​14. 79.3 + 46.1 =​ ​15. 188.3 + 15.9 =​ FO 148 MATH std 5.indd 148 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Addition of decimal numbers with two decimal places Example 1 ​2.45 + 0.31 =​ Solution Steps: LY 1. Arrange the two numbers in vertical position corresponding to their place 2.45 + 0.31 N values. O 2. Add the decimal digits:​ 45 + 31 = 76.​ Write 76 in the two decimal positions. 2.45 SE + 0.31 76 U 3. Add the ones: ​2 + 0 = 2​. Write 2 in 2.45 the ones position. + 0.31 E 2 76 N 4. Put a decimal point after the ones digits 2.45 to separate the decimal digits. + 0.31 LI 2.76 N Therefore, ​2.45 + 0.31 = 2.76​. O Example 2 R ​2.98 + 2.65 =​ FO 149 MATH std 5.indd 149 30/07/2021 14:49  FOR ONLINE USE ONLY Solution DO NOT DUPLICATE Steps: 1. Arrange the digits vertically corresponding 2.98 to their positions. + 2.65 2. Add the decimal digits: ​98 + 65 = 163​. 2.98 Write 63 in the two decimal places, carry + 2.65 LY 1 and take it to the ones. 63 3. Add the ones:​2 + 2 + 1 = 5​. 2.98 N Write 5 in the ones position. + 2.65 O 5 63 4. Put a decimal point after the ones digit 2.98 to separate the decimal digits. SE + 2.65 5.63 U Therefore, ​2.98 + 2.65 =  5.63​. E Example 3 N 32.25 + 14.27 = LI Solution 32.25 N + 14.27 O 46.52 Therefore, 32.25 + 14.27 = 46.52. R Exercise 6 FO Answer the following questions: ​1. 0.35 + 0.24 =​ ​2.  1.56 + 0.33 =​ ​3. 2.36 + 1.22 =​ 150 MATH std 5.indd 150 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE ​4. 21.57 + 9.24 =​ ​5. 38.64 + 6.27 =​ ​6.  26.72 + 3.18 =​ 7 ​.  37.26 + 2.83 =​ ​8. 4.85 + 43.37 =​ ​9. 3.68 + 72.44 =​ ​10. 95.25 + 6.76 =​ ​11. 33.75 + 12.26 =​ ​12. 94.18 + 24.32 =​ ​13. 84.34 + 13.88 =​ ​14. 76.09 + 21.05 =​ ​15. 86.45 + 3.79 =​ LY Subtraction of decimals Subtraction of decimals with one decimal place N Subtraction of decimals is done using the same procedure as subtraction of O whole numbers. Arrange the digits in their place values followed by subtraction from the right to the left. Example 1 SE U ​5.3 – 3.2 =​ Solution E Steps: 1. Start by subtracting the tenth as you subtract whole numbers: N 3 ​ – 2 = 1​. Write 1 in the tenth position. LI 2. Subtract the ones: 5 – 3 = 2. Write 2 in the ones position to the left of the decimal point. N Therefore, ​5.3 – 3.2 = 2.1​. O R Example 2 FO ​13.6 – 4.9   =​ 151 MATH std 5.indd 151 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Start by subtracting the tenth: ​6 – 9​. This is not sufficient. Take 1 from the 3 ones and change it to get 10 tenth. Add 10 tenth to the 6 tenth to get 16 tenth. Now, subtract the tenth: ​16 – 9 = 7​. Write 7 in the tenth position. 2. Subtract the whole numbers: 1 ​ 2 – 4 = 8​. Write 8 in the ones position to the left of the decimal point. LY Therefore, ​13.6 –   4.9   = 8.7​. N Example 3 O ​ 6.5 – 18.6 =​ 2 Solution 26.5 SE − 18.6 U 7.9 Therefore, ​26.5 – 18.6 =  7.9​. E N Exercise 7 LI Answer the following questions: ​1. 0.8 – 0.2 =​ ​2. 0.9 – 0.7 =​ ​3. 2.4 – 0.8 =​ N O ​4. 3.6 – 2.8 =​ ​5. 4.7 – 0.9 =​ ​6. 22.7 – 4 =​ ​7. 35.6 – 24.2 =​ ​8. 64.5 – 34.8 =​ ​9. 125.2 – 0.7 =​ R FO 1 ​ 0. 226.4 – 22.5 =​ ​11. 27.4 – 13.3 =​ ​12. 12.6 – 1.4 =​ 1 ​ 3. 17.8 – 9.7 =​ ​14. 45.1 – 22.8 =​ ​15. 125.2 – 94.8 =​ 152 MATH std 5.indd 152 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE ​16.  0.6 – 0.3 =​ ​17.  30.8 – 15.3 =​ ​18. 120.2 – 98.7 =​ ​19. 55.1 – 54.9 =​ ​20.  235.9 – 0.7 =​ Subtraction of numbers with two decimal places LY Example 1 N ​0.84 – 0.21  =​ O Solution Steps: 1. Arrange the numbers vertically corresponding to their place values. SE 0.84 − 0.21 U 2. Start by subtracting the decimal digits: ​ 0.84 84 − 21 = 63​. Write 63 in the two E − 0.21 decimal positions. N 63 LI 3. Subtract the ones: ​0 – 0 = 0​. 0.84 Write 0 in the ones position. − 0.21 N 0.63 O Therefore, ​0. 84  −  0. 21   =   0. 63​. R Example 2 FO ​2.45 – 1.64  =​ 153 MATH std 5.indd 153 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Arrange the numbers vertically 2.45 corresponding to their place values. − 1.64 2. Subtract the hundredth: ​5 – 4 = 1​. 2.45 LY Write 1 in the hundredth position. − 1.64 1 N 3. Subtract the tenth: ​4 – 6​. This is not 2.45 sufficient. Take 1 from the two ones. − 1.64 O Change it to get 10 tenth. Add the 10 81 tenth to the 4 tenth to obtain 14 tenth. Now, subtract the tenth: 14 – SE ​ ​6 = 8. Write 8 in the tenth position. The decimal digits become 81. U 4. Subtract the ones: ​1 – 1 = 0​. 2.45 Write 0 in the ones position. − 1.64 0.81 E N Therefore, ​2.45 – 1.64 = 0.81​. LI Example 3 N ​12.46 – 8.64 =​ O Solution Arrange the decimal numbers vertically as shown below: R 12.46 FO – 8.64 3.82 Therefore, ​12.46 – 8.64 =  3.82​. 154 MATH std 5.indd 154 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 8 Answer the following questions: ​1.        0.62 – 0.21 =​ ​2.        0.25 – 0.12 =​ ​3.        0.86 – 0.34 =​ ​4.        0.82 – 0.36 =​ LY ​5.        0.67 – 0.48 =​ ​6.       0.33 – 0.29 =​ N ​7.        2.45 – 0.26 =​ ​8.        3.68 – 1.23 =​ O ​9.        5.27 – 4.25 =​ ​10.      12.54 – 6.71 =​ 1 SE ​ 1.      47.76 – 34.25 =​ ​12.      42.26 – 13.47 =​ ​13.      126.57 – 52.36 =​ ​14.      364.20 – 72.66 =​ U ​15.      96.31 – 28.29 =​ ​16.      422.04 – 260.06 =​ E ​17.      10.14 – 3.05 =​ ​18.      0.05 – 0.03 =​ N ​19.      3.05 – 2.45 =​ ​20.      530.05 – 490.75 =​ LI N Multiplication of decimals O Multiplication of a number with one decimal place by a whole number Multiplication of a number with one decimal place by a whole number is done using the same procedure used in multiplying whole numbers. Once the result R is obtained, insert a decimal point before the last digit of the product to get FO the digit in the tenth position. 155 MATH std 5.indd 155 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 1 Example 2 4.1 ​8.3 × 12 =​ × 2 Solution Solution ​8.3 × 12 = 99.6​ Steps: 1. Multiply just like in whole numbers: ​41 × 2 = 82​. LY 2. Insert a decimal point between 8 and 2. Therefore, the answer is 8.2. N Example 3 O 219.8 × 23 SE U Solution 219.8 × 23 E 6 594 N + 4 396 LI 5 055.4 Therefore, the answer is 5 055.4. N O Exercise 9 Answer the following questions: R ​1.     0.6 × 4 =​ ​2.    2.3 × 3 =​ ​3.   3.1 × 4 =​ FO ​4.     4.7 × 21 =​ ​5.    18.9 × 34 =​ ​6.   112.6 × 11 =​ 156 MATH std 5.indd 156 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE ​7.    64.5 × 72 =​ ​8.    6.2 × 7 =​ ​9.   136.2 × 34 =​ ​10.   22.6 × 84 =​ ​11.    0.2 × 92 =​ ​12.   126.2 × 15 =​ ​13.   98.7 × 29 =​ ​14.    8.4 × 52 =​ 1 ​ 5.       1. 2 16.           6. 8 17.          21. 4 ‾         ​    ×       6  ​ ×        5 ×       8    LY ‾         ​                    ​​ N ​18.      699. 7 19.          324. 2 20.          5. 6 ‾         ​   ×             2 ​  ×     1 4       ×         6 O ‾         ​                        ​​ SE Multiplication of a number with two decimal places by a whole number Multiplication of a number with two decimal places by a whole number is done using the same procedure used in multiplying whole numbers. Once the result U is obtained, insert a decimal point before the second right most digit of the product to get the digits in the tenth position and hundredth position. E Example 1 N 1.02 LI × 3 N O Solution Steps: 1. Multiply just like in whole numbers as follows: R ​102 × 3 = 306.​ FO 2. Insert a decimal point to the left of the second rightmost digit of the product, that is 3.06. Therefore, the answer is 3.06. 157 MATH std 5.indd 157 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 31.25 × 26 Solution Steps: LY 1. Multiply just like in whole numbers as follows: ​3125 × 26 = 81250​. N 2. Insert a decimal point just to the left of the second rightmost digit, that is, 812.50. O Therefore, the answer is 812.50. Example 3 SE U 212.5 × 27 14875 E + 4250 N 5737.5 LI Therefore, the answer is 5 737.5. N Exercise 10 O Answer the following questions: ​1.        0.02 × 3 =​ ​2.     1.13 × 2 =​ R FO ​3.        4.15 × 6 =​ ​4.     2.38 × 7 =​ ​5.        216.45 × 8 =​ ​6.     1.83 × 4 =​ 158 MATH std 5.indd 158 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE ​7.        531.03 × 11 =​ ​8.    342.35 × 15 =​ ​9.        418.62 × 13 =​ ​10.     274.24 × 17 =​ 1 ​ 1.      135.71 × 32 =​ ​12.    386.08 × 22 =​ ​13.      0.08 × 29 =​ ​14.    25.02 × 16 =​ LY ​15.      336.01 × 4 =​ ​16.    442.07 × 12 =​ N ​17.      38.27 × 12 =​ O ​18.            506. 35 19.              3. 49 ‾ SE              ​    ×         28 ​    ×       38 ‾              ​                        ​​ U ​20.            180. 57 ‾              ​ ×           19 ​ ‾              ​                       ​​ E N Exercise 11 LI Answer the following questions: N 1. Write the following decimals in numerals: O (a) One point two (b) Zero point four (c) Zero point seven (d) Three point six eight (e) Twenty five point two eight R FO 2. Write the following decimals in words: (a) 4.6 (b) 33.5 (c) 51.8 (d) 0.08 (e) 91.66 (f) 16.49 159 MATH std 5.indd 159 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Change the following fractions into decimals: 6 _ 17 _ 2 _ (a) ​​   ​​ (b) ​​   ​​ (c) ​​   ​​ 10 10 10 _ 83 5 _ 108 _ (d) ​​   ​​ (e) ​​   ​​ (f) ​​   ​​ 100 100 100 LY _ 365 (g) ​​   ​​ 100 N ​4.        23.2 + 0.8 =​ ​5.         0.5 + 3.6 =​ ​6.         0.23 + 8.52 =​ O ​.             38. 5 7 8.             12.9 9. 180. 57      ​         ‾    ‾ ×           8    ​  ×      44      ​                            ​​ SE × 19 U 1 ​ 0.          99. 15 ‾         ​   ×              86​ ‾         ​                          ​​ E N 1 ​ 1.   19.9 – 14.5 =​ ​12.   0.8 – 0.3 =​ ​13.  12.1 – 9.8 =​ LI 14. 13.07 – 5.04 = ​15.  87.25 – 64.96 =​ ​16. 35.34 – 26.45 = ​ N ​17.    2.3 × 22 =​ ​ 18. 0.4 × 15 =​ ​19. 0.45 × 13 =​ O ​20.   6.08 × 11 =​ ​ 21.  30.25 × 14 =​ ​ 22. 1.16 × 9 =​ R ​23.   5.02 × 6 =​ ​24.  85.18 × 8 =​ ​25.   27.58 × 31 =​ FO 160 MATH std 5.indd 160 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Summary 1. Decimal numbers are read from left to right. Digits to the left of a decimal point are read as whole numbers, while digits to the right of a decimal point are read one after the other. 2. In adding and subtracting decimals, one must take note of the place value of digits on both sides of the decimal point. LY 3. Multiplication of decimals by whole numbers is done as follows: Multiply the numbers as whole numbers and then put a decimal point. If the decimal number being multiplied has one decimal place, put a N decimal point to the left of the rightmost first digit. If the decimal number O being multiplied has two decimal places, put a decimal point to the left of the rightmost second digit. SE U E N LI N O R FO 161 MATH std 5.indd 161 30/07/2021 14:49