# Spectrum Math Grade 5 Chapter 3 Lesson 11 Answer Key Dividing Decimals Using Rules

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## Spectrum Math Grade 5 Chapter 3 Lesson 3.11 Dividing Decimals Using Rules Answers Key

When the divisor of a division problem contains a decimal point, multiply both the divisor and the dividend by the power-of ten needed to make the divisor a whole number. Then, solve the problem.
94.5 ÷ 0.9 =
(9.45 × 10) ÷ (0.9 × 10) =
94.5 ÷ 9 = 10.5
When multiplying by 10 to the first power, move the decimal point to the right one place. Add or remove zeros if necessary.

Write the power of ten needed to solve each problem. Then, solve the problem.

Question 1.
a.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division.
In this division, the dividend and the divisor are decimals, so we need to convert the divisor to a whole number using the following steps.
step 1: The dividend is 1.87 and the divisor is 0.11. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 0.11 x 10 = 1.1
step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 1.87 x 10 = 18.7. In other words, we need to move both decimal points to the right until the divisor becomes a whole number.
step 3: Now, we have 18.7 as the dividend and 1.1 as the divisor. This can be divided as we do the usual division and we get 17 as the quotient.
– If we multiply the divisor and dividend by 100 then we get 11 and 187

b.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division.
In this division, the dividend and the divisor are decimals, so we need to convert the divisor to a whole number using the following steps.
step 1: The dividend is 1.95 and the divisor is 0.13. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 0.13 x 10 = 1.3
step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 1.95 x 10 = 19.5. In other words, we need to move both decimal points to the right until the divisor becomes a whole number.
step 3: Now, we have 19.5 as the dividend and 1.3 as the divisor. This can be divided as we do the usual division and we get 1.5 as the quotient.  (or)
– – If we multiply the divisor and dividend by 100 then we get 13 and 195 then we get 15.
Or

c.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
In this division, the dividend and the divisor are decimals, so we need to convert the divisor to a whole number using the following steps.
step 1: The dividend is 2.4 and the divisor is 1.5. We need to change the divisor to a whole number and so we will multiply it by 10 so that the decimal point shifts to the right and it becomes a whole number. This means, 1.5 x 10 = 15
step 2: We need to treat the dividend in the same way as we had treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 2.4 x 10 = 24. In other words, we need to move both decimal points to the right until the divisor becomes a whole number.
step 3: Now, we have 24 as the dividend and 15 as the divisor. This can be divided as we do the usual division and we get 1.6 as the quotient.

Question 2.
a.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
In this division, the dividend and the divisor are decimals, so we need to convert the divisor to a whole number using the following steps.
– Change the divisor 0.18 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
162 ÷ 18 = 9
and therefore:
1.62 ÷ 0.18 = 9
Both were calculated to 3 decimal places.

b.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
Change the divisor 0.12 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
156 ÷ 12 = 13
and therefore:
1.56 ÷ 0.12 = 13
Both were calculated to 3 decimal places.

c.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
Change the divisor 1.8 to a whole number by moving the decimal point 1 place to the right. Then move the decimal point in the dividend the same, 1 place to the right.
We then have the equations:
16.2 ÷ 18 = 0.9
and therefore:
1.62 ÷ 1.8 = 0.9
Both were calculated to 3 decimal places.

Question 3.
a.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
Change the divisor 1.25 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
1100 ÷ 125 = 8.80
and therefore:
11 ÷ 1.25 = 8.80
Both were calculated to 3 decimal places.

b.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
Change the divisor 1.3 to a whole number by moving the decimal point 1 place to the right. Then move the decimal point in the dividend the same, 1 place to the right.
We then have the equations:
23.4 ÷ 13 = 1.8
and therefore:
2.34 ÷ 1.3 = 1.8
Both were calculated to 3 decimal places.

c.

Power of 10 _______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
Change the divisor 0.18 to a whole number by moving the decimal point 2 places to the right. Then move the decimal point in the dividend the same, 2 places to the right.
We then have the equations:
234 ÷ 18 = 13.000
and therefore:
2.34 ÷ 0.18 = 13.000
Both were calculated to 3 decimal places.

Question 4.
a.

Power of 10 ______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
Change the divisor 1.3 to a whole number by moving the decimal point 1 place to the right. Then move the decimal point in the dividend the same, 1 place to the right.
We then have the equations:
24.7 ÷ 13 = 1.900
and therefore:
2.47 ÷ 1.3 = 1.900
Both were calculated to 3 decimal places.

b.

Power of 10 ______
For dividing decimals by another decimal, we need to convert the divisor into a whole number and then continue the division
Change the divisor 0.1 to a whole number by moving the decimal point 1 place to the right. Then move the decimal point in the dividend the same, 1 place to the right.
We then have the equations:
16 ÷ 1 = 16
and therefore:
1.60 ÷ 0.1 = 16
Both were calculated to 3 decimal places.

c.

Power of 10 ______