# WORKSHEET ON DIVIDING DECIMALS

Problems 1-17 : Evaluate each of the following division.

Problem 1 :

2.1 ÷ 0.7

Problem 2 :

4.8 ÷ 0.6

Problem 3 :

2.7 ÷ 0.03

Problem 4 :

0.72 ÷ 0.006

Problem 5 :

35 ÷ 0.007

Problem 6 :

4325.78 ÷ 10

Problem 7 :

4325.78 ÷ 100

Problem 8 :

4325.78 ÷ 1000

Problem 9 :

3.96 ÷ 10

Problem 10 :

7.89 ÷ 100

Problem 11 :

5.9 ÷ 1000

Problem 12 :

0.4 ÷ 100

Problem 13 :

0.09 ÷ 100

Problem 14 :

0.001 ÷ 1000

Problem 15 :

0.15 ÷ 0.5

Problem 16 :

14.7 ÷ 7

Problem 17 :

106.9 ÷ 25

Problem 18 :

A car travelled for 4.5 hours and covered a distance of 290.25 miles. Find the speed of the car in miles per hour.

Problem 19 :

Jasmine was preparing a design to decorate her classroom. She needed a few colored strips of paper of length 1.8 cm each. She had a strip of colored paper of length 7.2 cm. How many pieces of the required length will she get out of this strip?

Problem 20 :

There are 54.25 liters of oil in 4 cans. First three cans are completely filled and in the fourth can, only half of it is filled. How much oil can be filled in one can?

= 2.1 ÷ 0.7

²¹⁄₁₀ ÷ ⁷⁄₁₀

Change division to multiplication and take reciprocal of the fraction ⁷⁄₁₀.

²¹⁄₁₀ x ¹⁰⁄₇

Simplify.

³⁄₁ x ¹⁄₁

³⁄₁

= 3

= 4.8 ÷ 0.6

⁴⁸⁄₁₀ ÷ ⁶⁄₁₀

Change division to multiplication and take reciprocal of the fraction ⁶⁄₁₀.

⁴⁸⁄₁₀ x ¹⁰⁄₆

Simplify.

⁸⁄₁ x ¹⁄₁

⁸⁄₁

= 8

= 2.7 ÷ 0.03

²⁷⁄₁₀ ÷ ³⁄₁₀₀

Change division to multiplication and take reciprocal of the fraction ³⁄₁₀₀.

²⁷⁄₁₀ x ¹⁰⁰⁄₃

Simplify.

⁹⁄₁ x ¹⁰⁄₁

= 9 x 10

= 90

= 0.72 ÷ 0.006

⁷²⁄₁₀₀ ÷ ⁶⁄₁₀₀₀

Change division to multiplication and take reciprocal of the fraction ⁶⁄₁₀₀₀.

⁷²⁄₁₀₀ x ¹⁰⁰⁰⁄₆

Simplify.

= ¹²⁄₁ x ¹⁰⁄₁

= 12 x 10

= 120

= 35 ÷ 0.007

= 35 ÷ ⁷⁄₁₀₀₀

Change division to multiplication and take reciprocal of the fraction ⁷⁄₁₀₀₀.

= 35 x ¹⁰⁰⁰⁄₇

= 5 x ¹⁰⁰⁰⁄₁

= 5 x 1000

= 5000

Since we divide 4325.78 by 10, we have to move the decimal point one digit to the left.

4325.78 ÷ 10 = 432.578

Since we divide 4325.78 by 100, we have to move the decimal point two digits to the left.

4325.78 ÷ 100 = 43.2578

Since we divide 4325.78 by 1000, we have to move the decimal point three digits to the left.

4325.78 ÷ 1000 = 4.32578

Since we divide 3.96 by 10, we have to move the decimal point one digit to the left.

3.96 ÷ 10 = 0.396

Since  we divide 7.89 by 100, we have to move the decimal point two digits to the left.

But, we have only one digit '7' to the left of the decimal point in 7.89. To get one more digit to the left of the decimal point, we have to add one zero.

7.89 ÷ 100 = 0.0789

Since we divide 5.9 by 1000, we have to move the decimal point three digits to the left.

But, we have only one digit to the left of the decimal point in 5.9. To get two more digits to the left of the decimal point, we have to add two zeros.

5.9 ÷ 1000 = 0.0059

Since we divide 0.4 by 100, we have to move the decimal point two digits to the left.

But, we have no digit to the left of the decimal point in 0.4. To get two digits to the left of the decimal point, we have add two zeros.

0.4 ÷ 100 = 0.004

Since we divide 0.09 by 100, we have to move the decimal point two digits to the left.

But, we have no digit to the left of the decimal point in 0.4. To get two digits to the left of the decimal point, we have add two zeros.

0.09 ÷ 100 = 0.0009

Since we divide 0.001 by 1000, we have to move the decimal point three digits to the left.

But, we have no digit to the left of the decimal point in 0.4. To get two digits to the left of the decimal point, we have add three zeros.

0.001 ÷ 1000 = 0.000001

= 0.15 ÷ 0.5

¹⁵⁄₁₀₀ ÷ ⁵⁄₁₀

Change division to multiplication and take reciprocal of the fraction ⁵⁄₁₀.

¹⁵⁄₁₀₀ x ¹⁰⁄

Simplify.

³⁄₁₀¹⁄

³⁄₁₀

Since we divide 3 by 10, there should be one digit to the right of the decimal point in the answer.

= 0.3

= 14.7 ÷ 7

¹⁴⁷⁄₁₀ ÷ ⁷⁄₁

Change division to multiplication and take reciprocal of the fraction ⁷⁄₁.

¹⁴⁷⁄₁₀ x

Simplify.

¹⁴⁷⁄₁₀ x

²¹⁄₁₀ x ¹⁄₁

²¹⁄₁₀

Since we divide 21 by 10, there should be one digit to the right of the decimal point in the answer.

= 2.1

= 1069 ÷ 25

= ¹⁰⁶⁹⁄₁₀ ÷ ²⁵⁄₁

Change division to multiplication and take reciprocal of the fraction ²⁵⁄₁.

= ¹⁰⁶⁹⁄₁₀ x ¹⁄₂₅

Multiply both numerator and denominator of the fraction ¹⁄₂₅ by 4 to make the denominator as 100.

= ¹⁰⁶⁹⁄₁₀ x ⁽¹ˣ⁴⁾⁄₍₂₅ₓ₄₎

= ¹⁰⁶⁹⁄₁₀ x ⁴⁄₁₀₀

⁽¹⁰⁶⁹ˣ⁴⁾⁄₍₁₀ₓ₁₀₀₎

⁴²⁷⁶⁄₁₀₀₀

Since we divide 4276 by 1000, there should be three digits to the right of the decimal point in the answer.

= 4.276

The time is given in hours and the distance is given in miles.

To find the speed of the car, we have to divide the given distance in miles by the time in hours.

Speed of the car :

= 290.25 ÷ 4.5

= ²⁹⁰²⁵⁄₁₀₀ ÷ ⁴⁵⁄₁₀

Change division to multiplication and take reciprocal of the fraction ⁴⁵⁄₁₀.

= ²⁹⁰²⁵⁄₁₀₀ ¹⁰⁄₄₅

= ⁵⁸⁰⁵⁄₁₀ x ⅑

= ¹⁹³⁵⁄₁₀

= ⁶⁴⁵⁄₁₀ ¹⁄₁

= ⁶⁴⁵⁄₁₀

Since 645 is divided by 10, there should be one digit to the right of the decimal point in the answer.

= 64.5

Therefore, the speed of the car was 64.5 miles per hour.

Number of pieces of the required length :

= 7.2/1.8

= 7.2 ÷ 1.8

= ⁷²⁄₁₀ ÷ ¹⁸⁄₁₀

Change division to multiplication and take reciprocal of the fraction ¹⁸⁄₁₀.

= ⁷²⁄₁₀ ¹⁰⁄₁₈

Simplify.

= ⁴⁄₁ ¹⁄₁

= 4 x 1

= 4

From the given information, it is clear that 54.25 liters of oil is filled in 3.5 cans.

Amount of oil can be filled in one can :

= 54.25/3.5

= ⁵⁴²⁵⁄₁₀₀ ÷ ³⁵⁄₁₀

Change division to multiplication and take reciprocal of the fraction ³⁵⁄₁₀.

= ⁵⁴²⁵⁄₁₀₀ x ¹⁰⁄₃₅

Simplify.

= ⁵⁴²⁵⁄₁₀₀ x ¹⁰⁄₃₅

= ¹⁰⁸⁵⁄₁₀ x

= ¹⁵⁵⁄₁₀ x ¹⁄₁

= ¹⁵⁵⁄₁₀

Since 155 is divided by 10, there should be one digit to the right of the decimal point in the answer.

= 15.5

Therefore, 15.5 liters of oil can be filled in one can.

## Practice Questions

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