DIVIDING DECIMALS

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 ?

She thought it would be 7.2/1.8.

Is she correct ?

Both 7.2 and 1.8 are decimal numbers. So we need to know the division of decimal numbers.

For example,

141.5 ÷ 10 = 14.15

141.5 ÷ 100 = 1.415

141.25 ÷ 1000 = 0.1415

To get the quotient, we shift the decimal point in the decimal number to the left by as many places as there are zeros over 1.

Dividing Decimals by Whole Numbers 

Method 1 :

Find 4.2 ÷ 3.

Solution :

4.2 ÷ 3 = ⁴²⁄₁₀ ÷ 3

4.2 ÷ 3 = ⁴²⁄₁₀ ÷ ⅓

4.2 ÷ 3 = ¹⁴⁄₁₀

4.2 ÷ 3 = 1.4

Method 2 :

Find 18.5 ÷ 5

Solution :

First, let us find 185 ÷ 5. We get 37

There is one digit to the right of the decimal point in 18.5.

Place the decimal point in 37 such that there would be one digit to its right. We will get 3.7

Dividing Decimals by Decimals

Example 1 :

Evaluate :

17.6 ÷ 0.4

Solution :

17.6 ÷ 0.4 = ¹⁷⁶⁄₁₀ ÷ ⁴⁄₁₀

Change division to multiplication and take reciprocal of the fraction ⁴⁄₁₀.

= ¹⁷⁶⁄₁₀ x 10⁄4

Simplify.

= ¹⁷⁶⁄₁ x 1⁄4

= ¹⁷⁶⁄4

= 44

Example 2 :

Evaluate :

1.2 ÷ 0.2

Solution :

1.2 ÷ 0.2 = 12⁄10 ÷ 2⁄10

Change division to multiplication and take reciprocal of the fraction 2⁄10.

= 12⁄10 x 10⁄2

Simplify.

= 12⁄1 x 1⁄2

= 12⁄2

= 6

Example 3 :

Evaluate :

1.8 ÷ 0.03

Solution :

1.8 ÷ 0.03 = 18⁄10 ÷ 3⁄100

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

= 18⁄10 x 100⁄3

Simplify.

= 6⁄1 x 10⁄1

= 6 x 10

= 60

Solved Problems

Problem 1 :

Evaluate :

1.8 ÷ 0.3

Solution :

1.8 ÷ 0.3 = ¹⁸⁄₁₀ ÷ ³⁄₁₀

Change division to multiplication and take reciprocal of the fraction ³⁄₁₀.

= ¹⁸⁄₁₀ x ¹⁰⁄₃

Simplify.

= ⁶⁄₁ x ¹⁄₁

= 6 x 1

= 6

Problem 2 :

Evaluate :

2.4 ÷ 0.6

Solution :

1.2 ÷ 0.2 = ²⁴⁄₁₀ ÷ ⁶⁄₁₀

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

= ²⁴⁄₁₀ x ¹⁰⁄₆

Simplify.

= ⁴⁄₁ x ¹⁄₁

= 4 x 1

= 4

Problem 3 :

Evaluate :

3.6 ÷ 0.006

Solution :

3.6 ÷ 0.006 = ³⁶⁄₁₀ ÷ ⁶⁄₁₀₀₀

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

= ³⁶⁄₁₀ x ¹⁰⁰⁰⁄₆

Simplify.

= 6⁄1 x ¹⁰⁰⁄₁

= 6 x 100

= 600

Problem 4 :

Evaluate :

3782.56 ÷ 10

Solution :

Since 3782.56 is divided by 10, the decimal point has to be shifted one digit to the left.

3782.56 ÷ 10 = 378.256

Problem 5 :

Evaluate :

3782.56 ÷ 100

Solution :

Since 3782.56 is divided by 100, the decimal point has to be shifted two digits to the left.

3782.56 ÷ 10 = 37.8256

Problem 6 :

Evaluate :

3782.56 ÷ 1000

Solution :

Since 3782.56 is divided by 1000, the decimal point has to be shifted three digits to the left.

3782.56 ÷ 1000 = 3.78256

Problem 7 :

Evaluate :

2.87 ÷ 10

Solution :

Since 2.87 is divided by 10, the decimal point has to be shifted one digit to the left.

2.87 ÷ 10 = 0.287

Problem 8 :

Evaluate :

3.65 ÷ 100

Solution :

Since 3.65 is divided by 100, the decimal point has to be shifted two digits to the left.

But, there is only one digit '3' to the left of the decimal point in 3.65. To get one more digit to the left of the decimal point, add one zero.

3.65 ÷ 100 = 0.0365

Problem 9 :

Evaluate :

7.5 ÷ 1000

Solution :

Since 7.5 is divided by 1000, the decimal point has to be shifted three digits to the left.

But, there is only one digit to the left of the decimal point in 7.5. To get two more digits to the left of the decimal point, add two zeros.

7.5 ÷ 1000 = 0.0075

Problem 10 :

Evaluate :

0.3 ÷ 100

Solution :

Since 0.3 is divided by 100, the decimal point has to be shifted two digits to the left.

But, there is no digit to the left of the decimal point in 0.3. To get two digits to the left of the decimal point, add two zeros.

0.3 ÷ 100 = 0.003

Problem 11 :

Evaluate :

0.005 ÷ 1000

Solution :

Since 0.005 is divided by 1000, the decimal point has to be shifted three digits to the left.

But, there is no digit to the left of the decimal point in 0.005. To get three digits to the left of the decimal point, add three zeros.

0.005 ÷ 1000 = 0.000005

Problem 12 :

Evaluate :

49 ÷ 0.07

Solution :

= 49 ÷ 0.07

= 49 ÷ ⁷⁄₁₀₀

Change division to multiplication and take reciprocal of the fraction ⁷⁄₁₀₀.

= 49 x ¹⁰⁰⁄₇

Simplify.

= 7 x ¹⁰⁰⁄₁

= 7 x 100

= 700

Problem 13 :

Evaluate :

6.5 ÷ 5

Solution :

= 6.5 ÷ 5

= ⁶⁵⁄₁₀ ÷ ⁵⁄₁

Change division to multiplication and take reciprocal of the fraction ⁵⁄₁.

= ⁶⁵⁄₁₀ x ⅕

Simplify.

= ¹³⁄₁₀ x ¹⁄₁

= ¹³⁄₁₀

Since 13 is divided by 10, there should be one digit to the right of the decimal point in the answer.

= 1.3

Problem 14 :

A car covers a distance of 129.92 miles in 3.2 hours. What is the distance covered by it in 1 hour ?

Solution :

Distance covered by the car = 129.92 miles

Time required to cover this distance = 3.2 hours

So, distance covered by it in 1 hour :

= 129.92/3.2

Multiply both numerator and denominator by 100 to get rid of the decimal points.

= 12992⁄320

= 40.6 miles

Practice Questions

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