HOW TO WRITE A FRACTION AS A DECIMAL

What is a decimal fraction?

A decimal fraction is a fraction whose denominator is 10 or a multiple of 10 like 100, 1000, 10,000, etc.

To convert fraction to decimal, we follow these steps.

• If the given fraction is having 10 in the denominator, we will move the decimal one digit to the left.
  
• If the given fraction is having 10 in the denominator, we will move the decimal one digit to the left.
• In general, based on number of zeroes, we will move the decimal to n number of digits.

For example,

Write the following in decimal form :

Problem 1 :

2/10

Solution :

= 2/10

Here, the denominator is 10, it consists of one zero. Then we move the decimal one digit to the left (backward).

So, 0.2 is the decimal form of 2/10.

Problem 2 :

13/100

Solution :

= 13/100

Here, the denominator is 100, it consists of two zeroes. Then we move the decimal two digits to the left (backward).

So, 0.13 is the decimal form of 13/100.

Problem 3 :

241/1000

Solution :

= 241/1000

Here, the denominator is 1000, it consists of three zeroes.

Then we move the decimal three digits to the left (backward).

So, 0.241 is the decimal form of 241/1000.

Problem 4 :

83/100

Solution :

= 83/100

Here the denominator is 100, it consists of two zeroes. Then we move the decimal two digits to the left (backward).

So, 0.83 is the decimal form of 83/100.

Problem 5 :

1/10 + 3/100

Solution :

= 1/10 + 3/100

Step 3 :

0.1 + 0.03 = 0.13

So, 0.13 is the decimal form of 1/10 + 3/100.

Problem 6 :

37/1000

Solution :

= 37/1000

Here, the denominator is 1000, it consists of three zeroes.

Then we move the decimal three digits to the left left (backward).

So, 0.037 is the decimal form of 37/1000.

Problem 7 :

3/100 + 7/1000

Solution :

= 3/100 + 7/1000

Step 3 :

0.03 + 0.007 = 0.037

So, 0.037 is the decimal form of 3/100 + 7/1000.

Problem 8 :

6/10 + 5/100 + 9/1000

Solution :

= 6/10 + 5/100 + 9/1000

Step 3 :

= 9/1000

It has three zeroes. So, 0.009

Step 4 :

0.6 + 0.05 + 0.009 = 0.659

So, 0.659 is the decimal form of 6/10 + 5/100 + 9/1000.

Problem 9 :

3/1000 + 7/10000

Solution :

= 3/1000 + 7/10000

3/1000 = 0.003 (it has three zeroes)

7/1000 = 0.0007 (it has four zeroes)

Then,

0.003 + 0.0007 = 0.0037

So, 0.0037 is the decimal form of 3/1000 + 7/10000.

Problem 10 :

9/100 + 1/1000

Solution :

= 9/100 + 1/1000

9/100 = 0.09 (it has three zeroes)

1/1000 = 0.001 (it has four zeroes)

Then,

0.09 + 0.001 = 0.091

So, 0.091 is the decimal form of 9/100 + 1/1000.

Problem 11 :

9/10 + 6/100

Solution :

= 9/10 + 6/100

9/10 = 0.9 (it has one zero)

6/100 = 0.06 (it has two zeroes)

Then,

0.9 + 0.06 = 0.96

So, 0.96 is the decimal form of 9/10 + 6/100.

Problem 12 :

7/10 + 5/100 + 1/1000  + 7/10000

Solution :

= 7/10 + 5/100 + 1/1000  + 7/10000

7/10 = 0.7

5/100 = 0.05

1/1000 = 0.001

7/10000 = 0.0007

Then,

0.7 + 0.05 + 0.001 + 0.0007 = 0.7517

So, 0.7517 is the decimal form of 7/10 + 5/100 + 1/1000 + 7/10000. 

Problem 13 :

Write the fraction as a decimal. Is it terminating or repeating?

a) 3/5         b) 1/9         c) 9/20        d) 8/5

Solution :

a) 3/5

Dividing 3 by 5, we get the quotient = 0.6 and remainder = 0

So, the decimal is terminating.

b) 1/9

Dividing 1 by 9, we get the quotient = 0.1111.....

It is repeating decimal.

c) 9/20

By decomposing 20, we get 2² x 5. Since it is being expressed as multiple of 2 and 5, the decimal must be terminating decimal.

9/20 = 0.45

d) 8/5

The denominator is multiple of 2, it must be a terminating decimal.

8/5 = 0.4

Problem 14 :

You run the 40-yard dash in 6 21/25 seconds. Your teammate runs it in the time shown. Who is faster and by how much?

Solution :

Distance covered = 40 yards

Time taken = 6  21/25

= 6 + 21/25

= 6 + (21/25) x (4/4)

= 6 + 84/100

= 6 + 0.84

= 6.84 seconds

Your teammate covers the same distance at the time 6.9 seconds.

= 6.9 - 6.84

= 0.06 seconds

You are faster by 0.06 seconds.

Problem 15 :

The length of a goldfish is 5/16 foot. Write the length of the goldfish as a decimal.

Solution :

Length of goldfish = 5/16 foot

The denominator is a multiple of 2 but not a multiple of 5. By converting it as decimal, we will get the terminating decimal. 

The length of goldfish in decimal is 0.3125 foot