# Converting Decimals to Fractions

In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps:

Step I: Obtain the decimal.

Step II: Remove the decimal points from the given decimal and take as numerator.

Step III: At the same time write in the denominator, as many zero or zeros to the right of 1(one) (For example 10, 100 or 1000 etc.) as there are number of digit or digits in the decimal part. And then simplify it.

We can express a decimal number as a fraction by keeping the given number as the numerator without a decimal point and writing 1 in the denominator followed by as many zeroes on the right as the number of decimal places in the given decimal number has.

For example:

(i) 124.6 = $$\frac{1246}{10}$$

(ii) 12.46 = $$\frac{1246}{100}$$

(iii) 1.246 = $$\frac{1246}{1000}$$

The problem will help us to understand how to convert decimal into fraction.

In 0.7 we will change the decimal to fraction.

First we will write the decimal without the decimal point as the numerator.

Now in the denominator, write 1 followed by one zeros as there are 1 digit in the decimal part of the decimal number. = 7/10

Therefore, we observe that 0.7 (decimal) is converted to 7/10 (fraction).

Worked-out examples on converting decimals to fractions:

1. Convert each of the following into fractions.

(i) 3.91

Solution:

3.91

Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by two zeros as there are 2 digits in the decimal part of the decimal number.

= 391/100

(ii) 2.017

Solution:

2.017

= 2.017/1

= 2.017 × 1000/1 × 1000 In the denominator, write 1 followed by three zeros as there are 3 digits in the decimal part of the decimal number.

= 2017/1000

2. Convert 0.0035 into fraction in the simplest form.

Solution:

0.0035 Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by four zeros to the right of 1 (one) as there are 4 decimal places in the given decimal number.

Now we will reduce the fraction 35/10000 and obtained to its lowest term or the simplest form.

= 7/2000

3. Express the following decimals as fractions in lowest form:

(i) 0.05

Solution:

0.05

= 5/100 Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by two zeros to the right of 1 (one) as there are 2 decimal places in the given decimal number.

= 5/100 ÷ 5/5 Reduce the fraction obtained to its lowest term.

= 1/20

(ii) 3.75

Solution:

3.75

= 375/100 Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by two zeros to the right of 1 (one) as there are 2 decimal places in the given decimal number.

= 375/100 ÷ 25/25 Reduce the fraction obtained to its simplest form.

= 15/4

(iii) 0.004

Solution:

0.004

= 4/1000 Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by three zeros to the right of 1 (one) as there are 3 decimal places in the given decimal number.

= 4/1000 ÷ 4/4 Reduce the fraction obtained to its lowest term.

= 1/250 (iv) 5.066

Solution:

5.066

= 5066/1000  Write the given decimal number without the decimal point as numerator.

In the denominator, write 1 followed by three zeros to the right of 1 (one) as there are 3 decimal places in the given decimal number.

= 5066/1000 ÷ 2/2  Reduce the fraction obtained to its simplest form.

= 2533/500

Practice Problems on Converting Decimals to Fractions:

1. Convert the given decimal numbers to fractions in the lowest term:

(i) 1.3

(ii) 0.004

(iii) 4.005

(iv) 7.289

(v) 0.56

(vi) 21.08

(vii) 0.067

(viii) 6.66

(i) $$\frac{13}{10}$$

(ii) $$\frac{1}{250}$$

(iii) $$\frac{801}{200}$$

(iv) $$\frac{7289}{1000}$$

(v) $$\frac{14}{25}$$

(vi) $$\frac{527}{25}$$

(vii) $$\frac{67}{1000}$$

(viii) $$\frac{333}{50}$$

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