Percentage into Decimal

We know that percentage represents parts per hundred. So, any number written as percent is a fraction with 100 as its denominator. We write the number as the numerator of a fraction and 100 in the denominator. The symbol % is not written in the fraction form. So, 75% is written as \(\frac{75}{100}\) = 0.75.


How to convert a given percentage into decimal?

We will follow the following steps for converting a percentage into a decimal:

Step I: Obtain the percentage which is to be converted into decimal

Step II: Remove the percentage sign (%) and divide it by 100.

Step III: Express the fraction in the decimal form

Remember: Remove % sign and move the decimal two places to the left.

1. Express each of the following percentage as decimals:

(i) 23 % = 23/100 = 0.23

(ii) 16 % = 16/100 = 0.16

(iii) 47 % = 47/100 = 0.47

(iv) 1 % = 1/100 = 0.01

(v) 25 % = 25/100 = 0.25

Note: Decimal shifts by 2 places to the left.


2. Express each of the following decimal percentage as decimals:

(i) 1.75 % = 1.75/100 = (1.75 × 100)/(100 × 100) = 175/10000 = 0.0175

(ii) 7.5 % = 7.5/100 = (7.5 × 10)/(100 × 10) = 75/1000 = 0.075

(iii) 31.5 % = 31.5/100 = (31.5 × 10)/(100 × 10) = 315/1000 = 0.315

(iv) 0.18 % = 0.18/100 = (0.18 × 100)/(100 × 100) = 18/10000 = 0.0018

(v) 231.2 % = 231.2/100 = (231.2 × 10)/(100 × 10) = 2312/1000 = 2.312


3. Express the percentage as fraction and in decimal form.

Percentage into Decimal
Percent into Decimal
Convert Percentage into Decimal

4. Express each of the following fraction percentage as decimals:

(i) 4/5 % = 0.8 % = 0.8/100 = (0.8 × 10)/(100 × 10) = 8/1000 = 0.008

(ii) 9/20 % = 0.45 % = 0.45/100 = (0.45 × 100)/(100 × 100) = 45/10000 = 0.0045

(iii) 1/80 % = 0.0125 % = 0.0125/100 = (0.0125 × 10000)/(100 × 10000) = 125/1000000 = 0.000125

(iv) 13/50 % = 0.26 % = 0.26/100 = (0.26 × 100)/(100 × 100) = 26/10000 = 0.0026

(v) 44/5 % = 8.8 % = 8.8/100 = (8.8 × 10)/(100 × 10) = 88/1000 = 0.088


Questions and Answers on Percentage into Decimal:

I. Convert the following percentages to decimals:

(i) 5%

(ii) 13%

(iii) 20%

(iv) 75%

(v) 44%

(vi) 96%


Answers:

(i) 0.05

(ii) 0.13

(iii) 0.2

(iv) 0.75

(v) 0.44

(vi) 0.96

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