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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.
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
Expressing a Percent as Decimal:
Let us understand it by considering some more examples.
5. convert the following into decimals.
(i) 18%
(ii) 24%
(iii) 110%
(iv) 2%
Solution:
(i) 18% = \(\frac{18}{100}\) = 0.18
(ii) 24% = \(\frac{24}{100}\) = 0.24
(iii) 110% = \(\frac{110}{100}\) = 1.1
(iv) 2% = \(\frac{2}{100}\) = 0.02
Note: If we say that Matthew earned 365% profit, it means Matthew earned ₹ 365 per ₹ 100.
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
Percentage of the given Quantity
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Real Life Problems on Percentage
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