Page 169 - Start Up Mathematics_8 (Non CCE)

11 Percentage

Percent is derived from the Latin word per centum meaning in one hundred or per hundred. It is denoted by
the symbol %.
Consider the statement “Rahul scored 60% marks in Mathematics”. This implies that Rahul scored 60 out of
hundred marks in Mathematics.

Percent as a Fraction
A fraction with its denominator as 100 is equal to the percent of that numerator.

2 34 217
For example, = 2%, = 34%, = 217%, etc.
100 100 100

If we multiply a fraction by 100 and mark the percent sign (%), the fraction is converted into percent.
3 Ê 3 ˆ 2 Ê 2 ˆ
For example, = Á ¥ 100 % = 75%, = Á ¥ 100 % = 40%
˜
˜
4 Ë 4 ¯ 5 Ë 5 ¯
Conversely, if a percent is divided by 100 and the percent sign (%) is removed, the percent is converted into
a fraction.
35 42
For example, 35% = , 42% =
100 100

Percent as a Ratio
Percent can also be expressed as a ratio with the first term being the given percent and the second term
being 100.
42 21 23
For example, 42% = = = 21 : 50, 23% = = 23 : 100
100 50 100

Conversion of ratio into percent
To convert ratio into percent, convert the ratio into a fraction, multiply the fraction with 100 and place the
percent sign.
7 7 11 11
For example, 7 : 4 = = ¥ 100 = 175%, 11 : 25 = = ¥ 100 = 44%
4 4 25 25

Percent as a Decimal
To convert percent into decimal, express the percent as a fraction and express the fraction in the decimal form.
35 73
For example, 35% = = 0.35, 73% = = 0.73
100 100

Conversion of decimal into percent

To convert decimal into percent, shift the decimal point by 2 places towards the right and place the percent
sign (%).

For example, 0.334 = 33.4%