(1 + 3%) × 21 = ? Percentage increase change: increment the number 21 by 3% (percent) of its value and Calculate the actual change (the absolute difference)

Increase the number 21 by 3% of its value

A brief introduction. Definitions and formulas

Percent, p%

'Percent (%)' means 'out of one hundred':


3% = 3 'out of one hundred',


p% is read p 'percent',


p% = p/100 = p ÷ 100


3% = 3/100 = 3 ÷ 100 = 0.03


100% = 100/100 = 100 ÷ 100 = 1


How to increase the number 21
by 3% of its value?

The value of the percentage increase = 3% × 21


The new value = 21 + The value of the percentage increase


Detailed calculations and the calculation proof

1. Calculate the new value of the number...
... increased by percentage of its initial value

The new value =


21 + The value of the percentage increase =


21 + (3% × 21) =


21 + 3% × 21 =


(1 + 3%) × 21 =


(100% + 3%) × 21 =


103% × 21 =


103 ÷ 100 × 21 =


103 × 21 ÷ 100 =


2,163 ÷ 100 =


21.63


2. Calculate the actual change (the absolute difference)...
... between the new value and the initial one

The actual change =


The new value - 21 =


21.63 - 21 =


0.63


Proof of calculation

We will prove below that the calculations are correct:

Calculate the value of the percentage increase and see if we get as a result the actual change (the absolute difference) between the new value and the initial one.


For positive numbers, the actual change = The value of the percentage increase

Calculate the value of the percentage increase:

The value of the percentage increase =


3% × 21 =


3 ÷ 100 × 21 =


3 × 21 ÷ 100 =


63 ÷ 100 =


0.63

The value of the percentage increase = The actual change =>


The calculations are correct.


The answer:

21 increased by 3% of the value = 21.63
The actual change:
21.63 - 21 = 0.63

The symbols used: % percent, ÷ division, × multiplication, = the equal sign, / the fraction bar, ≈ approximately the same. Writing numbers: comma ',' - as a thousands separator, point '.' as a decimal mark.

The latest 5 numbers increased by percentages of their values

The number 21 increased by 3% (3 percent) of its value = 21.63 Feb 02 10:22 UTC (GMT)
The number 70,720 increased by 10% (10 percent) of its value = 77,792 Feb 02 10:22 UTC (GMT)
The number 12.51 increased by 15% (15 percent) of its value = 14.3865 Feb 02 10:21 UTC (GMT)
The number 165,000 increased by 28% (28 percent) of its value = 211,200 Feb 02 10:21 UTC (GMT)
The number 32.22 increased by 151% (151 percent) of its value = 80.8722 Feb 02 10:21 UTC (GMT)
All the numbers increased by percentages of their values

Increase numbers by percentage of their value, calculate the percentage increased values

Increase numbers by percentage of their initial value and calculate the absolute percentage change (difference). Examples

How to calculate the new value of a number when increasing it by percentage of its initial value and how to calculate the absolute percentage change (difference)?

Four examples of calculations below.

Example 1:

Example 2:

Example 3:

Example 4: