Percentage Expert - Background information

How to convert percentages to fractions and fractions to percentages

Percentage is a hundredth of a number and is denoted by the symbol "%" (1% = 0.01, 37% = 0.37, 158% = 1.58). Percentage is a dimensionless quantity. For ease of use, the share of any number is often represented as a percentage, for example, 100% = 1, that is, the number itself, 50% = 0.5, that is, half of the number, 25% = 0.25 is a quarter, 20% = 0.2 is a fifth of the number. Thus, to represent a percentage number as a fraction, you just need to divide it by 100. And to represent a fraction as a percentage, you need to multiply it by 100.
Examples of representing percentages as a fraction:
100% = 1; 61.7% = 0.617; 0.02% = 0.0002; 3/7% = 3/700.
Examples of representing fractions as percentages:
0.161 = 16.1%; 0.007 = 0.7%; 2/5 = 40%; 8/11= 800/11%.

How to find a number z if z is x% percent of a number y

To find x% percent of the number y means to find the corresponding fraction of the number y. Therefore, you just need to convert the percentages into fractions (x%=x/100) and multiply the original number y by the resulting fraction (x/100). Here is the corresponding formula:

If z is x% of y, then z = y*x/100.

Examples.
1) find 500% of the number 27: 27*500/100 = 135;
1) find 25% of the number 270: 270*25/100=67.5;
2) find 0.123% of the number 48: 48*0.00123=0.05904;
3) find 305% of the number 256: 256*305/100=780.8.

How to find a number y if it is known that x% of the number y is equal to z

If it is known that the number z is x% of the number y, then using the previous formula we write the corresponding equality: z=y*x/100. From this equality we obtain a formula for the number y: y=z/(x/100). That is, to find a number y, if it is known that x% of y is equal to a number z, you need to divide z by the fraction x/100:

If it is known that x% of the number y is equal to z, then y = z/(x/100) = 100z/x.

Examples.
1) 35% of an unknown number is 14, find this number: 14/(35/100) = 35*100/14 = 250;
2) 23% of an unknown number is 6.9, find this number: 6.9/(23/100) = 6.9*100/23 = 690/23 = 30;
3) 0.02% of an unknown number is 12.1, find this number: 12.1/(0.02/100) = 12.1*100/0.02 = 121000/2 = 60500.

How to calculate what percentage (x%) a number y is of a number z

Since the fraction of a number y from a number z is y/z, then to represent this fraction as a percentage, you just need to multiply it by 100. Let us give the corresponding formula:

What percentage (x%) is the number y of the number z?: x% = (у/z)*100.

Examples.
1) find what percentage the number 11 is of the number 55: (11/55)*100 = 20%;
2) find what percentage the number 175 is of the number 25: (175/25)*100 = 700%;
3) find what percentage the number 0.3 is of the number 0.36: (0.3/0.36)*100 = 83.(3)%;

How to calculate the percentage change of a number

The problem of calculating the change in a number can be formulated in two ways: by what percentage is the number y greater than the number z, or by what percentage is the number z less than the number y. In the first case, we find the fraction of the number (y-z) relative to the number z: (y-z)/z and multiply it by 100. In the second case, we are looking for the fraction of the number (y-z) relative to the number y: (y-z)/y and multiply it by 100. Here are the corresponding formulas.

By what percentage is y greater than z: x% = ((y-z)/z)*100.

By what percentage is z less than y? x% = ((y-z)/y)*100.

Examples.
1) find by what percentage the number 16 is greater than the number 4:((16-4)/4)*100 = 300%;
2) find by what percentage the number 4 is less than the number 16:((16-4)/16)*100 = 75%;
3) find by what percentage the number 75 is less than the number 525:((525-75)/525)*100 = (600/7)%;
4) find by what percentage the number 525 is greater than the number 75:((525-75)/75)*100 = 600%;