Math Skill: Percentages
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## Percentages

The meaning of a percentage is best explained by the Percentage Pictures topic. Click here for the lesson.

This lesson pertains to the conversion between fractions, decimals, and percentages. Conceptually, this topic demonstrates that fractions, decimals, and percentages are all interchangeable.

### Converting from a decimal to a percentage

Example: Convert 0.56 to a percentage.
Multiply the decimal by 100 to get a percentage. 0.56 × 100 = 56%

Example: Convert 1.205 to a percentage.
Multiply the decimal by 100 to get a percentage. 1.205 × 100 = 120.5%

### Converting from a percentage to a decimal

Example: Convert 78% to a decimal.
Divide the percentage by 100 to get a decimal. 78/100 = 0.78
78% = 78/100 = 0.78

Example: Convert 163% to a decimal.
Divide the percentage by 100 to get a decimal. 163/100 = 1.63
163% = 163/100 = 1.63

### Converting from a fraction to a percentage

To convert a fraction to a percentage, follow these steps:
 1 Convert the fraction to a decimal 2 Multiply by 100 to get a percentage 3 If needed, round to the nearest percentage

Example: Convert the fraction to a percentage:
 68 = % 1. Convert 6/8 to a decimal 6/8 = 0.75 2. Multiply the decimal by 100 to get a percentage. 0.75 × 100 = 75%

Example: Convert the fraction to a percentage and round to the nearest percentage:

 1 37 = % 1. Convert 13/7 to a decimal 13/7 = 1.42857... 2. Multiply the decimal by 100 to get a percentage. 1.42857... × 100 = 142.857...% 3. Round 142.857...% 142.857...% rounds to 143%

FAQ: How does 13/7 become 1.42857...?
Answer: 3 divided by 7 = 0.42857... (verify with a calculator or refer to the Small Decimal Division topic), so 13/7 is 1.42857...

### Complexity=100, Mode=decimal

Convert the decimal into a percentage.
 1.   0.57 % 2.   0.88 %

### Complexity=200, Mode=decimal

Convert the decimal into a percentage.
 1.   0.01 % 2.   0.54 %

### Complexity=200, Mode=perc

Convert the percentage into a decimal.
 1.   48% 2.   95%

### Complexity=4, Mode=simple

Calculate the percentage. If necessary, round to the nearest percentage.
1.
 23
%
2.
 22
%

### Complexity=15, Mode=simple

Calculate the percentage. If necessary, round to the nearest percentage.
1.
 16
%
2.
 28
%

### Complexity=8, Mode=mixed

Calculate the percentage. If necessary, round to the nearest percentage.
1.
 3 37
%
2.
 2 38
%

### Complexity=15, Mode=mixed

Calculate the percentage. If necessary, round to the nearest percentage.
1.
 3 610
%
2.
 68
%

### Complexity=40, Mode=mixed

Calculate the percentage. If necessary, round to the nearest percentage.
1.
 1 1535
%
2.
 2340
%

### Complexity=70, Mode=mixed-imp

Calculate the percentage. If necessary, round to the nearest percentage.
1.
 2 108
%
2.
 2 4836
%

### Complexity=100, Mode=decimal

Convert the decimal into a percentage.
10.57 %
Solution
Multiply the decimal by 100 to get a percentage.
0.57 × 100 = 57%
20.88 %
Solution
Multiply the decimal by 100 to get a percentage.
0.88 × 100 = 88%

### Complexity=200, Mode=decimal

Convert the decimal into a percentage.
10.01 %
Solution
Multiply the decimal by 100 to get a percentage.
0.01 × 100 = 1%
20.54 %
Solution
Multiply the decimal by 100 to get a percentage.
0.54 × 100 = 54%

### Complexity=200, Mode=perc

Convert the percentage into a decimal.
148%
Solution
Divide the percentage by 100 to get the decimal.
48/100 = 0.48
295%
Solution
Divide the percentage by 100 to get the decimal.
95/100 = 0.95

### Complexity=4, Mode=simple

Calculate the percentage. If necessary, round to the nearest percentage.
1
 23
%
Solution
Convert 2/3 to a decimal
2/3 = 0.66666666666667
Multiply the decimal by 100 to get a percentage.
0.66666666666667 × 100 = 66.666666666667%
Round 66.666666666667 to 67%
2
 22
%
Solution
Convert 2/2 to a decimal
2/2 = 1
Multiply the decimal by 100 to get a percentage.
1 × 100 = 100%

### Complexity=15, Mode=simple

Calculate the percentage. If necessary, round to the nearest percentage.
1
 16
%
Solution
Convert 1/6 to a decimal
1/6 = 0.16666666666667
Multiply the decimal by 100 to get a percentage.
0.16666666666667 × 100 = 16.666666666667%
Round 16.666666666667 to 17%
2
 28
%
Solution
Convert 2/8 to a decimal
2/8 = 0.25
Multiply the decimal by 100 to get a percentage.
0.25 × 100 = 25%

### Complexity=8, Mode=mixed

Calculate the percentage. If necessary, round to the nearest percentage.
1
 3 37
%
Solution
Convert 33/7 to a decimal
33/7 = 3.4285714285714
Multiply the decimal by 100 to get a percentage.
3.4285714285714 × 100 = 342.85714285714%
Round 342.85714285714 to 343%
2
 2 38
%
Solution
Convert 23/8 to a decimal
23/8 = 2.375
Multiply the decimal by 100 to get a percentage.
2.375 × 100 = 237.5%
Round 237.5 to 238%

### Complexity=15, Mode=mixed

Calculate the percentage. If necessary, round to the nearest percentage.
1
 3 610
%
Solution
Convert 36/10 to a decimal
36/10 = 3.6
Multiply the decimal by 100 to get a percentage.
3.6 × 100 = 360%
2
 68
%
Solution
Convert 6/8 to a decimal
6/8 = 0.75
Multiply the decimal by 100 to get a percentage.
0.75 × 100 = 75%

### Complexity=40, Mode=mixed

Calculate the percentage. If necessary, round to the nearest percentage.
1
 1 1535
%
Solution
Convert 115/35 to a decimal
115/35 = 1.4285714285714
Multiply the decimal by 100 to get a percentage.
1.4285714285714 × 100 = 142.85714285714%
Round 142.85714285714 to 143%
2
 2340
%
Solution
Convert 23/40 to a decimal
23/40 = 0.575
Multiply the decimal by 100 to get a percentage.
0.575 × 100 = 57.5%
Round 57.5 to 58%

### Complexity=70, Mode=mixed-imp

Calculate the percentage. If necessary, round to the nearest percentage.
1
 2 108
%
Solution
Convert 210/8 to a decimal
210/8 = 3.25
Multiply the decimal by 100 to get a percentage.
3.25 × 100 = 325%