Fractions, decimals, and percentages are three different ways to express the same value. Knowing how to convert between them is essential for everyday math, from comparing prices and reading statistics to solving test problems quickly and accurately.
Different situations call for different formats. A store might advertise a discount as a percentage, but you need the decimal form to calculate the actual savings. A recipe might call for 3/4 of a cup, but your measuring tool shows decimals. Test scores often appear as fractions that you want to express as percentages. Being comfortable switching between all three forms makes mental math faster and helps you compare values at a glance.
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). Some fractions produce exact decimals, while others result in repeating decimals.
Example: Convert 3/4 to a decimal
3 ÷ 4 = 0.75
So 3/4 = 0.75 (exact).
Example: Convert 1/3 to a decimal
1 ÷ 3 = 0.333...
So 1/3 ≈ 0.333 (repeating decimal). You can round to as many places as you need.
To convert a decimal to a percentage, multiply it by 100 and add the percent sign. This is the same as moving the decimal point two places to the right.
Example: Convert 0.75 to a percentage
0.75 × 100 = 75%
So 0.75 = 75%.
Example: Convert 0.125 to a percentage
0.125 × 100 = 12.5%
So 0.125 = 12.5%.
To convert a percentage to a fraction, write the percentage as a number over 100, then simplify by dividing both the numerator and denominator by their greatest common factor (GCF).
Example: Convert 60% to a fraction
60% = 60/100
The GCF of 60 and 100 is 20. Divide both: 60 ÷ 20 = 3, 100 ÷ 20 = 5.
So 60% = 3/5.
Example: Convert 37.5% to a fraction
37.5% = 37.5/100 = 375/1000
The GCF of 375 and 1000 is 125. Divide both: 375 ÷ 125 = 3, 1000 ÷ 125 = 8.
So 37.5% = 3/8.
To convert a fraction directly to a percentage, divide the numerator by the denominator to get a decimal, then multiply by 100. This combines the two steps you already know into one.
Example: Convert 4/5 to a percentage
4 ÷ 5 = 0.8, then 0.8 × 100 = 80%
So 4/5 = 80%.
Example: Convert 5/8 to a percentage
5 ÷ 8 = 0.625, then 0.625 × 100 = 62.5%
So 5/8 = 62.5%.
These conversions come up frequently in school and everyday life. Having them memorized saves time and reduces errors.
| Fraction | Decimal | Percentage |
|---|---|---|
1/2 | 0.5 | 50% |
1/3 | 0.333... | ≈33.3% |
1/4 | 0.25 | 25% |
1/5 | 0.2 | 20% |
1/8 | 0.125 | 12.5% |
2/3 | 0.666... | ≈66.7% |
3/4 | 0.75 | 75% |
3/5 | 0.6 | 60% |
5/8 | 0.625 | 62.5% |
7/8 | 0.875 | 87.5% |
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