Calculate decimal to ratio conversions, ratio to decimal, and simplified a:b ratios with fractions and percents in one place instantly.
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Decimal to Ratio Formula
To convert a decimal to a ratio, write the decimal as a fraction over a power of ten, then divide both sides by the greatest common divisor.
- x = the decimal value
- n = number of digits after the decimal point
- GCD = greatest common divisor of the numerator and denominator
- a : b = the simplified ratio
For the reverse direction, divide the two sides of the ratio: x = a / b, with b nonzero. The calculator reports the exact simplified ratio; decimal and percent displays are rounded to eight places when needed. For example, 1.7778 is exactly 8889 : 5000 and only approximately 16 : 9.
Common Decimal and Ratio Values
Aspect ratios and fractions you are likely to see in real use; rounded decimal entries are approximate equivalents:
| Decimal | Ratio | Common Use |
|---|---|---|
| 1.7778 | 16 : 9 | HDTV, YouTube, monitors |
| 1.3333 | 4 : 3 | Older TVs, iPad |
| 1.5000 | 3 : 2 | 35mm photo, DSLR |
| 2.3333 | 21 : 9 | Ultrawide cinema |
| 1.6000 | 16 : 10 | Some laptop screens |
| 1.6180 | ≈ 55 : 34 | Golden ratio |
| 1.0000 | 1 : 1 | Square (Instagram) |
Simple fraction equivalents:
| Decimal | Fraction | Ratio |
|---|---|---|
| 0.25 | 1/4 | 1 : 4 |
| 0.333… | 1/3 | 1 : 3 |
| 0.5 | 1/2 | 1 : 2 |
| 0.625 | 5/8 | 5 : 8 |
| 0.75 | 3/4 | 3 : 4 |
| 0.875 | 7/8 | 7 : 8 |
Worked Example
Convert 0.45 to a ratio.
- Two digits after the decimal, so multiply numerator and denominator by 100: 45 / 100.
- Find the GCD of 45 and 100. GCD = 5.
- Divide both sides: 45 ÷ 5 = 9, and 100 ÷ 5 = 20.
- Result: 9 : 20.
FAQ
What about repeating decimals like 0.333…? Type as many digits as you have. The calculator treats your input as a terminating decimal, so 0.3333 returns 3333 : 10000. The exact repeating value 0.333… equals 1 : 3, but finite typed digits do not.
Why do I get a huge ratio for something like 1.7778? The exact conversion of 1.7778 is 8889 : 5000. The headline preserves that exact ratio rather than replacing it with the approximation 16 : 9.
Can I enter negative decimals? Yes. The sign is preserved on the numerator of the resulting ratio.
