Ratios, Fractions and Decimals Explained

Ratio, fraction and decimal can describe related quantities

A ratio a:b compares two quantities. A fraction a/b represents division and often, but not always, a part of a whole. A decimal is another representation of a quotient. Because all three can involve division, conversions are common, but the interpretation still matters.

Part-to-part and part-to-whole are different

If a basket has 2 red apples and 3 green apples, the part-to-part ratio red:green is 2:3. The fraction of all apples that are red is 2/5, not 2/3. Writing 2:3 as the quotient 2/3 is mathematically useful for comparing the two parts, but it does not turn the denominator into the whole automatically.

The Ratio Calculator helps simplify and compare ratio forms.

Fractions to decimals

Divide the numerator by the denominator. For 3/8, 3 ÷ 8 = 0.375. The Fraction to Decimal Calculator performs this conversion directly.

Terminating and repeating decimals

Some fractions terminate, such as 1/4 = 0.25. Others repeat, such as 1/3 = 0.333…. A rounded decimal like 0.33 is an approximation of one third, not an exact replacement. This distinction matters when converting back to a fraction.

Decimals to fractions

A terminating decimal can be written over a power of ten and simplified. For example, 0.125 = 125/1000 = 1/8. The Decimal to Fraction Calculator automates the exact simplification for supported decimal inputs.

Equivalent forms

The ratio 2:4 simplifies to 1:2. The fraction 2/4 simplifies to 1/2, and the quotient is 0.5. These are equivalent numerically when the same two numbers are being divided, but context determines whether you should describe the result as a ratio, a proportion, a fraction of a whole or a decimal rate.

Worked conversions

Common mistakes

• Using a part-to-part ratio as though the second term were the whole.
• Forgetting to simplify a fraction or ratio when a simplest form is required.
• Treating a rounded repeating decimal as exact.
• Dividing by zero.
• Dropping units when a ratio compares unlike quantities.