Fractions, Decimals, and Ratios
A fuller guide to fractions, decimals, and ratios, focused on choosing the most readable form, preserving proportional meaning, and moving cleanly between equivalent representations.
Key formulas
Use division to convert the fraction into a decimal.
Write the decimal over a power of ten, then simplify.
Divide both parts by the greatest common divisor.
Equivalent forms are useful because they emphasise different things
A fraction preserves part-to-whole structure, a decimal is convenient for arithmetic and percentages, and a ratio highlights comparison between quantities. None is inherently superior. The best form depends on what you need to communicate or calculate next.
For example, 3/4, 0.75, 75%, and the ratio 3:4 are related but not interchangeable in every sentence. 75% describes a proportion of a whole. A ratio such as 3:4 compares two linked quantities. Recognising the role of each format stops many interpretation errors.
Fractions to decimals and back again
To convert a fraction to a decimal, divide the numerator by the denominator. Fractions such as 1/2, 1/4, and 3/5 produce terminating decimals because their denominators reduce to factors of 2 and 5. Others, such as 1/3, recur indefinitely and require rounding or recurring notation.
To convert a decimal to a fraction, first write the decimal over the correct power of ten, then simplify. For 0.375, write 375/1000 and divide numerator and denominator by 125 to obtain 3/8. The simplification step is what turns a technically correct fraction into a readable one.
Ratios are comparisons, not percentages wearing a different hat
A ratio such as 2:3 means that for every 2 parts of one quantity there are 3 parts of the other. Ratios can be scaled up or down without changing the relationship. That is why 2:3, 4:6, and 20:30 all describe the same proportion.
When simplifying a ratio, divide both terms by their greatest common divisor. If the terms have units, make sure the units are consistent before simplifying. A ratio of 50 cm to 2 m is not 50:2; convert first to 50:200 or 0.5:2, then simplify to 1:4.
- Use fractions when exact part-to-whole reasoning matters.
- Use decimals when calculation efficiency or spreadsheet input matters.
- Use ratios when comparison between quantities is the main idea.
- Normalise units before simplifying any ratio based on measurements.
Worked examples
Example 1: Convert 7/16 to a decimal. Dividing 7 by 16 gives 0.4375. If you needed a percentage, multiply by 100 to get 43.75%.
Example 2: Convert 0.875 to a fraction. Write 875/1000, then divide both parts by 125 to get 7/8.
Example 3: Simplify the ratio 18:24. The greatest common divisor is 6, so the simplified ratio is 3:4. If the original numbers represented quantities in the same units, the proportion is preserved exactly.
Common mistakes and how to avoid them
- Rounding a recurring decimal too early and then converting the rounded value back into a misleading fraction.
- Calling a fraction a ratio without checking whether the context is part-to-whole or quantity-to-quantity.
- Simplifying ratio terms before converting their units to a common base.
- Leaving a fraction unsimplified, which makes comparison and checking harder than it needs to be.
Apply the topic straight away.
Fraction to Decimal Calculator
Use the Fraction to Decimal Calculator for a quick fraction to decimal result with clear inputs and a readable answer.
Decimal to Fraction Calculator
Use the Decimal to Fraction Calculator for a quick decimal to fraction result with clear inputs and a readable answer.
Ratio Simplifier Calculator
Use the Ratio Simplifier Calculator for a quick ratio simplifier result with clear inputs and a readable answer.