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W.1 Convert fractions to decimals

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What does it mean to convert fractions to decimals?

Converting fractions to decimals means changing a fraction into a number that uses a decimal point instead of a fraction bar. Both forms show the same value, just in different ways.

Example:
  • 12 = 0.5
  • 34 = 0.75
Note

A fraction and its decimal form are equal in value. They are just two different ways to write the same number.

How to convert a fraction to a decimal

To change a fraction into a decimal, divide the numerator (the top number) by the denominator (the bottom number).

Steps:
  • Take the fraction 35.
  • Divide 3 ÷ 5 using long division or other division methods.
  • The result is 0.6, so 35 = 0.6.
Note

The denominator tells how many equal parts make one whole. Dividing shows what part of one whole the numerator represents.

Understanding terminating and repeating decimals

When a fraction is turned into a decimal, the result may stop after a few digits (a terminating decimal) or continue in a pattern that repeats forever (a repeating decimal).

Examples:
  • Terminating: 14 = 0.25
  • Repeating: 13 = 0.333... (the 3 repeats forever)
Note

If the denominator has a factor of only 2, 5, or both, the decimal will stop. Other denominators often make repeating decimals.

Comparing fractions and decimals

Once a fraction is written as a decimal, it becomes easier to compare it with other decimals using place value.

Example:
  • 34 = 0.75 and 23 = 0.666...
  • Since 0.75 > 0.666..., 34 is greater than 23.
Note

Always line up the decimal points when comparing decimals to decide which is larger or smaller.

Why converting fractions to decimals matters

Understanding how to convert fractions to decimals helps you work with money, measurements, and data more easily in everyday life.

Example:
  • If a recipe calls for 34 of a cup of sugar, that is the same as 0.75 cups.
  • If you scored 45 on a quiz, that equals 0.8 or 80%.
Note

Knowing both forms—fraction and decimal—helps you understand numbers better and apply them in real-world problems.