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X.1 Compare decimals and fractions using signs

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What does it mean to compare decimals and fractions?

Comparing decimals and fractions means deciding which number is greater, smaller, or if they are equal. We use comparison signs (<, >, =) to show the relationship between them.

Examples:
  • 0.5 < 34 because 0.5 equals 12, and 12 is less than 34.
  • 0.75 = 34 because both represent the same value.
  • 0.9 > 45 because 0.9 is greater than 0.8.
Note

Always compare numbers that are written in the same form. You can change a fraction into a decimal or a decimal into a fraction before comparing.

How to compare a decimal and a fraction

To compare a decimal with a fraction, you can convert one to match the other. Most students find it easier to change the fraction into a decimal.

Steps:
  • Step 1: Write the fraction as a division problem (numerator ÷ denominator).
  • Step 2: Solve to find the decimal form of the fraction.
  • Step 3: Compare the two decimals using <, >, or =.
Example:
  • Compare 0.6 and 23
  • 23 = 0.666… (repeating)
  • 0.6 < 0.666… → 0.6 < 23
Note

When a decimal repeats (like 0.333… or 0.666…), it keeps going forever. Use rounding to help compare values more easily.

How to identify which number is greater or smaller

After both numbers are in the same form, compare their place values starting from the leftmost digit.

Example:
  • Compare 0.58 and 12
  • 12 = 0.5
  • Compare 0.58 and 0.5 → 0.58 > 0.5
  • So, 0.58 > 12
Note

Remember that a number with more digits does not always mean it is larger. The value of each digit depends on its place.

Comparing with mixed numbers

A mixed number has a whole number and a fraction part. To compare it with a decimal, change both to decimals or both to improper fractions.

Example:
  • Compare 1.25 and 1 14
  • 1 14 = 1 + 14 = 1.25
  • They are equal → 1.25 = 1 14
Note

Always compare the whole number parts first. If they are the same, then compare the fractional or decimal parts.

Helpful tips for comparing decimals and fractions

Use estimation and reasoning to check your comparison. Visual models, like number lines or fraction bars, can also help you see which number is greater.

Tips:
  • Line up decimals by the decimal point before comparing.
  • Think of fractions as parts of a whole. For example, 34 is greater than 23 because three parts out of four is more than two parts out of three.
Note

The goal is to understand why one number is greater or smaller, not just to memorize which symbol to use.