Ordering fractions, decimals and negatives
Compare rational numbers using a common scale and interpret inequalities.
Before you begin
- Equivalent fractions and decimals
- Negative numbers on a number line
Put every value on the same scale
A rational number can be written as a fraction of integers with a nonzero denominator. Fractions, terminating decimals and repeating decimals can name the same value. To compare a short list, convert to convenient equivalent forms. On a horizontal number line, values increase to the right. The negative sign changes which side of zero a number occupies, so comparing digits alone is unreliable.
Read an inequality in context
The statement −1.5 < −1.2 says that −1.5 lies farther left. If these are temperatures, −1.5 °C is colder. For negative numbers, a larger distance from zero means a smaller signed value. Write an ordered list from left to right, check the signs, and then translate the comparison back into words with the appropriate units.
Worked example
Order −3/4, 0.2, −0.6 and 1/5 from least to greatest.
Show the worked solution
- Convert −3/4 to −0.75 and 1/5 to 0.2.
- The negative numbers come before the positive numbers, and −0.75 is left of −0.6.
- The final two quantities are equal, so use an equals sign for them.
−3/4 < −0.6 < 0.2 = 1/5.
Try it yourself
Which temperature is warmer?
Common mistakes
- Do not remove negative signs before deciding the order.
- Equality is possible when different representations name the same value.
What can you explain now?
Order −1/2, −0.05 and −2/5 from least to greatest.
Compare with the explanation
−1/2 < −2/5 < −0.05.
The decimals are −0.50, −0.40 and −0.05. Moving toward zero from the left increases the value.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗