Decimal Comparison

Comparing Decimals

Comparing decimals is a simple task if you know the trick. While there is a clear and logical reason one decimal may be smaller (or larger) than another decimal, there is a quick trick to determining the relation. The trick for comparing decimals is to:

  1. Make the numbers have the same number of digits to the right of the decimal point( you can add as many zeros to the end of the decimal as you need to make the numbers the same length)
  2. Compare the adjusted numbers

To compare 0.5 and 0.11, you must

  • (1) Change the 0.5 to 0.50,
  • (2) Then compare the 0.50 and 0.11.

Once you have the decimals the same length, simply ignore the decimal point and compare the 50 and 11. Since 50 > 11, 0.50 > 0.11. But 0.50 = 0.5. So, 0.5 > 0.11.

The following are examples of decimal comparisons.

  • because 0.031 < 0.100 because 31 < 100
  • because 0.011 > 0.100, because 11 > 10
  • because 0.0012 > 0.0010, because 12 > 10
  • because 0.9 < 1.0, because 9 < 10
  • because 1.90 > 1.22, because 190 > 122

There is a reason the "trick" works, and it is not actually a trick. This is simply a short cut method to thinking about the decimal comparison. Looking at the page on equivalent decimals, you learned that numbers like 0.5, 0.50, and 0.500 are all equivalent. When you change 0.3 to 0.30, you are simply saying that 3 tenths = 30 hundredths, which is true. When you are comparing 0.34 and 0.30, you are comparing 34 hundredths and 30 hundredths. 34 hundredths is more hundredths than 30 hundredths. Therefore, when you mentally compare 34 and 30, your are actually comparing 34 hundredths and 30 hundredths. 34 > 30, so 0.34 > 0.30 and 0.34 > 0.3

Check Your Understanding

Explain why the following comparisons are true ...

  1. 0.2 > 0.10
  2. 0.72 > 0.7
  3. 1.032 < 1.04
  4. 2.04 < 2.4
  5. 32.5 > 3.25

Enter two numbers between 0 and 999.9999 that are not equivalent. In your mind, decide how they compare.  Then, click the button "Check" and check your answer.