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A decimal is a number that consists of a whole number and a fractional part. To put it in another way, decimals are fractions and mixed numbers with denominators that are powers of 10. For example, the decimal 0.6 is the same as the fraction \(\frac{6}{10}\), or the decimal 1.2 is the same as the fraction \(\frac{12}{10}\) or the mixed number 1 \(\frac{2}{10}\). You can convert fractions and mixed numbers to decimals. For instance, instead of writing 4 \(\frac{3}{5}\), you can write 0.8.

Steps to Compare Two Decimals:

  1. Compare the whole parts first. If the whole part of one decimal is greater, it means that this decimal is greater than the other.
  2. If the whole parts are the same, compare the decimals from the left. (hundreds, tens, ones, tenths, hundredths, etc.)
  3. To compare decimals, use the following symbols:
    • Equal to \(=\)
    • Less than \(<\)
    • Greater than \(>\)
    • Greater than or equal \(\geq\)
    • Less than or equal \(\leq\)

Example: 2.67 > 0.267

Exercises for Comparing Decimals

  1. 43.97 □ 2.83
  2. 58.75 □ 55.24
  3. 65.5 □ 42.81
  4. 6.18 □ 6.18
  5. 199.5 □ 19.95
  6. 462.7 □ 46.27
  7. 13.24 □ 13.29
  8. 789.5 □ 78.95
  9. 31.43 □ 31.62
  10. 46.82 □ 15.66

Answers

  1. 43.97 > 2.83

    Solution:

    In this example, because the whole number of 43.97 is greater than 2.83, therefore 43.97 > 2.83

  2. 58.75 > 55.24

    Solution:

    In this example, because the whole number of 58.75 is greater than 55.24, therefore 58.75 > 55.24

  3. 65.5 > 42.81

    Solution:

    In this example, because the whole number of 65.5 is greater than 42.81, therefore 65.5 > 42.81

  4. 6.18 = 6.18

    Solution:

    In this example, because the whole numbers and fractional parts are the same. Therefore they are equal: 6.18 = 6.18

  5. 199.5 > 19.95

    Solution:

    In this example, because the whole number of 199.5 is greater than 19.95, therefore 199.5 > 19.95

  1. 462.7 > 46.27

    Solution:

    In this example, because the whole number of 462.7 is greater than 46.27, therefore 462.7 > 46.27

  2. 13.24 < 13.29

    Solution:

    In this example, the whole numbers are the same, therefore we compare the fractional parts. Since the fractional part 0.29 is greater than 0.24, so 13.24 < 13.29

  3. 789.5 > 78.95

    Solution:

    In this example, because the whole number of 789.5 is greater than 78.95, therefore 789.5 > 78.95

  4. 31.43 < 31.62

    Solution:

    In this example, the whole numbers are the same, therefore we compare the fractional parts. Since the fractional part 0.62 is greater than 0.43, so 31.43 < 31.62

  5. 46.82 > 15.66

    Solution:

    In this example, because the whole number of 46.82 is greater than 15.66, therefore 46.82 > 15.66