Read, 3 minutes

A decimal is a number that consists of a whole number and a fractional part. To put it 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.

Expanded Form of a Decimal Number:

Take the decimal number 12.457:

  • Expanded form: \(10 + 2 + \frac{4}{10} + \frac{5}{100} + \frac{7}{1000}\)
  • Mixed fraction form: \(12 \frac{457}{1000}\)

Rounding Off Decimals:

To round off decimals to the nearest whole number, look at the digit in the tenths place:

  • If the digit in the tenths place is 5 or greater, round up the whole number by 1.
  • If the digit in the tenths place is less than 5, keep the whole number as it is.

Examples:

  • 12.395 rounded to the nearest whole number: 12
  • 12.678 rounded to the nearest whole number: 13

To round off decimals to the nearest tenth, look at the digit in the hundredths place:

  • If the digit in the hundredths place is 5 or greater, round up the tenths place by 1.
  • If the digit in the hundredths place is less than 5, keep the tenths place as it is.

Examples:

  • 2.67 becomes 2.7
  • 2.34 becomes 2.3

Exercises for Rounding Decimals

  1. 34.697 \(\rightarrow\)
  2. 14.584 \(\rightarrow\)
  3. 11.405 \(\rightarrow\)
  4. 18.152 \(\rightarrow\)
  5. 41.496 \(\rightarrow\)
  6. 19.209 \(\rightarrow\)
  7. 12.332 \(\rightarrow\)
  8. 2.971 \(\rightarrow\)
  9. 50.922 \(\rightarrow\)
  10. 57.125 \(\rightarrow\)

Answers

  1. 34.697 \(\rightarrow\) 35

    Solution:

    First, look at the next place value to the right of the ones place. It’s 6 and it is greater than 5, thus add 1 to the digit in the ones place.

  2. 14.584 \(\rightarrow\) 15

    Solution:

    First, look at the next place value to the right of the tenth place. It’s 8 and it is greater than 5, thus add 1 to the digit in the tenth place.

  3. 11.405 \(\rightarrow\) 11.4

    Solution:

    First, look at the next place value to the right of the hundredth place. It’s 0 and it is less than 5 thus removing all the digits to the right. Then, the answer is 11.4.

  4. 18.152 \(\rightarrow\) 18.2

    Solution:

    First, look at the next place value to the right of the tenth place. It’s 5 and it is equal to 5, thus add 1 to the digit in the tenth place.

  5. 41.496 \(\rightarrow\) 41

    Solution:

    First, look at the next place value to the right of the ones place. It’s 4 and it is less than 5, thus the digit in the ones place remains the same.

  6. 19.209 \(\rightarrow\) 19

    Solution:

    First, look at the next place value to the right of the ones place. It’s 2 and it is less than 5, thus the digit in the ones place remains the same.

  7. 12.332 \(\rightarrow\) 12

    Solution:

    First, look at the next place value to the right of the ones place. It’s 3 and it is less than 5, thus the digit in the ones place remains the same.

  8. 2.971 \(\rightarrow\) 3

    Solution:

    First, look at the next place value to the right of the ones place. It’s 9 and it is greater than 5, thus add 1 to the digit in the ones place.

  9. 50.922 \(\rightarrow\) 50.9

    Solution:

    First, look at the next place value to the right of the tenths place. It’s 2 and it is less than 5, thus the digit in the tenths place remains the same.

  10. 57.125 \(\rightarrow\) 57.1

    Solution:

    First, look at the next place value to the right of the tenths place. It’s 2 and it is less than 5, thus the digit in the tenths place remains the same.