Read, 4 minutes

Decimals are numbers that include a whole part and a fractional part separated by a decimal point. The whole part is greater than one, and the fractional part is less than one.

For example, the number 15.74 can be split into two parts:

  • The whole part: 15
  • The fractional part: 74

Terminating and Non-Terminating Decimals

Decimals can be categorized into two types:

  • Terminating Decimals: These are decimals that have an end. For example, 2.50 is a terminating decimal.
  • Non-Terminating Decimals: These are decimals that do not have an end. For example, 3.333333… is a non-terminating decimal.

The Concept of Preceding Powers of 10

The place value of digits in a decimal number decreases by a factor of 10 as you move from left to right. For example, the expanded form of 16.457 is:

  • 10 + 6 + \(\frac{4}{10}\) + \(\frac{5}{100}\) + \(\frac{7}{1000}\)

Additionally, 16.457 can be represented as \(16 \frac{457}{1000}\) in mixed fraction terms.

How to Multiply and Divide Decimals

To multiply two decimal numbers:

  1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
  2. Count the total number of decimal places in both the numbers. Place the decimal point in the result so that it has the same number of decimal places.

For example, \(2.89 \times 3.74\) becomes \(289 \times 374 = 108,086\). Since there are 4 decimal places in total, the result is 10.8086.

To divide two decimal numbers:

  1. Move the decimal point in the divisor to the right until it becomes a whole number. Move the decimal point in the dividend the same number of places.
  2. Divide the numbers as you would with whole numbers.

For example, \(34.75 \div 12.6\) becomes \(3475 \div 1260\). Divide as normal to get the result.

Exercises for Multiplying and Dividing Decimals

  1. 12.8 ÷ 5.7 =
  2. 27.8 × 17.3 =
  3. 88.8 ÷ 41.6 =
  4. 76.6 × 24.2 =
  5. 49.4 ÷ 21.2 =
  6. 27.8 ÷ 1.2 =
  7. 43.6 ÷ 34.2 =
  8. 61.6 × 39.5 =
  9. 46.2 × 22.5 =
  10. 29.6 ÷ 17.3 =

Answers

  1. 12.8 ÷ 5.7 = 2.2456…Solution:

    The divisor is not a whole number. Therefore, multiply it by 10 to get 128. Do the same for the dividend to get 57.

    Now, divide: \(128 ÷ 57 = 2.2456…\)

  2. 27.8 × 17.3 = 480.94Solution:

    Set up and multiply the numbers as you do with whole numbers. \(278 × 173 = 48094\). Count the total number of decimal places in both of the factors \(1 + 1 = 2\). Then place the decimal point in the product: 480.94.

  3. 88.8 ÷ 41.6 = 2.1346…Solution:

    The divisor is not a whole number. Therefore, multiply it by 10 to get 888. Do the same for the dividend to get 416.

    Now, divide: \(888 ÷ 416 = 2.1346…\)

  4. 76.6 × 24.2 = 1853.72Solution:

    Set up and multiply the numbers as you do with whole numbers. \(766 × 242 = 185372\). Count the total number of decimal places in both of the factors \(1 + 1 = 2\). Then place the decimal point in the product: 1853.72.

  5. 49.4 ÷ 21.2 = 2.3302…Solution:

    The divisor is not a whole number. Therefore, multiply it by 10 to get 494. Do the same for the dividend to get 212.

    Now, divide: \(494 ÷ 212 = 2.3302…\)

  1. 27.8 ÷ 1.2 = 23.1667…Solution:

    The divisor is not a whole number. Therefore, multiply it by 10 to get 278. Do the same for the dividend to get 12.

    Now, divide: \(278 ÷ 12 = 23.1667…\)

  2. 43.6 ÷ 34.2 = 1.2749…Solution:

    The divisor is not a whole number. Therefore, multiply it by 10 to get 436. Do the same for the dividend to get 342.

    Now, divide: \(436 ÷ 342 = 1.2749…\)

  3. 61.6 × 39.5 = 2433.2Solution: 
       61.6
×  39.5
—————
  308.00
 554.40
1848.00
2433.20

    Multiply the numbers as you do with whole numbers. Count the total number of decimal places in both of the factors \(1 + 1 = 2\). Then place the decimal point in the product: 2433.20

  4. 46.2 × 22.5 = 1039.5Solution: 
       46.2
×  22.5
—————
  231.00
  924.00
  924.00
1039.50

    Multiply the numbers as you do with whole numbers. Count the total number of decimal places in both of the factors \(1 + 1 = 2\). Then place the decimal point in the product: 1039.50

  5. 29.6 ÷ 17.3 = 1.711…Solution:

    The divisor is not a whole number. Therefore, multiply it by 10 to get 296. Do the same for the dividend to get 173.

    Now, divide: \(296 ÷ 173 = 1.711…\)