Dividing Decimals by 1-Digit Whole Numbers: Long Division Method

Dividing Decimals by 1-Digit Whole Numbers

Dividing decimals by whole numbers, especially when the whole number has a single digit, requires a different approach than integer division. The long division method, which is well-known for whole numbers, needs some adjustments to accommodate decimals. In this article, we'll explore the process of dividing decimals by 1-digit whole numbers using the long division method.

The Long Division Method

The long division method for decimals with a 1-digit whole number consists of the following steps:

1. Align the decimal point of both numbers so that they are in the same column.
2. Multiply the dividend by the first digit of the divisor, then write the product below the divisor.
3. Subtract the product from the dividend, writing the result below the dividend.
4. Bring down the next digit of the dividend, if there is one, and repeat from step 2.

Example: 0.375 ÷ 2

1. Align the decimal points:

      3  7  5
    __________
2   |     |

2. Multiply and write the product below the divisor:

      3  7  5
    __________
2   |  3  |
     7 - 3 

3. Subtract and write the result below the dividend:

      3  7  5
    __________
2   |  3  | 4
     7 - 3 
    ------------
    4

4. Bring down the next digit of the dividend (in this case, there is none):

      3  7  5
    __________
2   |  3  | 4
     7 - 3 
    ------------
    4

5. Multiply the divisor by the next digit of the dividend and write the product under the last digit of the dividend:

      3  7  5
    __________
2   |  3  | 4
     7 - 3 
    ------------
    4
2 * 5 = 10

6. Subtract and write the result below the dividend:

      3  7  5
    __________
2   |  3  | 4
     7 - 3 
    ------------
    4
2 * 5 = 10
     7 - 10
    ------------
  -3

7. Repeat step 6 as long as there are digits in the dividend:

      3  7  5
    __________
2   |  3  | 4
     7 - 3 
    ------------
    4
2 * 5 = 10
     7 - 10
    ------------
  -3
2 * 7 = 14
    3 - 14
    ------------
 -11

8. Look at the remainder to determine the quotient:

The quotient is 0.1625.

Rounding

If the result of the division contains digits after the decimal point, you must round the quotient to the desired precision. For example, if you want to round the quotient to two decimal places, the quotient would be 0.16.

Remember, when rounding, follow these guidelines:

1. If the first digit to be dropped is 5 or greater, round up.
2. If the first digit to be dropped is less than 5, do not round up.

In our example, the first digit to be dropped is 2, which is less than 5, so we do not round up.

Common Mistakes and Pitfalls

When dividing decimals by 1-digit whole numbers, you must be careful with the following:

1. Placing the decimal point correctly in the dividend and divisor, especially when bringing down the next digit of the dividend.
2. Multiplying the divisor by the correct digit in the dividend.
3. Subtracting correctly.
4. Rounding the quotient correctly.
5. Carrying the decimal point through the calculation.

Practice Problems

1. 0.67 ÷ 4
2. 0.125 ÷ 8
3. 0.004 ÷ 5
4. 0.825 ÷ 3
5. 0.0004 ÷ 9

For further practice and understanding, solve these problems and verify your answers using a calculator.