# Division of Decimal Rational Numbers

## Exact division

Consider the following division:

1,4 : 0,05.

Transforming into decimal fractions we have:

Practical method:

 1º) We equate the number of decimal places, with the addition of zeros;2º) We suppress the commas;3º) We made the division.

Examples:

1,4 : 0,05

 We match the decimal places: 1,40 : 0,05 Deleting Commas: 140 : 5

Performing the division:

Thus, the quotient of 1.4 by 0.05 is 28.

6 : 0,015

 We match the decimal places 6,000 : 0,015 Suppressing Commas 6.000 : 15

Performing the division:

Therefore, the ratio of 6 by 0.015 is 400.

4,096 : 1,6

 We match the decimal places 4,096 : 1,600 Suppressing Commas 4.096 : 1.600

Performing the division:

Note that in the above division the integer quotient is 2 and the remainder corresponds to 896 units. We can proceed with division by determining the decimal part of the quotient. To determine the tenths, we put a comma in the quotient and add a zero rest, since 896 units corresponds to 8,960 tenths.

We continue the division to determine the hundredths, adding another zero to the new remainder, since 960 tenths corresponds to 9600 hundredths.

The quotient 2.56 is exact because the rest is null.

Thus, the quotient of 4.096 per 1.6 is 2.56.

Another examples:

0,73 : 5

 We match the decimal places 0,73 : 5,00 Suppressing Commas 73 : 500

Performing the division:

We can proceed to division by placing a comma in the quotient and adding a zero to the right of the three. Like this:

Continuing the division, we obtain:

Thus, the quotient of 0.73 per 5 is 0.146.

In some divisions, adding a zero to the rest does not yet make division possible. In this case, we must put a zero in the quotient and add another zero to the rest. Examples:

• 2,346 : 2,3

Verify that 460 (tenths) is less than the divisor (2,300). We then put a zero in the quotient and add one more zero to the rest.

Thus, the quotient of 2.346 by 2.3 is 1.02.

Note:

To divide a decimal number by 10, 100, 1,000,…, just move the comma left one, two, three,…, decimal places. Examples:

Next: Not Exact Division