# Arithmetic : Decimals

To divide a decimal (dividend) by a natural number (divisor), - divide the numbers in the same way as whole numbers (ignoring the decimal point); and
- insert a decimal point in the result such that the quotient has the same number of decimal places as the dividend.
For example to divide 42.056 by 7, the whole numbers are first divided to obtain 42056 / 7 = 6008. Since there are 3 decimal places in the dividend 42.056, there must be 3 decimal places in the quotient. So, 42.056 / 7 = 6.008
Note that division can be viewed as a fraction, and a fraction can be viewed as division.
because 50 ÷ 8 = 6 (remainder is 2); 20 ÷ 8 = 2 (remainder is 4); and 40 ÷ 8 = 5 (remainder is 0).
The following decimal equivalents of fractions are worth noting:
For example, 54.1266 / 10 = 5.41266, 54.1266 / 100 = 0.541266, 54.1266 / 1000 = 0.0541266
To divide a decimal (dividend) by another decimal (divisor), multiply both the dividend and the divisor by 10, 100, 1000, ... such that there is no decimal fraction in the divisor. Then, perform the division by the natural number.
Division may be always verified by multiplication, e.g., 9021.1 x 0.006 = 54.1266
Both 3.12 and 0.39 are multiplied by 100 to convert them into whole numbers. This essentially changes the problem into 'how many peaches can be bought for 312 cents if each peach costs 39 cents?'
GMAT Math Review - Arithmetic : Practice Exercise for Decimals |

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