Arithmetic : Decimals

Division of 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.
To convert a fraction to a decimal, the numerator is divided by the denominator. For example,

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:
1/100 = 0.01 ; 1/50 = 0.02 ; 1/25 = 0.04 ; 1/20 = 0.05 ; 1/10 = 0.1 ;
1/8 = 0.125 ; 3/8 = 0.375 ; 5/8 = 0.625 ; 7/8 = 0.875 ;
1/5 = 0.2 ; 2/5 = 0.4 ; 3/5 = 0.6 ; 4/5 = 0.8 ;
1/4 = 0.25 ; 1/2 = 0.5 ; 3/4 = 0.75
Some fractions give an infinite decimal, where the last digit recurs with each division step and the division does not terminate with a zero remainder. This is indicated by three dots at the end.
For example, 1/6 = 0.1666... ; 1/3 = 0.333... ; 2/3 = 0.666... ; 5/6 = 0.8333...

MUST-KNOW : When a decimal is divided by 10, 100, 1000, ..., the decimal point moves to the left by 1, 2, 3, ... places.

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.
For example to divide 54.1266 by 0.006, first multiply both numbers by 1000 and then perform the division as shown below.

Division may be always verified by multiplication, e.g., 9021.1 x 0.006 = 54.1266

Example
Michelle paid $3.12 to buy peaches costing $0.39 each. How many peaches did she buy?
Solution.
The answer is 8 peaches.

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?'