Arithmetic : Decimals

Equivalent Decimals

A fraction with a denominator that is a multiple of 10 is equivalent to a decimal.
To convert such a fraction to a decimal, a decimal point is inserted in the numerator such that the number of decimal places equals the number of zeros in the denominator.
For example, the fraction 164327/10000 is equivalent to the decimal 16.4327 (which has 4 places to the right of the decimal point corresponding to the 4 zeros in 10000).

While converting a fraction to a decimal, zeros need to be inserted before the numerator in case the numerator does not have enough digits.

For example to convert the fraction 27/10000 to a decimal equivalent, 4 decimal places are required because the denominator is 10000. But 27 has just 2 places, so 2 zeros are inserted to the left of 27. Therefore, 27/10000 = 0.0027
It is very important to note where the zeros are inserted (i.e., to the left or the right).
For example, 2700/10000 = 27/100 = 0.27

MUST-KNOW : A decimal fraction does not change in value when zeros are inserted to its right.

For example, 7/10 = 70/100 = 700/1000 = 7000/10000 = ..., and therefore 0.7 = 0.70 = 0.700 = 0.7000 = ...
As another example, a whole number can be expressed as 7 = 7.0 = 7.00 = 7.000 = ...