Question

How do you convert fractions into decimal notation?

Answer 1

Hint: We define fractions and decimal numbers first. Then use the concept that the fractions on solving i.e. on division of numerator by denominator we either get an integer or a decimal number.

Complete step by step answer:
We define fractions and decimal numbers firstly.
Fractions: fraction represents a part of a whole i.e. when a whole is divided into equal parts, we can write fraction of any amount of equal parts. Fraction is written as \[\dfrac{p}{q}\], where ‘p’ is the numerator and ‘q’ is the denominator.
Decimal number: A number that has decimal value along with its integer value i.e. of the type ‘a.b’ where ‘a’ is integer and ‘b’ is a decimal part of the number.
We know that fraction is written as \[\dfrac{p}{q}\], where ‘p’ is the numerator and ‘q’ is the denominator. To solve a fraction we have to divide ‘p’ by ‘q’.
This has two parts:
(i)
If the denominator is some power of 10 i.e. of the type \[{10^n}\]; then we convert the fraction into decimal numbers just by placing ‘n’ digits of the numerator to the right of the decimal.
Example: We have to convert \[\dfrac{{3198}}{{{{10}^2}}}\] into a decimal number. We see 10 has power 2. So we write 2 digits of the numerator at right hand side of the decimal
So, decimal form of fraction \[\dfrac{{3198}}{{{{10}^2}}}\] is 31.98
(ii)
The denominator is any other number other than 10 or power of 10.
We know that fraction is written as \[\dfrac{p}{q}\], where ‘p’ is the numerator and ‘q’ is the denominator. To solve a fraction we have to divide ‘p’ by ‘q’.
So, in these types of fractions we simply divide the numerator by denominator and write the answer as decimal value.
Example: We have to convert \[\dfrac{{13}}{4}\] into decimal numbers. We divide 13 by 4.
\[\therefore \] Decimal form of fraction \[\dfrac{{13}}{4}\] is 3.25

Note: Many students just consider one type of solution here i.e. they write we simply divide numerator by denominator. Keep in mind when we are given denominator as powers of 10, we need not divide numerator by denominator, we can simply write the answer.