Question

How do you change \[ - 1.31\] into a fraction?

Answer 1

Hint: A decimal number is used to represent a non-whole number where a decimal point is used followed by digits that represent a value that is smaller than one. A fraction is a ratio between the numerator and the denominator. As here we have asked to change \[ - 1.31\] into a fraction, hence we need to divide the number by 1 and then multiply both the numerator and the denominator by \[{10^n}\] , then simplify the terms to obtain the fraction value.

Complete step by step solution:
Given,
 \[ - 1.31\] …………… 1
In which we need to change the given decimal number into fraction.
Hence, rewrite the decimal number over one in equation 1 (as a fraction where the decimal number is numerator and the denominator is one) i.e.,
 \[ = \dfrac{{ - 1.31}}{1}\] …………... 2
Multiply both the numerator and the denominator by \[{10^n}\] i.e., if there is one value after the decimal, multiply by 10, if there are two then multiply by 100, if there are three then multiply by 1,000, etc.
Hence, here to convert \[ - 1.31\] to a fraction, there are two digits after the decimal point. Since 10 to the 2nd power is 100 i.e., \[{10^n} = {10^2} \Rightarrow 100\] , Hence, we have to multiply both the numerator and denominator by 100 in equation 2 as:
 \[ = \dfrac{{ - 1.31 \times 100}}{{1 \times 100}}\]
Expressing the obtained value in simplest or reduced form we get the fraction value as:
 \[ \Rightarrow \dfrac{{ - 131}}{{100}}\]
or \[\dfrac{{ - 131}}{{100}}\] also be written in mixed fraction; as we have the whole number as 1 we get:
 \[ \Rightarrow - 1\dfrac{{31}}{{100}}\]
So, the correct answer is “ \[ - 1\dfrac{{31}}{{100}}\] ”.

Note: The key point to change the given decimal number to fraction is that we need to find \[{10^n}\] properly such that the n value mainly depends on the number of values after decimal. We must note that the answer to this example is a mixed number i.e., a whole number and a fraction combined as a fraction represents a part of a whole number.