Question

How do you convert \[2.5\] (5 being repeated) to a fraction?

Answer 1

Hint: To convert a decimal to fraction, first divide decimal by 1 to make given decimal to fraction, then multiply both numerator and denominator by 10 to make a decimal to whole number in number and further simplify by using highest common factor of both numerator and denominator.

Complete step by step solution:
To find the equivalent fraction for decimal point number 2.5 manually,
Consider the given decimal value
 \[ \Rightarrow x = 2.5\]
To write it as a fraction by divide 1
 \[ \Rightarrow \dfrac{{2.5}}{1}\]
To make decimal to whole number in numerator
Multiply both numerator and denominator by 10 for every number after the decimal point:
As we have one number after the decimal point, hence we multiply both numerator and denominator by 10. then,
 \[ \Rightarrow \dfrac{{2.5}}{1} \times \dfrac{{10}}{{10}}\]
 \[ \Rightarrow \dfrac{{25.5555..}}{{10}}\]
since 5 being repeated so number is written as above
 \[ \Rightarrow x = \dfrac{{25.5}}{{10}}\]
Take 10 to LHS
 \[ \Rightarrow 10x = 25.5555..\]
Add -x on both sides we have
 \[ \Rightarrow 10x - x = 25.5555.. - x\]
As we know that the value of x is 2.5, by substituting we have
 \[ \Rightarrow 9x = 25.5555.. - 2.5555...\]
 \[ \Rightarrow 9x = 23\]
Divide the above equation by 9 we get
 \[ \Rightarrow x = \dfrac{{23}}{9}\]
Hence, we have converted the decimal into a fraction. The obtained fraction is an improper fraction.
Hence, the equivalent fraction of the given decimal point number \[2.5\] (5 being repeated) is \[\dfrac{{23}}{9}\] .
So, the correct answer is “ \[\dfrac{{23}}{9}\] ”.

Note: The number can be converted from one form to the other form. For the conversion of numbers, we have some rule or method. By using the specific methods and rules we can convert the number. So to convert the decimal number we have to multiply and divide the number by multiples of 10. The multiple of 10 depends on the number present after the decimal point.