Question

How do you convert \[0.065\] (65 repeating) 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 1000 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 answer:
To find the equivalent fraction for decimal point number 0.065 manually,
Consider the given decimal value
 \[ \Rightarrow \,\,\,\,0.065\]
To write it as a fraction by divide 1
 \[ \Rightarrow \,\,\,\,\dfrac{{0.065}}{1}\]
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 3 numbers after the decimal point, hence we multiply both numerator and denominator by 1000. then,
 \[ \Rightarrow \,\,\,\,\dfrac{{0.065}}{1} \times \dfrac{{1000}}{{1000}}\]
 \[ \Rightarrow \,\,\,\,\dfrac{{65}}{{1000}}\]
To simplify or reduce the fraction to simplest form.
The factors of 65 are 1, 5, 13, and 65
The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 and 1000
The highest common factor of 65 and 1000 is 5
Divide the fraction both numerator and denominator by 5, then
 \[ \Rightarrow \,\,\,\,\dfrac{{13}}{{200}}\]
Hence, the equivalent fraction of the given decimal point number \[0.065\] is \[\dfrac{{13}}{{200}}\].
So, the correct answer is “ \[\dfrac{{13}}{{200}}\]”.

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.