Question

Convert \[3.125\] into a fraction and a percent.

Answer 1

Hint: To convert a number to a percentage we express it as a fraction of 100, and a fraction represents a part of a whole.

Complete step by step solution:
The given number \[3.125\] is expressed in the decimal form.
First, convert the number to a fraction. A fraction is the expression of a part of a whole thing. The following fraction \[\dfrac{a}{b}\] represents that \[a\] is a part of the whole system \[b\].
 So the given number:
 \[3.125\] \[ = \] \[\dfrac{{3125}}{{1000}}\] [as there are three digits after the decimal point hence the decimal point can \[\] be removed by dividing the number with \[1000\]].
Reduce the fraction to the simplest form by removing the common factors:
\[3.125\] \[ = \] \[\dfrac{{3125}}{{1000}}\] \[ = \] \[\dfrac{{125 \times 25}}{{125 \times 8}}\]
Cancel out the common factor of \[125\]:
\[ \Rightarrow \] \[3.125\] \[ = \] \[\dfrac{{25}}{8}\]
\[\dfrac{{25}}{8}\] is an improper fraction, it can also be expressed as a mixed fraction:
\[ \Rightarrow \] \[3.125\] \[ = \] \[\dfrac{{25}}{8}\] \[ = \] \[3\dfrac{1}{8}\].
To convert the number to a percentage it needs to be expressed as a fraction of 100. That is the denominator of the fraction should be 100, as percentage means out of 100. So if we can express any number in the fraction form as \[\dfrac{x}{{100}}\] then it is equal to \[x\% \].
\[\therefore \] \[3.125\] \[ = \] \[\dfrac{{3125}}{{1000}}\]
\[ \Rightarrow \] \[3.125\] \[ = \] \[\dfrac{{312.5}}{{100}}\]
\[ \Rightarrow \] \[3.125\] \[ = \] \[312.5\% \]

Hence, \[3.125\] can be expressed as a fraction as \[\dfrac{{25}}{8}\] and as a percentage as \[312.5\% \].

Additional information:
To convert a given decimal to a fraction, the number(without the decimal point) needs to be divided by a number whose first digit is \[1\] followed by the number of zeroes equal to the number of digits after the decimal point in the original number. For example to convert \[2.4567\] to a fraction we need to divide the number \[24567\] by \[10000\] (it has \[4\] zeroes after the 1 as there were four digits after the decimal point in the original number).

Note: Any fraction has two parts: a numerator and a denominator. That is for any fraction \[\dfrac{a}{b}\] the numerator is \[a\] and the denominator is \[b\]. For example for the fraction \[\dfrac{5}{9}\], the numerator is \[5\] and the denominator is \[9\].