Question

How do you convert \[0.1875\] into a fraction and percent?

Answer 1

Hint: In the given question, we have been asked to convert a decimal number to a fraction as well as a percent. First, we are going to convert the given decimal to a fraction by counting the number of digits after the decimal point; let it be ‘c’. Then we take the complete number without the decimal point as the numerator and make the denominator equal to \[1\] followed by \[c\] zeroes, or \[{10^c}\]. Then, we convert the decimal to a percent. To do that, we simply multiply the whole number by \[100\] and attach a percent sign at the end of the obtained number.

Complete step by step answer:
The given number is \[0.1875\].
First, we convert it into a fraction.
Number of digits after the decimal point, \[c = 4\].
Now, our denominator is, \[d = {10^c} = {10^4} = 10000\].
Numerator is the complete number without the decimal point, \[n = 1875\].
So, the required fraction is \[f = \dfrac{n}{d} = \dfrac{{1875}}{{10000}}\]
Now, we convert it to the lowest term by dividing by their HCF, which is \[625\], and we get,
\[f = \dfrac{3}{{16}}\]
Hence \[0.1875 = \dfrac{3}{{16}}\]
Now, to convert to percent, we just multiply by \[100\], and we get,
\[0.1875 = \left( {0.1875 \times 100} \right)\% \]

Hence, \[0.1875 = 18.75\% \].

Note: To convert any decimal to fraction, we take the complete number without the decimal point as the numerator, and the denominator as the power of ten, depending on the number of digits after the decimal point, and then just divide and find their lowest term. To convert to percent, just multiply the decimal by 100.