Question

How do you convert \[0.23\] 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 take the denominator equal to \[1\] followed by \[c\] zeroes, or \[{10^c}\]. Then, we convert the decimal to 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 solution:
The given number is \[0.23\].
First, we convert it to a fraction.
Number of digits after the decimal point, \[c = 2\].
Now, our denominator is, \[d = {10^c} = {10^2} = 100\].
Numerator is the complete number without the decimal point, \[n = 23\].
So, the required fraction is \[f = \dfrac{n}{d} = \dfrac{{23}}{{100}}\]
Hence \[0.23 = \dfrac{{23}}{{100}}\]
Now, to convert to percent, we just multiply by \[100\], and we get,
\[0.23 = \left( {0.23 \times 100} \right)\% \]
Hence, \[0.23 = 23\% \]

Note: In the given question, we were given a decimal number. We had to convert the decimal number to fraction and percent. 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 the decimal number to percent, we just multiply the decimal by 100.