Question Video: Converting a Terminating Decimal to a Fraction Mathematics

Write −0.15 as a fraction in its simplest form.


Video Transcript

Write negative 0.15 as a fraction in its simplest form.

We want to convert the given decimal to a fraction. We should note that converting between decimals and fractions does not change the positive or negative value of the number. Since we are given a negative decimal, the equivalent fraction will also be negative. That means that we may reason through our answer without regard for the negative sign, as long as we remember to reinstate the negative sign in our final answer.

To begin, we must identify the place value where the decimal terminates. A decimal system place value table can be used to help determine this. We have one in the tenths place and a five in the hundredths place. Since the decimal terminates in the hundredths place, we will create a fraction with a denominator of 100. The numerator will be the numerical digits from the original decimal, 15. Putting that together gives us the fraction 15 over 100.

Finally, we must determine if the fraction can be simplified or written as a mixed number. Since 15 over 100 is less than one, it cannot be written as a mixed number. However, 15 and 100 have a highest common factor of five. So, we proceed to divide the numerator and denominator by five, as shown. Hence, the terminating decimal 0.15 can be written as three over 20. Thus, negative 0.15 can be written as negative three twentieths.

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