Rewriting decimals as fractions: 0.15 (video) | Khan Academy (2024)
Video transcript
Let's see if we canwrite 0.15 as a fraction. So the importantthing here is to look at what place thesedigits are in. So this 1 right over here,this is in the tenths place, so you could viewthat as 1 times 1/10. This 5 right over here isin the hundredths place, so you could viewthat as 5 times 1/100. So if I were to rewritethis, I can rewrite this as the sum of-- this 1represents 1 times 1/10, so that would literallybe 1/10 plus-- and this 5 represents5 times 1/100, so it would be plus 5/100. And if we want toadd them up, we want to find acommon denominator. The common denominator is 100. Both 10 and-- theleast common multiple. 100 is a multipleof both 10 and 100. So we can rewrite thisas something over 100 plus something over 100. This isn't going to change. This was already 5/100. If we multiply thedenominator here by 10-- that's what we did;we multiplied it by 10-- then we're going to have tomultiply this numerator by 10. And so this is thesame thing as 10/100. And now we're ready to add. This is the same thingas-- 10 plus 5 is 15/100. And you could have done thata little bit quicker just by inspecting this. You would say, look, mysmallest place right over here is in the hundredths place. Instead of calling this1/10, I could call this literally 10/100. Or I could say thiswhole thing is 15/100. And now if I want to reducethis to lowest terms, we can-- let's see, both thenumerator and the denominator are divisible by 5. So let's divide them both by 5. And so the numerator,15 divided by 5, is 3. The denominator, 100divided by 5, is 20. And that's about assimplified as we can get.
Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.
Multiply the decimal by 10 and subtract the original decimal from it.Finally, divide both sides by 9 to obtain the fractional form of the decimal. For example, 0.7 repeating would be 7/9, and 1.2 repeating would be 11/9.
Introduction: My name is Terrell Hackett, I am a gleaming, brainy, courageous, helpful, healthy, cooperative, graceful person who loves writing and wants to share my knowledge and understanding with you.
We notice you're using an ad blocker
Without advertising income, we can't keep making this site awesome for you.
