![]() So the decimal number 0.875 is equal toīut instead of worrying about how to actually add up all of these fractions (which is another topic that we’ll talk about in a future article), we can simplify things by first writing 0.875 as As we talked about in the earlier article on opens in a new windowdecimals, the 8 in 0.875 represents 8/10, the 7 represents 7/100, and the 5 represents 5/1000. Let’s convert a terminating decimal like 0.875 into a fraction. Okay, we’re now ready to move on to a more complex problem. How to convert terminating decimals to fractions But don’t worry if that all sounds like a bunch of crazy talk right now-we’ll look at it in more detail soon enough. We’ll talk about this in a future article, but this fraction can be rewritten so that it’s what’s called “reduced to lowest terms.” Without going into too much detail, the basic idea is that we can divide both the opens in a new windownumerator and denominator of the fraction 5/10 by 5 to find that it has an equivalent and simpler representation of 1/2. ![]() Well, it turns out that we can actually do a bit more with this fraction. And believe it or not, that’s the answer to the problem! So, the decimal 0.5 is equivalent to the fraction 5/10. As we learned back in the article called “ opens in a new windowWhat are Decimals?”, a decimal number like 0.5 means “five of the fraction one-tenth.” Which, of course, is just equal to the fraction 5/10. Let’s start by converting a simple terminating decimal number like 0.5 into a fraction. How to convert single Digit Decimals to Fractions But now let’s figure out how to do this problem backward so that we can take a decimal number, like 0.818181…, and convert it into a fraction with an equivalent value. In other words, in the examples we gave earlier, we said things like “the fraction 1/4 is equal to the terminating decimal 0.25” and “the fraction 7/9 is equal to the repeating decimal 0.7777…,” and so on. Now that we know the lingo and can tell the difference between a terminating and repeating opens in a new windowdecimal, let’s figure out how to convert them into opens in a new windowfractions. And that’s why usually when we say “repeating decimal,” we mean a decimal number where something other than only zeros are doing the repeating! How to Convert Decimals to Fractions But in this case, none of this really matters since the value of the number is exactly the same no matter how it’s written. How? Well, since you can always attach an infinite number of zeros to the very end of a number without changing its value, you can put an infinitely long string of zeros on the end of an otherwise terminating decimal…and you’ll have turned it into a repeating decimal!įor example, you can think of the terminating decimal 0.25 as 0.25000… instead. If you think about it though, you’ll see that any terminating decimal number can actually be written as a repeating decimal too. (Remember, a decimal that just goes on and on with no repeating pattern is irrational.) Can a Terminating Decimal Be Written as a Repeating Decimal? So a repeating decimal is a rational number whose decimal representation has some repeating pattern, and a terminating decimal is a rational number whose decimal representation eventually stops. 9/11 = 0.818181… is another repeating decimal since the pattern of digits “81” repeat forever.7/9 = 0.7777… is a repeating decimal since 7 goes on forever.3/5 = 0.6 is another terminating decimal number.1/3 = 0.3333… is a repeating decimal since the number 3 goes on forever.1/4 = 0.25 is a terminating decimal since it has a finite number of decimal digits. ![]() To see what the difference is, let’s take a look at a few examples of decimal representations of rational numbers: What are Terminating and Repeating Decimals?īefore we get into the details of how to actually convert terminating and repeating decimals into opens in a new windowfractions, we’d better make sure we understand what it means for a rational number to be a “terminating” or “repeating” decimal in the first place.
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