![]() For example, how do you convert a decimal number like 0.1111… into an equivalent fraction? I’ll start by giving you the quick and dirty tip, and then we’ll talk about why it works. Okay, it’s now time to figure out how to do the same type of conversion with repeating decimals. How to Turn Repeating Decimals Into Fractions ![]() With this in mind, you can see that 0.5 just means 5/10 (which is equal to 1/2 after reducing it) and 0.3125 is equal to the fraction 3,125/10,000 (which can be reduced to 5/16). Namely, the first digit to the right of a decimal point is the number of tenths, the next digit to the right is the number of hundredths, the next is the number of thousandths, and so on. To opens in a new windowconvert a terminating decimal into a fraction, you just need to remember what decimal notation means. The first repeats after one digit, and the second requires six digits before it starts repeating. On the other hand, repeating decimals are numbers whose decimal representations don’t stop, but instead repeat some pattern forever. For example, the opens in a new windowfractions 1/2 and 5/16 have decimal representations of 0.5 and 0.3125-both of which stop after some number of digits. The quick and dirty summary is that terminating decimals are numbers that have opens in a new windowdecimal representations that eventually stop. Recap: How to Convert Terminating Decimals to Fractionsīefore we get too far into today’s topic, let’s take a minute to recap what we learned opens in a new windowlast time.
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