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Converting Repeating Decimals to FractionsName: Date:Remember these skills?*To convert fractions to decimals, we divide the numerator by the denominator 25 =*There are two types of decimals, ___________________ and _____________________*To convert a terminating decimal into a fraction, find the place value of the last digit, and divide the decimal by that place value.0.7= 0.23= *To convert a repeating decimal into a fraction, we have to follow a few steps. Suppose you have a number like 0.5777777…This number is equal to some fraction; we’ll call this fraction “x” for now.x=0.5777777…There is one repeating digit in this decimal so multiply x by “1,” followed by one zero. In other words, multiply by 10.10x=5.777777…Now subtract x from 10x.10x=5.777777…- x=0.577777…____________________________ 9x=5.200000…So 9x=5.2. Using what we already know about terminating decimals, we know5.2= 5210 = 2659x= 265x= 265÷91= 265×19=2645If you type 26 ÷45 into your calculator, you’d see 0.5777777…*Say there had been two repeating digits (such as 0.181818…), then you would multiply x by “1” followed by two zeroes, or 100. Same idea with three repeating digits, four repeating digits, etc…Let’s try a few more examples together:0.70.160.670.43 ................
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