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Find the value sum of

Your answer must be in the form
of a mixed number in the simplest
form and cannot use decimal
notation.
_ _ _ _ _
0.1+0.3+0.5+0.7+0.9.

Find the value sum of Your answer must be in the form of a mixed number in the simplest-example-1

1 Answer

5 votes

The answer is 2 and 7/9

The way to convert a repeating decimal into a fraction is by taking in the repeating decimals (let's say 0.3) and putting it over 9 (3/9). If you have 2-digit repeating decimals (let's say 0.83), then you put it over 99 (83/99), and so on. So you convert all decimals into fractions (1/9, 3/9, 5/9, 7/9, 9/9). Now the confusing part is the repeating decimal 0.9 since if we follow the steps we get 9/9, which equals 1. It might be confusing to accept this at the start, but we can think of it this way. We could separate 0.9 into 0.3, 0.3, and 0.3. One 0.3 equals 3/9, and if we have 3 of those, we add 3/9 + 3/9 + 3/9 = 9/9. So 0.9 = 9/9. Now we add 1/9 + 3/9 + 5/9 + 7/9 + 9/9 adding the numerators (the top number, in the case of 3/9 we would add the 3 to the rest of the numerators), which gives us 25/9. Then we turn it into a mixed fraction. 9 fits into 27 two times. Then we subtract 27 - 18 = 7, which will be our numerator, and our denominator will stay as 9. So in the end, we have 2 and 7/9.

User Taylor Austin
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