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2 years ago

What is the equivalent decimal to this fraction? 10/45 0.2 0.222222222... 0.232323232323... 0.181818181818...

Mathematics

1 answer:

Ivan2 years ago

5 0

Factorize the numerator and denominator, then simplify:

10/45 = (2×5)/(9×5) = 2/9

Now,

1/9 = 1/10 + 1/90

1/90 = 1/10 × 1/9 = 1/10 × (1/10 + 1/90) = 1/100 + 1/900

1/900 = 1/100 × 1/9 = 1/100 × (1/10 + 1/90) = 1/1000 + 1/9000

and so on, which is to say

1/9 = 1/10 + 1/100 + 1/1000 + …

1/9 = 0.111…

so that multiplying both sides by 2 gives

2/9 = 0.222…

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What is the equivalent decimal to this fraction? 10/45 0.2 0.222222222... 0.232323232323... 0.181818181818...​

What is the equivalent decimal to this fraction? 10/45 0.2 0.222222222... 0.232323232323... 0.181818181818...