Question

What is the fraction of the repeating decimal?

Answer 1

Answer: C) 46/99

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Step-by-step explanation:

Let x = 0.464646...

Multiplying both sides by 100 gets to 100x = 46.464646... which moves the decimal point over two spots to the right.

Then subtract the two equations

100x - x = 46.464646... - 0.464646...

99x = 46

x = 46/99

Notice how the decimal portions cancel out when we subtract. This is because they line up perfectly.

To confirm the answer, your calculator should show that

46/99 = 0.46464646

The "46"s going on forever.

At some point, your calculator may round the last '4' to a 5 to have it read something like 0.464646465 but this is of course rounding error.

On some calculators I tried, I noticed it displayed 0.46464646464647 which is even more strange considering the next digit (4) isn't five or larger. So that 6 shouldn't have bumped up to the 7.

Answer 2

it's 46/99

whenever you get a question like this, you need to think: what would those fractions even be?

well it sure is not a bc 3/6 is already 0.5 and you need a lower number

it's not b either bc 4/16= 1/4 and that is 0.25

and well it can't be d either bc 13/16 is that not far away from 1