hasanloubani wrote:
how do you calculate decimals of high denominator value plz?
That's not something you need to do here - if you notice we're adding ten fractions roughly equal to 1/50, the sum will roughly be 10/50. Or you can notice we're adding ten things that are all less than or equal to 1/45, and also are adding ten things greater than or equal to 1/54. So
10/54 < S < 10/45
and 10/50 = 0.2 is the only value from among the answer choices that S can approximately equal.
If you did want to find the decimal equivalents of 10/45 and 10/54, in the first case, 10/45 = 2/9. You can find the decimal of 2/9 if you know the decimal of 1/3:
1/3 = 0.33333....
so dividing by 3 on both sides
1/9 = 0.1111....
and multiplying by 2 on both sides
2/9 = 0.2222....
We can do something similar for 10/54, though it's a bit trickier. Since 10/54 = 5/27, we can start from
1/9 = 0.111111....
and divide by 3 on both sides (using the fact that 111/3 = 37) to get
1/27 = 0.037037....
and then multiply by 5 to get
5/27 = 0.185185....
So for these specific fractions, you can find their decimal equivalent without using long division, because their denominators are somewhat convenient to work with. But in general, if you invent a fraction with a random denominator, most of the time you'd have no practical choice other than long division to find the decimal. So if you need the decimal equivalent of 3/29, say, you'd need to use long division (or a calculator) to find it. Fortunately you never need to do that on the GMAT -- all you might need to notice on the GMAT is that 3/29 is very slightly larger than 3/30, so is very slightly larger than 0.1.
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