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Re: If x is the decimal 8.1d5, with d as an unknown digit, and x [#permalink]

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20 Apr 2013, 23:14

iikarthik wrote:

Hi,

This is a question from MGMAT Study Guides.

If x is the decimal 8.1d5, with d as an unknown digit, and x rounded to the nearest tenth is equal to 8.1, which digits could not be the value of d?

Solution: In order for x to be 8.1 when rounded to the nearest tenth, the right-digit-neighbor, d, must be less than 5. Therefore, d cannot be 5, 6, 7, 8 or 9.

But i feel that d Cannot be 4 as well,bcos 8.145,when rounded off will become 8.15 and then 8.2

Pls correct if my understanding is incorrect

When rounding, you only look at the closest digit to the cutoff point, not any of the ones past it.

Rounding .145 to .2 because you first round the 4 to a 5 would be the same as rounding the number 145 up to 200. 145 is closer to 100 than to 200.. For another example, if we had .4999999 we would never round that number up to 1, because it's closer to 0 than to 1... and that is why we only look at the closest digit.

Re: If x is the decimal 8.1d5, with d as an unknown digit, and x [#permalink]

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21 Apr 2013, 04:14

Expert's post

iikarthik wrote:

Hi,

This is a question from MGMAT Study Guides.

If x is the decimal 8.1d5, with d as an unknown digit, and x rounded to the nearest tenth is equal to 8.1, which digits could not be the value of d?

Solution: In order for x to be 8.1 when rounded to the nearest tenth, the right-digit-neighbor, d, must be less than 5. Therefore, d cannot be 5, 6, 7, 8 or 9.

But i feel that d Cannot be 4 as well,bcos 8.145,when rounded off will become 8.15 and then 8.2

Pls correct if my understanding is incorrect

Rounding rules

Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, ROUND UP the last digit that you keep. If the first dropped digit is 4 or smaller, ROUND DOWN (keep the same) the last digit that you keep.

Example: 5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5. 5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5. 5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

BACK TO THE ORIGINAL QUESTION: 8.1d5 rounded to the nearest tenth is equal to 8.1 --> the dropped digit is d, thus we are only concerned with it: d cannot be 5, 6, 7, 8, or 9.

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