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manhattan decimal - round off example

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manhattan decimal - round off example

by tanmay9 » Thu Oct 10, 2013 11:36 am
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?

according to me 4 should also be one of the digit values that cant be "d" but somehow manhattan says its till 5.

Pl help me understand.
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by Brent@GMATPrepNow » Thu Oct 10, 2013 11:52 am
tanmay9 wrote: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?

according to me 4 should also be one of the digit values that cant be "d" but somehow manhattan says its till 5.

Pl help me understand.
8.105 rounded to the nearest tenth is 8.1
8.115 rounded to the nearest tenth is 8.1
8.125 rounded to the nearest tenth is 8.1
8.135 rounded to the nearest tenth is 8.1
8.145 rounded to the nearest tenth is 8.1

8.155 rounded to the nearest tenth is 8.2
8.165 rounded to the nearest tenth is 8.2
8.175 rounded to the nearest tenth is 8.2
etc

Are you sure that the MGMAT book says that 8.155 rounded to the nearest tenth is 8.1??


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by [email protected] » Thu Oct 10, 2013 11:53 am
Hi tanmay9,

If we're rounding the number 8.1d5 to the nearest tenth and ending up with 8.1, then here's what we know about the digit d:

It COULD be 0, 1, 2, 3, or 4 because these numbers would round DOWN to the nearest tenth, giving us 8.1

It CANNOT be 5, 6, 7, 8, 9 because these numbers would round UP to the nearest tenth, giving us 8.2, which is NOT a match for what we're told.

In this question, it's worth noting that since we're rounding to the nearest tenth, the "5" in the thousanths place has NO EFFECT on the rounding.

The question asks for which digits COULD NOT be the value of d, so the answer is 5, 6, 7, 8, 9

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by tanmay9 » Thu Oct 10, 2013 12:37 pm
Hi Rich.c / Brent,
So 5 has no role.

I was rounding off the value 5 also.

So if the question was rounding off to nearest tenth for this particular number - 4.24459 the answer would have been 4.24 and not rounding off first value 9 then value 5 to 6 then next 4 to 5 and so on.

Brent MGMAT has not said that. It says that 5 changes it to 8.2
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by Brent@GMATPrepNow » Thu Oct 10, 2013 12:45 pm
If you're rounding a number to the nearest tenth, then look at ONLY the hundredths digit. If it's 5 or greater, round up. If it's 4 or less, round down.

If you're rounding a number to the nearest hundredth, then look at ONLY the thousandths digit. If it's 5 or greater, round up. If it's 4 or less, round down.

If you're rounding a number to the nearest thousandth, then look at ONLY the ten-thousandths digit. If it's 5 or greater, round up. If it's 4 or less, round down.

etc

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by iamsaipavan » Sat Oct 12, 2013 9:22 am
What significance does 5 carry in 8.1d5. We cant just remove the 5 there and start substituting numbers to d and check. Like say I am substituting d=4. The number becomes 8.145. And I cant round it directly to the tenth saying its only 8.1.

The number 8.145 will become 8.15 after the initial rounding and now rounding to tenth it will become 8.2
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by theCodeToGMAT » Sat Oct 12, 2013 11:32 am
iamsaipavan wrote:What significance does 5 carry in 8.1d5. We cant just remove the 5 there and start substituting numbers to d and check. Like say I am substituting d=4. The number becomes 8.145. And I cant round it directly to the tenth saying its only 8.1.

The number 8.145 will become 8.15 after the initial rounding and now rounding to tenth it will become 8.2
The question asks to round to TENTH digit.. So, you need to consider Thousandth Digit as well.


ALso, 8.145 doesn't mean 8.2 .. it's infact 8.14 --> 8.1

Rules for Rounding
In the Decimal sequence if the following digit is between 1 to 5,inclusive, don't change the digit
For Example
123.45 --> 123.4
123.41 --> 123.4


In the Decimal sequence if the following digit is between 6 to 9,inclusive, increment the digit by 1
123.46 --> 123.5
123.49 --> 123.5
R A H U L
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