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Rounding Numbers Confusion..

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by ProGMAT » Fri Aug 16, 2013 12:47 am
If d = 2.0453 and d* is the decimal obtained by rounding d to the nearest hundredth, what is the value of d* - d ?
(A) -0.0053
(8) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153
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by GMATGuruNY » Fri Aug 16, 2013 3:00 am
ProGMAT wrote:If d = 2.0453 and d* is the decimal obtained by rounding d to the nearest hundredth, what is the value of d* - d ?
(A) -0.0053
(8) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153
d = 2.0453.
Since the digit to the right of the hundredth digit is 5 or greater, we round UP to the nearest hundredth:
2.0453 --> 2.05.

Thus:
*d - d = 2.0500 - 2.0453= 0.0047.

The correct answer is D.
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by ProGMAT » Fri Aug 16, 2013 3:25 am
GMATGuruNY wrote:
ProGMAT wrote:If d = 2.0453 and d* is the decimal obtained by rounding d to the nearest hundredth, what is the value of d* - d ?
(A) -0.0053
(8) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153
d = 2.0453.
Since the digit to the right of the hundredth digit is 5 or greater, we round UP to the nearest hundredth:
2.0453 --> 2.05.

Thus:
*d - d = 2.0500 - 2.0453= 0.0047.

The correct answer is D.
Thanks for the solution GMATGuruNY.
But i am confused as in some solutions in OG, the round off rang of a number is till next 5 pointer. Example: range of 4 is from 3.5 to 4.5. Why is that so?
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by GMATGuruNY » Fri Aug 16, 2013 3:38 am
ProGMAT wrote: Example: range of 4 is from 3.5 to 4.5. Why is that so?
The given range is not quite correct.
If x is rounded to the nearest integer, the following range is rounded to 4:
3.5 ≤ x < 4.5.
Any value LESS than 4.5 is rounded DOWN to 4.
But once we reach HALFWAY between 4 and 5 -- once we reach 4.5 -- we round UP to 5.
Thus:
Any value of x such that 4.5≤x<5 is rounded UP to 5.

For more on rounding, check my posts here:
https://www.beatthegmat.com/decimals-t267013.html
https://www.beatthegmat.com/all-my-probl ... 81383.html
https://www.beatthegmat.com/rounding-nee ... 57876.html
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Re: Rounding Numbers Confusion..

by Scott@TargetTestPrep » Fri Feb 05, 2021 2:37 pm
ProGMAT wrote: ↑
Fri Aug 16, 2013 12:47 am
 If d = 2.0453 and d* is the decimal obtained by rounding d to the nearest hundredth, what is the value of d* - d ?
(A) -0.0053
(8) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153
Solution:

We see that d* = 2.05, which is the value of d when rounded to the nearest hundredth. Therefore, d* - d = 2.05 - 2.0453 = 0.0047.

Answer: D

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