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Math Expert V
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If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Question Stats: 82% (01:00) correct 18% (01:08) wrong based on 1068 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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
(B) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153

Problem Solving
Question: 65
Category: Arithmetic Operations on rational numbers
Page: 70
Difficulty: 600

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Math Expert V
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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SOLUTION

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
(B) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153

2.0453 rounding the nearest hundredth is 2.05, thus d* - d = 2.05 - 2.0453 = 0.0047.

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.
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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d=2.0453 rounded to the nearest hundredth is 2.0450=d*. So d*-d=-0.0003. Answer B
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Bunuel 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
(B) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153

]

Sol: given d=2.0453 so when rounded to nearest hundredth will be 2.05 so
d* - d = 2.05. - 2.0453 = 0.0047

Ans D
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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1
+1 for D

2.0453 rounded to nearest hundredth is 2.05
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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1
d = 2.0453;
Here, the hundredth digit is 4 and thousandth's digit is 5; Therefore, rounding off to the hundredth digit to a higher number will give 2.05;
So, d* = 2.05;

d* - d = 2.05 - 2.0453 = 0.0047;

Ans is (D).
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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1
Rounded to nearest 100 d=2.0500
Hence d*-d=2.0500-2.0453=.0047
Ans D
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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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
(B) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153

d = 2.0453

Rounding d to the nearest hundredth, d* = 2.05

So, d* - d = 2.05 - 2.0453 = 0.0047

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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Hi Buenel

Quick one

You quoted : 5.3485 rounded to the nearest tenth is 5.3, since the dropped 4 is less than 5.

But shouldnt it be 5.4 , as 5.3485 rounded to nearest thousand = 5.349, rounded to nearest hundred = 5.35 and hence rounded to nearest ten = 5.4?
Math Expert V
Joined: 02 Sep 2009
Posts: 61524
Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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gaurav1418z wrote:
Hi Buenel

Quick one

You quoted : 5.3485 rounded to the nearest tenth is 5.3, since the dropped 4 is less than 5.

But shouldnt it be 5.4 , as 5.3485 rounded to nearest thousand = 5.349, rounded to nearest hundred = 5.35 and hence rounded to nearest ten = 5.4?

No, it should be as written.

When rounding to the nearest tenth the FIRST dropped digit is 4, less than 5, thus 5.3485 rounded to the nearest tenth = 5.3.
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Sorry a little confused Bunuel

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.

I get the logic of the second and the third statement. As per second statement , 5.3485 rounded to hundredth= 5.35, and hence if we go ahead and further round 5.35 to the nearest tenth , shouldnt we get 5.4

If it was 5.34, it should yield 5.3, but for 5.3x, where x= 5,6,7,8,9 , shouldnt it round off to 5.4?
Math Expert V
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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6
gaurav1418z wrote:
Sorry a little confused Bunuel

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.

I get the logic of the second and the third statement. As per second statement , 5.3485 rounded to hundredth= 5.35, and hence if we go ahead and further round 5.35 to the nearest tenth , shouldnt we get 5.4

If it was 5.34, it should yield 5.3, but for 5.3x, where x= 5,6,7,8,9 , shouldnt it round off to 5.4?

Rounding is not cumulative, that is we are NOT rounding first to the hundredth and only then to the tenth. We are rounding directly to the tenth digit based on the hundredth digit. Thus, the only thing we are interested in when rounding to the nearest tenth is the hundredth digit, the only thing we are interested when rounding to the nearest hundredth is the thousandth digit, and so on.
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Many Thanks Bunuel, i get it now.
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GRE 1: Q169 V154 Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Here D* = 2.05 as the next digit immediately after the hundredths is 5.

Hence D*-D=0.0047 => Smash that D
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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when 2.0453 rounded to nearest hundredth then it will become 2.05

Now 2.05-2.0453=0.0047
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Hi,

As the hundredth digit is an even number before 5, isn't 2.0453 should be 2.04?

Hence 2.04 - 2.0453 = -0.0053?

Please correct me if I am wrong.

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 61524
Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Codebug4it wrote:
Hi,

As the hundredth digit is an even number before 5, isn't 2.0453 should be 2.04?

Hence 2.04 - 2.0453 = -0.0053?

Please correct me if I am wrong.

Thanks

Rounding rules explained in detail in this post: https://gmatclub.com/forum/if-d-2-0453- ... l#p1323005
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d  [#permalink]

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Thank you Bunuel for the link. Re: If d = 2.0453 and d* is the decimal obtained by rounding d   [#permalink] 08 Jan 2020, 20:35
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