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If d = 2.0453 and d* is the decimal obtained by rounding d

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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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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.

Answer: D.

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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New post 28 Jan 2014, 03:36
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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New post 28 Jan 2014, 10:26
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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 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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New post 28 Jan 2014, 23:30
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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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New post 29 Jan 2014, 03:17
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Rounded to nearest 100 d=2.0500
Hence d*-d=2.0500-2.0453=.0047
Ans D

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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.

Answer: D.

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 02 Feb 2014, 07:45
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

Answer: (D)

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

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New post 11 May 2014, 15:21
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?

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

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New post 12 May 2014, 00:07
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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New post 12 May 2014, 02:49
Sorry a little confused Bunuel

You stated in your posts-

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?

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

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New post 12 May 2014, 02:56
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gaurav1418z wrote:
Sorry a little confused Bunuel

You stated in your posts-

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

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New post 28 Sep 2016, 02:57
sorry Bunuel, it is not completely clear to me.

I've a question: if n was 2.0450 how would you approximate it to the nearest hundredth?

2.05 and 2.04 have the same distance from n (0.005)
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Re: If d = 2.0453 and d* is the decimal obtained by rounding d [#permalink]

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Re: If d = 2.0453 and d* is the decimal obtained by rounding d   [#permalink] 18 Oct 2017, 02:05
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