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28 Jan 2014, 02:06
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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
(A) -0.0053
(B) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153
28 Jan 2014, 02:06
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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.
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.
12 May 2014, 02:56
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gaurav1418z
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?
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.
