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a is the hundredths digit of b, which
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19 Dec 2022, 04:40
19 Dec 2022, 04:40
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Question Stats:
61% (00:57) correct
38% (00:53) wrong based on 21 sessions
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\( a\) is the hundredth digit of b, which is equal to \(1.5a4\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
b rounded to the nearest hundredth |
b rounded to the nearest tenth |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: a is the hundredths digit of b, which
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22 Jan 2023, 01:33
22 Jan 2023, 01:33
Expert Reply
OE
To approximate a decimal to the nearest hundredth, you must keep the first two digits after the decimal point, rounding up if the following digit is 5 or greater. In this case, the thousandths digit is 4, so no rounding up is performed and, therefore, Quantity A is 1.5a
Likewise, to approximate a decimal to the nearest tenth, you must keep the first digit after the decimal point, rounding up if the following digit is 5 or greater. In this case, the hundredth digit is equal to 0, which may or may not be 5 or greater. Thus, you do not know whether Quantity B should be 1.5 or 1.6. Accordingly, you cannot tell whether Quantity B would be less than, equal to, or greater than 1.50. You do not have enough information to answer the question.
To approximate a decimal to the nearest hundredth, you must keep the first two digits after the decimal point, rounding up if the following digit is 5 or greater. In this case, the thousandths digit is 4, so no rounding up is performed and, therefore, Quantity A is 1.5a
Likewise, to approximate a decimal to the nearest tenth, you must keep the first digit after the decimal point, rounding up if the following digit is 5 or greater. In this case, the hundredth digit is equal to 0, which may or may not be 5 or greater. Thus, you do not know whether Quantity B should be 1.5 or 1.6. Accordingly, you cannot tell whether Quantity B would be less than, equal to, or greater than 1.50. You do not have enough information to answer the question.
Re: a is the hundredths digit of b, which
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09 Jan 2024, 21:46
09 Jan 2024, 21:46
1
Quantity A = b rounded to the nearest hundredth.
Since QA = 1.5a4, and 4 is less than 5, the value of QA = 1.5a
Quantity A = b rounded to the nearest tenth
Since QB = 1.5a4, and we do not know the value of a, we have two possibilities. Either a is between 0 and 4, in which case the value of QB = 1.5 which is less than QA if a is non-zero and equal to QA if a = zero, OR if a is between 5 and 9, then QB = 1.6 which is greater than QA.
Thus we do not have sufficient information to answer this question.
The answer is Choice D.
Since QA = 1.5a4, and 4 is less than 5, the value of QA = 1.5a
Quantity A = b rounded to the nearest tenth
Since QB = 1.5a4, and we do not know the value of a, we have two possibilities. Either a is between 0 and 4, in which case the value of QB = 1.5 which is less than QA if a is non-zero and equal to QA if a = zero, OR if a is between 5 and 9, then QB = 1.6 which is greater than QA.
Thus we do not have sufficient information to answer this question.
The answer is Choice D.
