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14 Nov 2025, 00:15
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Difficulty:
25%
(medium)
Question Stats:
81% (01:34) correct
19%
(01:36)
wrong
based on 58
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Which of the following fractions expressed in the form P/Q is most nearly approximated by the decimal 0.PQ, where P is the tenths' digit and Q is the hundredths' digit?
(A) 1/8
(B) 2/9
(C) 3/4
(D) 4/5
(E) 8/9
(A) 1/8
(B) 2/9
(C) 3/4
(D) 4/5
(E) 8/9
14 Nov 2025, 01:00
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This is a fun little "test the options" problem. The question asks us to compare two different values for each answer choice:
The fraction itself: P/Q
The new decimal: 0.PQ (which is P in the tenths spot and Q in the hundredths spot)
We need to find the option where these two values are closest to each other. The easiest way to compare them is to convert everything to decimals and find the difference. We want the smallest difference.
Let's go through each option:
(A) 1/8
Here, P=1 and Q=8.
Fraction (P/Q): 1/8 = 0.125
Decimal (0.PQ): 0.18
Difference: |0.18 - 0.125| = 0.055
(B) 2/9
Here, P=2 and Q=9.
Fraction (P/Q): 2/9 = 0.222... (repeating)
Decimal (0.PQ): 0.29
Difference: |0.29 - 0.222...| = 0.067...
(C) 3/4
Here, P=3 and Q=4.
Fraction (P/Q): 3/4 = 0.75
Decimal (0.PQ): 0.34
Difference: |0.75 - 0.34| = 0.41 (This is a huge difference, so it's definitely not this one.)
(D) 4/5
Here, P=4 and Q=5.
Fraction (P/Q): 4/5 = 0.80
Decimal (0.PQ): 0.45
Difference: |0.80 - 0.45| = 0.35 (Also a very large difference.)
(E) 8/9
Here, P=8 and Q=9.
Fraction (P/Q): 8/9 = 0.888... (repeating)
Decimal (0.PQ): 0.89
Difference: |0.89 - 0.888...| = 0.001... (This is a tiny difference!)
🏁 Conclusion
Let's compare the differences we found:
(A) 0.055
(B) 0.067...
(C) 0.41
(D) 0.35
(E) 0.001...
The smallest difference by far is 0.001... from option (E). The fraction 8/9 (0.888...) is extremely close to the decimal 0.89.
Therefore, the correct answer is (E) 8/9.
The fraction itself: P/Q
The new decimal: 0.PQ (which is P in the tenths spot and Q in the hundredths spot)
We need to find the option where these two values are closest to each other. The easiest way to compare them is to convert everything to decimals and find the difference. We want the smallest difference.
Let's go through each option:
(A) 1/8
Here, P=1 and Q=8.
Fraction (P/Q): 1/8 = 0.125
Decimal (0.PQ): 0.18
Difference: |0.18 - 0.125| = 0.055
(B) 2/9
Here, P=2 and Q=9.
Fraction (P/Q): 2/9 = 0.222... (repeating)
Decimal (0.PQ): 0.29
Difference: |0.29 - 0.222...| = 0.067...
(C) 3/4
Here, P=3 and Q=4.
Fraction (P/Q): 3/4 = 0.75
Decimal (0.PQ): 0.34
Difference: |0.75 - 0.34| = 0.41 (This is a huge difference, so it's definitely not this one.)
(D) 4/5
Here, P=4 and Q=5.
Fraction (P/Q): 4/5 = 0.80
Decimal (0.PQ): 0.45
Difference: |0.80 - 0.45| = 0.35 (Also a very large difference.)
(E) 8/9
Here, P=8 and Q=9.
Fraction (P/Q): 8/9 = 0.888... (repeating)
Decimal (0.PQ): 0.89
Difference: |0.89 - 0.888...| = 0.001... (This is a tiny difference!)
🏁 Conclusion
Let's compare the differences we found:
(A) 0.055
(B) 0.067...
(C) 0.41
(D) 0.35
(E) 0.001...
The smallest difference by far is 0.001... from option (E). The fraction 8/9 (0.888...) is extremely close to the decimal 0.89.
Therefore, the correct answer is (E) 8/9.
Bunuel
15 Nov 2025, 08:23
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Which of the following fractions expressed in the form P/Q is most nearly approximated by the decimal 0.PQ, where P is the tenths' digit and Q is the hundredths' digit?
(A) 1/8
(B) 2/9
(C) 3/4
(D) 4/5
(E) 8/9
The question asks us to take numerator as ‘P’ and denominator as ‘Q’.
The question also asks us to take tenths digit as ‘P’ and hundredths digit as ‘Q’
The question wants us to find the closest value of when we approximate the fraction into two decimal places and then choose the fraction closest to this situation:
Tenths digit value = Digit value of numerator
Hundredths digit value = Digit value of denominator
Since we have to approximate it to 2 decimal places, I found the value of each fraction to 3 decimal places and rounded it to 2 decimal places.
(A) : 1/8 = 0.125 ~ 0.13
(B) : 2/9 = 0.222 ~ 0.22
(C) : 3/4 = 0.75(already in 2 decimal places)
(D) : 4/5 = 0.8 = 0.80(0 is just a place holder but we still want it to have two decimal places)
(E) : 8/9 = 0.889 ~ 0.89
Looking at our decimal numbers, we see that E is the only option that fits into situation we want perfectly.
8(tenths digit) = 8(numerator)
9(hundredths digit) = 9(denominator)
No other answer choice fits into the situation we want perfectly other than E.
Therefore,
Answer = E
(A) 1/8
(B) 2/9
(C) 3/4
(D) 4/5
(E) 8/9
The question asks us to take numerator as ‘P’ and denominator as ‘Q’.
The question also asks us to take tenths digit as ‘P’ and hundredths digit as ‘Q’
The question wants us to find the closest value of when we approximate the fraction into two decimal places and then choose the fraction closest to this situation:
Tenths digit value = Digit value of numerator
Hundredths digit value = Digit value of denominator
Since we have to approximate it to 2 decimal places, I found the value of each fraction to 3 decimal places and rounded it to 2 decimal places.
(A) : 1/8 = 0.125 ~ 0.13
(B) : 2/9 = 0.222 ~ 0.22
(C) : 3/4 = 0.75(already in 2 decimal places)
(D) : 4/5 = 0.8 = 0.80(0 is just a place holder but we still want it to have two decimal places)
(E) : 8/9 = 0.889 ~ 0.89
Looking at our decimal numbers, we see that E is the only option that fits into situation we want perfectly.
8(tenths digit) = 8(numerator)
9(hundredths digit) = 9(denominator)
No other answer choice fits into the situation we want perfectly other than E.
Therefore,
Answer = E
