Choose the best answer. If necessary, use the paper you were given.
What is rounded to the nearest hundredth? 48/27
- A. 1.7
- B. 1.77
- C. 1.78
- D. 1.8
Correct Answer & Rationale
Correct Answer: C
To find the value of \( \frac{48}{27} \), we perform the division, resulting in approximately 1.7778. Rounding this number to the nearest hundredth involves looking at the third decimal place (7) to determine whether to round up or down. Since 7 is 5 or greater, we round up, resulting in 1.78. - Option A (1.7) is too low, as it does not reflect the precise value. - Option B (1.77) rounds down incorrectly, failing to account for the third decimal. - Option D (1.8) rounds up too far, exceeding the correct value. Thus, 1.78 accurately represents the rounded result.
To find the value of \( \frac{48}{27} \), we perform the division, resulting in approximately 1.7778. Rounding this number to the nearest hundredth involves looking at the third decimal place (7) to determine whether to round up or down. Since 7 is 5 or greater, we round up, resulting in 1.78. - Option A (1.7) is too low, as it does not reflect the precise value. - Option B (1.77) rounds down incorrectly, failing to account for the third decimal. - Option D (1.8) rounds up too far, exceeding the correct value. Thus, 1.78 accurately represents the rounded result.
Other Related Questions
Which of the following is equivalent to 1.04?
- A. 52/51
- B. 51/50
- C. 27/25
- D. 26/25
Correct Answer & Rationale
Correct Answer: D
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.
To determine which option is equivalent to 1.04, we convert each fraction to a decimal. A: 52/51 equals approximately 1.0196, which is less than 1.04. B: 51/50 equals 1.02, also below 1.04. C: 27/25 equals 1.08, exceeding 1.04. D: 26/25 calculates to 1.04 exactly, matching the target value. Thus, option D accurately represents 1.04, while the other options do not meet the requirement.
Maria worked 2 weeks, earning $435.50 the first week and $278.38 the second week. If she paid one-half of her two-week earnings for tuition, how much did she pay for tuition?
- A. $713.88
- B. $356.94
- C. $217.75
- D. $139.19
Correct Answer & Rationale
Correct Answer: B
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
To find the amount Maria paid for tuition, first calculate her total earnings for the two weeks. Adding her earnings from both weeks: $435.50 + $278.38 = $713.88. Since she paid one-half of her total earnings for tuition, divide this amount by 2: $713.88 / 2 = $356.94. Option A ($713.88) represents her total earnings, not the tuition amount. Option C ($217.75) and Option D ($139.19) do not correctly reflect half of her total earnings. Therefore, $356.94 accurately represents the amount she paid for tuition.
Last year Joan's salary was $18,000. If she receives a $900 raise for this year, what percent of last year's salary is her raise?
- A. 2%
- B. 5%
- C. 20%
- D. 50%
Correct Answer & Rationale
Correct Answer: B
To find the percentage of last year's salary that Joan's raise represents, divide the raise amount by last year's salary and then multiply by 100. Here, $900 (raise) divided by $18,000 (last year's salary) equals 0.05. Multiplying by 100 gives 5%, which is the correct answer. Option A (2%) miscalculates the raise as a smaller fraction of the salary. Option C (20%) incorrectly interprets the raise as a larger proportion, perhaps confusing it with a different calculation. Option D (50%) vastly overestimates the raise, suggesting it is half of last year's salary, which is not accurate.
To find the percentage of last year's salary that Joan's raise represents, divide the raise amount by last year's salary and then multiply by 100. Here, $900 (raise) divided by $18,000 (last year's salary) equals 0.05. Multiplying by 100 gives 5%, which is the correct answer. Option A (2%) miscalculates the raise as a smaller fraction of the salary. Option C (20%) incorrectly interprets the raise as a larger proportion, perhaps confusing it with a different calculation. Option D (50%) vastly overestimates the raise, suggesting it is half of last year's salary, which is not accurate.
Charlotte is drilling three holes of different sizes in a bird house that she is making. The diameters of the holes are 1(1/2) inches, 1(3/4) inches, and 1(3/8) inches. Which of the following gives the diameters, in inches, in order from least to greatest?
- A. 1(1/2), 1(3/4), 1(3/8)
- B. 1(1/2), 1(3/8), 1(3/4)
- C. 1(3/8), 1(3/4), 1(1/2)
- D. 1(3/8), 1(1/2), 1(3/4)
Correct Answer & Rationale
Correct Answer: D
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).
To determine the correct order of the hole diameters from least to greatest, we first convert the mixed numbers to improper fractions for easier comparison. - 1(1/2) = 3/2 - 1(3/4) = 7/4 - 1(3/8) = 11/8 By comparing these values, we find that 11/8 (1(3/8)) is the smallest, followed by 3/2 (1(1/2)), and finally 7/4 (1(3/4)). Option A incorrectly lists 1(1/2) as the smallest. Option B misplaces 1(3/8) and 1(3/4). Option C arranges the sizes incorrectly, placing the largest first. Therefore, the correct order is D: 1(3/8), 1(1/2), 1(3/4).