Choose the best answer. If necessary, use the paper you were given.
The number p is obtained by moving the decimal point 2 places to the left in the positive number n. The number s is obtained by moving the decimal point 1 place to the right in the number n. The number p + s how many times n?
- A. 1.01
- B. 10.001
- C. 10.01
- D. 10.1
Correct Answer & Rationale
Correct Answer: C
When the decimal point in \( n \) is moved 2 places to the left, \( p \) becomes \( \frac{n}{100} \). Moving the decimal point 1 place to the right gives \( s \) as \( 10n \). Therefore, \( p + s = \frac{n}{100} + 10n \). To combine these, convert \( 10n \) to a fraction: \( 10n = \frac{1000n}{100} \). Thus, \( p + s = \frac{n}{100} + \frac{1000n}{100} = \frac{1001n}{100} \). This simplifies to \( 10.01n \). Option A (1.01) is too low, as it does not account for the large contribution from \( s \). Option B (10.001) and D (10.1) are also incorrect; they either underestimate or overestimate the sum of \( p \) and \( s \). Thus, the correct answer, \( 10.01 \), accurately reflects the relationship between \( p + s \) and \( n \).
When the decimal point in \( n \) is moved 2 places to the left, \( p \) becomes \( \frac{n}{100} \). Moving the decimal point 1 place to the right gives \( s \) as \( 10n \). Therefore, \( p + s = \frac{n}{100} + 10n \). To combine these, convert \( 10n \) to a fraction: \( 10n = \frac{1000n}{100} \). Thus, \( p + s = \frac{n}{100} + \frac{1000n}{100} = \frac{1001n}{100} \). This simplifies to \( 10.01n \). Option A (1.01) is too low, as it does not account for the large contribution from \( s \). Option B (10.001) and D (10.1) are also incorrect; they either underestimate or overestimate the sum of \( p \) and \( s \). Thus, the correct answer, \( 10.01 \), accurately reflects the relationship between \( p + s \) and \( n \).
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.
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.
2(1/2 + 1/3) =
- A. 1(2/3)
- B. 1(5/6)
- C. 2(1/6)
- D. 2(5/6)
Correct Answer & Rationale
Correct Answer: A
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.
To solve 2(1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. Rewrite the fractions: 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding these gives 5/6. Now, multiply by 2: 2 * 5/6 equals 10/6, which simplifies to 1(2/3). Option B, 1(5/6), results from miscalculating the addition. Option C, 2(1/6), misinterprets the multiplication step. Option D, 2(5/6), incorrectly applies the multiplication to the wrong sum. Each incorrect option reflects a misunderstanding of the operations involved.
0.4/0.04 =
- A. 100
- B. 10
- C. 0.1
- D. 0.01
Correct Answer & Rationale
Correct Answer: B
To solve 0.4 divided by 0.04, it’s helpful to convert both numbers to whole numbers for easier calculation. Multiplying both by 100 gives us 40 divided by 4. This simplifies to 10, confirming option B as the solution. Option A (100) results from miscalculating the division, possibly by incorrectly interpreting the decimal places. Option C (0.1) and Option D (0.01) suggest a misunderstanding of division, as they reflect values far smaller than the actual quotient. Thus, only option B accurately represents the result of the division.
To solve 0.4 divided by 0.04, it’s helpful to convert both numbers to whole numbers for easier calculation. Multiplying both by 100 gives us 40 divided by 4. This simplifies to 10, confirming option B as the solution. Option A (100) results from miscalculating the division, possibly by incorrectly interpreting the decimal places. Option C (0.1) and Option D (0.01) suggest a misunderstanding of division, as they reflect values far smaller than the actual quotient. Thus, only option B accurately represents the result of the division.