76 ÷ 0.01 =
- A. 0.76
- B. 7.6
- C. 760
- D. 7,600
Correct Answer & Rationale
Correct Answer: D
To solve 76 ÷ 0.01, it is helpful to recognize that dividing by a decimal is equivalent to multiplying by its reciprocal. The reciprocal of 0.01 is 100, so this operation can be rewritten as 76 × 100, which equals 7,600. Option A (0.76) incorrectly suggests a much smaller result, as it misinterprets the division. Option B (7.6) also underestimates the value, failing to account for the decimal's effect. Option C (760) is closer but still incorrect, as it does not fully account for the multiplication by 100. Therefore, D (7,600) accurately reflects the operation's outcome.
To solve 76 ÷ 0.01, it is helpful to recognize that dividing by a decimal is equivalent to multiplying by its reciprocal. The reciprocal of 0.01 is 100, so this operation can be rewritten as 76 × 100, which equals 7,600. Option A (0.76) incorrectly suggests a much smaller result, as it misinterprets the division. Option B (7.6) also underestimates the value, failing to account for the decimal's effect. Option C (760) is closer but still incorrect, as it does not fully account for the multiplication by 100. Therefore, D (7,600) accurately reflects the operation's outcome.
Other Related Questions
If 4 is x percent of 16, what is x?
- A. 1/4
- B. 4
- C. 16
- D. 25
Correct Answer & Rationale
Correct Answer: D
To find x, we start with the equation \(4 = \frac{x}{100} \times 16\). Rearranging this gives \(x = \frac{4 \times 100}{16}\), which simplifies to \(x = 25\). Option A (1/4) is incorrect as it does not represent a percentage of 16. Option B (4) misinterprets the relationship, as it does not reflect the percentage context. Option C (16) suggests that 4 is 16% of itself, which is also incorrect. Only option D (25) accurately represents that 4 is 25% of 16, confirming the correct calculation.
To find x, we start with the equation \(4 = \frac{x}{100} \times 16\). Rearranging this gives \(x = \frac{4 \times 100}{16}\), which simplifies to \(x = 25\). Option A (1/4) is incorrect as it does not represent a percentage of 16. Option B (4) misinterprets the relationship, as it does not reflect the percentage context. Option C (16) suggests that 4 is 16% of itself, which is also incorrect. Only option D (25) accurately represents that 4 is 25% of 16, confirming the correct calculation.
If 22,1/3% of a number n is 938, then n must be?
- A. 281,400
- B. 42,000
- C. 4,960
- D. 4,200
Correct Answer & Rationale
Correct Answer: D
To find the number \( n \), we start by converting \( 22 \frac{1}{3} \% \) to a decimal. This percentage equals \( \frac{67}{3} \% \), or \( \frac{67}{300} \) in decimal form. Setting up the equation \( \frac{67}{300} n = 938 \) allows us to solve for \( n \). Multiplying both sides by \( \frac{300}{67} \) gives \( n = 938 \times \frac{300}{67} = 4,200 \). Option A (281,400) is too high, as it would imply a much larger percentage. Option B (42,000) miscalculates the percentage relation. Option C (4,960) is incorrect, as it does not satisfy the equation derived from the percentage calculation.
To find the number \( n \), we start by converting \( 22 \frac{1}{3} \% \) to a decimal. This percentage equals \( \frac{67}{3} \% \), or \( \frac{67}{300} \) in decimal form. Setting up the equation \( \frac{67}{300} n = 938 \) allows us to solve for \( n \). Multiplying both sides by \( \frac{300}{67} \) gives \( n = 938 \times \frac{300}{67} = 4,200 \). Option A (281,400) is too high, as it would imply a much larger percentage. Option B (42,000) miscalculates the percentage relation. Option C (4,960) is incorrect, as it does not satisfy the equation derived from the percentage calculation.
The coordinate of pointP on the number line above is x. The value of 10x is between
- A. 1 and 4
- B. 4 and 6
- C. 6 and 8
- D. 8 and 12
Correct Answer & Rationale
Correct Answer: B
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
To determine the correct range for \(10x\), we first need to assess the implications of each option based on the value of \(x\). - **Option A: 1 and 4** suggests \(0.1 < x < 0.4\). This would yield \(10x\) values less than 4, which is too low. - **Option B: 4 and 6** indicates \(0.4 < x < 0.6\). This range results in \(10x\) values between 4 and 6, aligning perfectly with the requirement. - **Option C: 6 and 8** implies \(0.6 < x < 0.8\). Here, \(10x\) would exceed 6, which is not valid. - **Option D: 8 and 12** indicates \(0.8 < x < 1.2\), leading to values of \(10x\) that exceed 8, thus also incorrect. Therefore, only Option B accurately reflects the condition for \(10x\) being between 4 and 6.
If a number rounded to the nearest hundredth is 9.99, which of the following could be the number?
- A. 9.845
- B. 9.983
- C. 9.992
- D. 9.998
Correct Answer & Rationale
Correct Answer: C
Rounding to the nearest hundredth means looking at the third decimal place to determine if the second decimal place should round up or stay the same. For a number rounded to 9.99, the possible range is 9.985 to 9.995. Option A (9.845) rounds to 9.84, which is outside the range. Option B (9.983) rounds to 9.98, also outside the range. Option D (9.998) rounds to 10.00, exceeding the upper limit. Option C (9.992) falls within the range and correctly rounds to 9.99, making it the only viable option.
Rounding to the nearest hundredth means looking at the third decimal place to determine if the second decimal place should round up or stay the same. For a number rounded to 9.99, the possible range is 9.985 to 9.995. Option A (9.845) rounds to 9.84, which is outside the range. Option B (9.983) rounds to 9.98, also outside the range. Option D (9.998) rounds to 10.00, exceeding the upper limit. Option C (9.992) falls within the range and correctly rounds to 9.99, making it the only viable option.