Question

your grades for each class are rounded to the nearest \\(\frac{1}{10}\\) before they are reported. if your report card grade for math was 90.5, your actual grade is between: a 90.4 and 90.6 b 90.45 and 90.54 c 90.5 and 90.55 d 90 and 91 e 90.45 and 90.5

Explanation:

Step1: Recall rounding to nearest tenth

To round a number to the nearest $\frac{1}{10}$ (tenth), we look at the hundredth place. If the digit in the hundredth place is 5 or more, we round up the tenth place; if it's less than 5, we round down.

Step2: Determine the range

For a number to round to 90.5 (to the nearest tenth), the actual number $x$ must satisfy the inequality: $90.45 \leq x < 90.55$. This is because when the hundredth digit is 5, we round up (e.g., 90.45 rounds to 90.5), and numbers less than 90.55 (but not including 90.55) will round down to 90.5 (e.g., 90.549... rounds to 90.5).

Step3: Evaluate the options

• Option A: 90.4 to 90.6. But numbers like 90.44 would round to 90.4, not 90.5, so this range is too broad.
• Option B: 90.45 to 90.54. This fits the range we derived, since numbers from 90.45 (inclusive) up to but not including 90.55 will round to 90.5, and 90.54 is within that.
• Option C: 90.5 to 90.55. But numbers like 90.49 would round to 90.5, but 90.49 is not in this range, so this is incorrect.
• Option D: 90 to 91. This is way too broad, as numbers like 90.1 would round to 90.1, not 90.5.
• Option E: 90.45 to 90.5. But numbers like 90.51 would round to 90.5 and are greater than 90.5, so this range is too narrow.

Answer:

B. 90.45 and 90.54