Approximate the value of (50.003% of 99.8) ÷ 49.988 using sensible estimation. Which of the following is the closest approximate value?

Introduction:
This question tests approximation and estimation with percentages and decimals. The expression looks complex, but the numbers are deliberately chosen to simplify: 50.003% is extremely close to 50%, and 99.8 is close to 100. Also, the denominator 49.988 is close to 50. So the overall expression should be close to (50% of 100) / 50 = 50 / 50 = 1. The goal is not exact calculation but picking the closest option quickly and confidently.

Given Data / Assumptions:

• Expression: (50.003% of 99.8) ÷ 49.988
• 50.003% = 50.003/100 ≈ 0.50003
• 99.8 ≈ 100 and 49.988 ≈ 50 for estimation
• We choose the closest option (approximate answer)

Concept / Approach:
Convert percent to a multiplier and estimate stepwise. First estimate the “percent of” part, then divide by the denominator. Use closeness: 50.003% is almost half, and 99.8 is almost 100, so numerator is almost 50. Denominator is almost 50, so result is almost 1. We can also do a slightly tighter estimate to confirm it is still closest to 1.

Step-by-Step Solution:
50.003% = 0.50003 (approximately) Numerator ≈ 0.50003 * 99.8 0.5 * 99.8 = 49.9 Extra part: 0.00003 * 99.8 ≈ 0.002994 So numerator ≈ 49.902994 Denominator = 49.988 ≈ 50 Result ≈ 49.903 / 49.988 ≈ 0.998 (very close to 1)

Verification / Alternative check:
Using pure rounding: (50% of 100) / 50 = 1. Since our refined estimate is about 0.998, the nearest option remains 1, not 0 or 2.

Why Other Options Are Wrong:
0 is impossible because all quantities are positive. 2 would require numerator about twice the denominator (~100), which it is not. 50 is far too large and ignores the division. 0.5 would require numerator about half the denominator (~25), which is not the case.

Common Pitfalls:
Treating 50.003% as 50.003 (not dividing by 100), or rounding too aggressively without checking whether the result stays near 1.

Final Answer:
The closest approximate value is 1.