Question

an athlete has 15 % body fat by mass. what is the weight of fat, in pounds, of a 79-kg athlete? express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Calculate mass of fat in kg

First, find 15% of 79 kg. The formula for percentage is \( \text{Mass of fat (kg)} = 0.15 \times 79 \)
\( 0.15 \times 79 = 11.85 \, \text{kg} \)

Step2: Convert kg to pounds

We know that \( 1 \, \text{kg} = 2.20462 \, \text{pounds} \). So, multiply the mass in kg by 2.20462.
\( \text{Mass of fat (pounds)} = 11.85 \times 2.20462 \)
\( 11.85 \times 2.20462 \approx 26.12 \)

Step3: Round to two significant figures

26.12 rounded to two significant figures is 26 (wait, no, 26.12 with two significant figures: the first two digits are 2 and 6, the next digit is 1 which is less than 5, so it's 26? Wait, no, 11.85 is from 79*0.15. Wait, 79 has two significant figures? Wait, 79 is two significant figures, 15% is two significant figures (1.5 x 10^1 %). So when multiplying, the result should have two significant figures. Wait, 79 kg is two significant figures, 15% is two. So 0.15*79 = 11.85, which we can consider as 12 (two significant figures? Wait, no, 79 is two, 15 is two, so 0.15*79 = 11.85, which should be rounded to two significant figures: 12 (since the third digit is 8, which is more than 5, so 11.85 rounds to 12 when using two significant figures? Wait, no, 11.85: the first two significant figures are 1 and 1? Wait, no, 11.85 is 1.185 x 10^1. So two significant figures would be 1.2 x 10^1 (12). Then 12 kg * 2.20462 lb/kg = 26.45544 lb, which rounds to 26 lb? Wait, but maybe I made a mistake in significant figures. Wait, 79 is two significant figures, 15% is two. So 0.15 * 79 = 11.85. The rule for multiplication/division: the result has the same number of significant figures as the least precise measurement. So 79 (two) and 0.15 (two), so the product should have two. So 11.85 rounded to two significant figures is 12 (because the third digit is 8, which is more than 5, so we round up the second digit: 11.85 → 12 when using two significant figures). Then 12 kg * 2.20462 lb/kg = 26.45544 lb, which rounds to 26 lb? Wait, but 2.20462 is a conversion factor with more significant figures, so we can keep it as is. Wait, maybe I should do it without rounding intermediate steps. Let's recalculate:

0.15 * 79 = 11.85 kg (exact for the percentage calculation). Then 11.85 kg * 2.20462 lb/kg = 11.85 * 2.20462. Let's compute that:

11.85 * 2.20462 = (12 - 0.15) * 2.20462 = 12*2.20462 - 0.15*2.20462 = 26.45544 - 0.330693 = 26.124747 lb. Now, we need to round to two significant figures. The number is 26.124747. The first two significant figures are 2 and 6. The next digit is 1, which is less than 5, so we keep the second digit as is. Wait, but 26.124747 with two significant figures: 2.6 x 10^1, which is 26? Wait, no, 26.124747: the first significant figure is 2, the second is 6, the third is 1. So when rounding to two significant figures, we look at the third digit, which is 1, so we don't round up. So 26 (two significant figures). Wait, but 11.85 has four significant figures (from 79 (two) and 0.15 (two), so the product should have two. So 11.85 rounded to two is 12, then 12*2.20462=26.455, which rounds to 26 (two significant figures). Alternatively, maybe the problem considers 79 as two significant figures and 15% as two, so the answer should be two. So the weight of fat is approximately 26 pounds. Wait, but let's check the calculation again. 79 kg * 0.15 = 11.85 kg. 1 kg = 2.20462 lb, so 11.85 kg * 2.20462 lb/kg = 26.1247 lb. Rounded to two significant figures, that's 26 lb (since the third digit is 1, which is less than 5, so we keep the first two digits: 2 and 6). Wait, but 26.1247 is closer to 26 than 27. So the answer is 26 pounds.

Answer:

26 pounds