A human head weighs 160 ounces. What is that weight in kilograms? Analyze the work below.

1 pound = 16 ounces
1,000 grams = 1 kilogram
1 kilogram = 2.2 pounds

Student’s work:

\[
\frac{160 \text{ ounces}}{1} \times \frac{16 \text{ pounds}}{1 \text{ ounce}} \times \frac{1 \text{ kilogram}}{2.2 \text{ pounds}} \approx 1,163.6
\]

What is the student’s error?

Question

12-10-2024
Mathematics

College

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A human head weighs 160 ounces. What is that weight in kilograms? Analyze the work below.

1 pound = 16 ounces
1,000 grams = 1 kilogram
1 kilogram = 2.2 pounds

Student’s work:

\[
\frac{160 \text{ ounces}}{1} \times \frac{16 \text{ pounds}}{1 \text{ ounce}} \times \frac{1 \text{ kilogram}}{2.2 \text{ pounds}} \approx 1,163.6
\]

What is the student’s error?

Answer :

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HelenAbigail HelenAbigail · Answer 1 · 2024-12-29T11:32:08-05:00

Final answer:

The student made an error in the unit conversion, using incorrect ratios and the steps were not applied properly. Converting 160 ounces to kilograms should involve first converting ounces to pounds and then pounds to kilograms, yielding approximately 4.536 kilograms.

Explanation:

The student's error in converting 160 ounces to kilograms is in the incorrect use of conversion rates and multiplication. The correct conversion process would be:

Convert ounces to pounds: StartFraction 160 ounces Over 1 EndFraction × StartFraction 1 pound Over 16 ounces EndFraction, which simplifies to 10 pounds.
Then convert pounds to kilograms: StartFraction 10 pounds Over 1 EndFraction × StartFraction 0.4536 kilograms Over 1 pound EndFraction, which is approximately 4.536 kilograms.

The misunderstanding appears to be in the student's second step where they used 16 pounds for 1 ounce, instead of 1 pound for 16 ounces, and also in the incorrect arrangement of the units in the multiplication process.