Question

Multiply the following measurements using correct significant digits.

A. 22,209.9 ft³
B. 22,200 ft³
C. 22,000 ft³
D. 28,000 ft³
3.80 ft x 71 ft x 82.32 ft

Answer 1

Answer:
`22,000 \text{ ft}^3` (choice C)

Step-by-step explanation

Use a calculator, or scratch paper, to find that

3.80 x 71 x 82.32 = 22,209.936

We then round to 2 sig figs because the 71 is to 2 sig figs, and it's the lowest sig fig count. We always go for the weakest link, i.e. the least accurate input, when deciding the final sig fig count. Otherwise you might have a "garbage in garbage out" situation.

22,209.936 rounds to 22,000 when rounding to 2 sig figs. The first two digits remain the same. Everything else turns to 0s. Do not put a decimal point at the end of the number. If the decimal is there then it would make those 0s significant, when we don't want them to be.

The volume units are "cubic feet" which can be abbreviated to
`\text{ ft}^3`

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If we round all of the inputs to 2 sig figs, and then multiply, then we get

3.8*71*82 = 22,123.6

This result also rounds to 22,000 when rounding to 2 sig figs.