Question

units of measurement assessment 2025x
is the following dimensional analysis problem correct?
yardstick problem
how many centimeters (cm) are in a yardstick?
know: 1 inch = 2.54 cm (exactly)
\\(\frac{1\text{ yd}}{1}\times\frac{3\text{ ft}}{1\text{ yd}}\times\frac{12\text{ in.}}{1\text{ ft}}\times\frac{2.54\text{ cm}}{1\text{ in.}} = 91.44\text{ cm exactly}\\)
yes everything is correct
no answer is has too many sig. figs
no the answer does not have the correct units
no the problem has too many converting factors.

Explanation:

Step1: Recall unit - conversion relationships

We know that 1 yard (yd) = 3 feet (ft), 1 foot (ft)=12 inches (in), and 1 inch (in) = 2.54 cm.

Step2: Analyze the dimensional - analysis setup

The given expression $\frac{1\ yd}{1}\times\frac{3\ ft}{1\ yd}\times\frac{12\ in.}{1\ ft}\times\frac{2.54\ cm}{1\ in.}$ correctly cancels out the units. The yd in the numerator of the first fraction cancels with the yd in the denominator of the second fraction, the ft in the numerator of the second fraction cancels with the ft in the denominator of the third fraction, and the in. in the numerator of the third fraction cancels with the in. in the denominator of the fourth fraction, leaving us with cm as the final unit.

Step3: Calculate the result

$1\times3\times12\times2.54 = 91.44$ cm. The conversion factors are exact values (1 yd = 3 ft, 1 ft = 12 in, 1 in = 2.54 cm are all exact), so the number of significant figures is appropriate.

Answer:

Yes everything is correct