## Q. 2.11

Solving Multistep Unit Conversion Problems

One lap of a running track measures 255 m. To run 10.0 km, how many laps should you run?

## Verified Solution

 SORT Begin by sorting the information in the problem into given and find. You are given a distance in km and asked to find the distance in laps. You are also given the quantity 255 m per lap, which is a conversion factor between m and laps. GIVEN: 10.0 km 255 m = 1 lap FIND: number of laps STRATEGIZE Build the solution map beginning with km and ending at laps. Focus on the units. SOLUTION MAP $km\underset{\frac{10^3 m}{1 km} }{\longrightarrow } m \underset{\frac{1 lap}{255 m} }{\longrightarrow } laps$ RELATIONSHIPS USED 1 km = $10^3$ m (from Table 2.2) 1 lap = 255 m (given in problem) SOLVE Follow the solution map to solve the problem. Begin with 10.0 km and multiply by the appropriate conversion factor, canceling units to arrive at m. Then, use the second conversion factor to arrive at laps. Round the intermediate answer (in blue) to three significant figures because it is limited by the three significant figures in the given quantity, 10.0 km. SOLUTION $10.0 \cancel{ km}\times \frac{10^3 \cancel{m}}{1 \cancel{ km}}\times \frac{1 lap}{255 \cancel{m}}$ = 39.216 laps = 39.2 laps CHECK Check your answer. Are the units correct? Does the answer make physical sense? The units of the answer are correct, and the value of the answer makes sense. If a lap is 255 m, there are about 4 laps to each km (1000 m), so it seems reasonable that you would have to run about 40 laps to cover 10 km.

Table 2.2

 SI Prefix Multipliers Prefix Symbol Meaning Multiplier tera- T trillion 1,000,000,000,000 $(10^{12})$ giga- G billion 1,000,000,000 $(10^{9})$ mega- M million 1,000,000 $(10^{6})$ kilo- k thousand 1,000 $(10^{3})$ hecto- h hundred 100 $10^{2}$ deca- da ten 10 $10^{1}$ deci- d tenth 0.1 $(10^{-1})$ centi- c hundredth 0.01 $(10^{-2})$ milli- m thousandth 0.001 $(10^{-3})$ micro- µ millionth 0.000001 $(10^{-6})$ nano- n billionth 0.000000001 $(10^{-9})$ pico- p trillionth 0.000000000001 $(10^{-12})$ femto- f quadrillionth 0.000000000000001 $(10^{-15})$