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?

Chapter 2 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?

Step-by-Step

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	$(10^{-15})$