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Chapter 1

Q. 1.7

Unit Conversion

Convert 1.76 yards to centimeters.

Step-by-Step

Verified Solution

Procedure for…

Solving Unit Conversion Problems
SORT Begin by sorting the information in the problem into given and find. GIVEN: 1.76 yd
FIND: cm
STRATEGIZE Devise a conceptual plan for the problem. Begin with the given quantity and symbolize each conversion step with an arrow. Below each arrow, write the appropriate conversion factor for that step. Focus on the units. The conceptual plan should end at the find quantity and its units. In these examples, the other information you need consists of relationships between the various units CONCEPTUAL PLAN

RELATIONSHIPS USED

1.094 yd = 1 m
1 cm
= 10-²m

(These conversion factors are from Tables 1.2 and 1.3.)

SOLVE Follow the conceptual plan.

Begin with the given quantity and its units. Multiply by the appropriate conversion factor(s), canceling units, to arrive at the find quantity.

Round the answer to the correct number of significant figures following the rules in Section 1.7. Remember that exact conversion factors do not limit significant figures.

SLUTION

1.76  \cancel{yd} \times \frac{1 \cancel{m}}{1.094  \cancel{yd} }\times \frac{1 cm}{10^{-2}  \cancel{m} }

 

= 160.8775 cm

160.8775 cm = 161 cm

 

 

CHECK Check your answer. Are the units correct? Does the answer make sense? The units (cm) are correct. The magnitude of the answer (161) makes sense because a centimeter is a much smaller unit than a yard.

Tables 1.2

SI Prefix Multipliers
prefix Symbol Multiplier
exa E 1,000,000,000,000,000,000 (10^{18})
peta P 1,000,000,000,000,000 (10^{15})
tera T 1,000,000,000,000 (10^{12})
giga G 1,000,000,000 (10^{9})
mega M 1,000,000 (10^{6})
kilo K 1000 (10^{3})
deci d 0.1 (10^{-1})
centi c 0.01 (10^{-2})
milli m 0.001 (10^{-3})
micro μ 0.000001 (10^{-6})
nano n 0.000000001 (10^{-9})
pico p 0.000000000001 (10^{-12})
femto f 0.000000000000001 (10^{-15})
atto a 0.000000000000000001 (10^{-18})

Tables 1.3

Some Common Units and Their Equivalents
Length Mass Volume
1 kilometer (km) = 0.6214 mile (mi) 1 kilogram (kg) = 2.205 pounds (lb) 1 liter (L) = 1000 ml = 1000 cm³
1 meter (m) = 39.37 inches (in) = 1.094 yards (yd) 1 pound (lb) = 453.59 grams (g) 1 liter (L) = 1.057 quarts (qt)
1 foot (ft) = 30.48 centimeters (cm) 1 ounce (oz) = 28.35 grams (g) 1 U.S. gallon (gal) = 3.785 liters (L)
1 inch (in) = 2.54 centimeter (cm) (exact)