1. 9.1 Measuring Length; The Metric System
Chapter 9 Measurement
9.1 Measuring Length; The Metric System

2. Length
English System
12 inches (in) = 1 foot (ft)
3 ft = 1 yard (yd)
36 in = 1 yard
5280 ft = 1 mile (mi)
Unit Fractions (Each fraction equals 1.) in ft ft yd ft mi ft in 1 yd ft mi ft

3. Dimensional Analysis To convert a measurement to a different unit:
Multiply by unit fraction (or unit fractions).
The given unit of measurement should appear in the denominator of the unit fraction, so that units cancel out.
E.g.
Convert 40 in to feet in ft ft ft in = · = = ≈ 3.3 ft in

4. Dimensional Analysis
Convert 13,200 feet to miles ,000 ft mi 13,000 ft = · ft ,000 mi = ≈ 2.5 mi

5. Your Turn
Given: 12 in ft ft yd ft mi ft in 1 yd ft mi ft
Convert 13 miles to feet
13 𝑚𝑖 1 · 𝑓𝑡 1 𝑚𝑖 = 13 · ft = 68,640 ft
Convert 8 feet to inches
8 𝑓𝑡 1 · 12 𝑖𝑛 1 𝑓𝑡 = 8 · 12 in = 96 in
Convert 5 yards to inches
5 𝑦𝑑 1 · 3 𝑓𝑡 1 𝑦𝑑 · 12 𝑖𝑛 1 𝑓𝑡 = 5 · 3 · 12 in = 180 in

6. Length and the Metric System
Used in most industrialized countries.
Based on power of ten Metric Prefixes
Prefix
Symbol
Meaning
kilo k
1000 x
hecto h
100 x
deka da
10 x
deci d
1/10
centi C
1/100
milli m
1/1000
micro
1/1,000,000
nano n
1/1,000,000,000

7. Linear Measure in the Metric System
Symbol
Unit
Meaning km
kilometer
103 m m
meter
1 m cm
centimeter
10-2 m mm
millimeter
10-3 m
micron
10-6 m

8. Conversions in Metric System
Convert m to kilometers.
504.7 m = x 1m = x 10-3 km = km
Convert 27 m to centimeters.
27 m = 27 x 1m = 27 x 102 cm = 2700 cm

9. Conversion between Metric and English Systems
1 inch (in.) = 2.54 centimeters (cm)
1 foot (ft) = centimeters (cm)
1 yard (yd) ≈ 0.9 meter (m)
1 mile (mi) ≈ 1.6 kilometers (km)

10. Conversion between Metric and English Systems
Convert 125 miles to kilometers.
125 mi = 125 x 1mi = 125 x 1.6 km = 200 km
Convert 26,800 millimeters to inches.
26,800 mm = 26,800 x 1 mm = 26,800 x 10-1 cm = 2680 cm = 2680 x 1 cm = 2680 x (1 /2.54) in = 2680 / ≈ 1055 in

11. Your Turn Aloha Run is 8.2 miles. Convert this to kilometers.
8.2 mi = 8.2 x 1 mi = 8.2 x 1.6 km = km
Speed of light is about 3 x 108 m/sec Convert this to mi / sec.
3 x 108 m = 3 x 108 x 1 m = 3 x 108 x 10-3 km = 3 x 105 km = 3 x 105 km x (1 mi / 1. 6 km) = 3 x 105 x (1 mi / 1.6) = mi
Thus , 3 x 108 m/sec ≈ 188,000 mi/sec