Measurement

• Measuring Length; Customary US System.
  • Length is the measurement of the distance between two points.
  • We measure length in linear measurement units.
  • The US Customary, or English system is cumbersom
    • 12 inches = 1 foot
    • 3 feet = 1 yard
    • 5280 feet = 1 mile
  • We can use dimensional analysis to convert between these.
  • Example 1: How many yards are in a mile?

    
    5280 ft   1 yard     5280
    ------- x ------ =  -----  yd/mile or 1,760 yd/mile
    mile      3 ft        3
    	

• The Metric System
  • Length measurement is based on the meter.
  • 1 m = 39.37 in
  • Example 2: How many yards in a meter?

    1 yd   1 ft   39.37 in    39.37
    ---- x ---- x --------  = ----- = 1.0936 yd/m
    3 ft   12 in   1 m        3x12
    	

  • The metric system uses the SI units.
  • These scale by a factor of 10.

  • Prefix	Scale
    kilo	k	1000 x base
    hecto	h	100 x base
    deka	da	10 x base
    base	-	1 x base
    centi	c	.1 x base
    mili	m	.01 x base

  • To convert between units, we just could the slots we move up and divide by 10 each time.
  • Example 3: Convert 230m to hm

    hm is two steps above m, so 1 hm = 10x10 m  (1hm = 100m)
           1 hm
    230m x ----- = 230/100 hm = 2.3 hm
           100 m
    	

  • Example 4: Convert .34 dam to mm

    mm is 3 spaces below dam so 1000mm = 1 dam
             1000 mm
    .34dam x ------- = 1000 x .34 or 340 mm
             1 dam
    	

  • He does some kind of wierd wiggle the decimal place thing, use it fi you wish.
  US Customary to Metric conversions.
  • This is easily solved with dimensional analysis.

  • US	Metric
    1 inch	2.54 cm
    1 ft	30.48 cm
    1 yd	.9 m
    1 mile	1.6 km

  • Measuring Area
    • Area is measured in a square unit
    • Volume is measured in a cubic unit.
    • A = l×w
    • V = l×w×h
    • We need to be careful when converting.
    • Convert 12 in² to ft²

      Wrong  12 in = 1 ft, so 12 in2 = 1ft2
                                     1 ft     1 ft
      correct   12 in2 x ------- x ----- = 1/12 ft2
                                    12 in     12 in
      
      	

    • With land, area is measured in the acre in the US Cust. system.
    • It is measured in hectare (ha) in the metric system.
    • 1 acre = .4 ha
  • Measuring Volume
    • Tables on pages 521, 522
    • 1 gal = 231 in³
    • 1000 cm³ = 1 L
    • 1 m³ = 1 kL
  • P 523, 6, 12, 28,

  Homework

  Page 516, 1-50 eoo, 75, 77

  Page 523, 5-38 odd.