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0.2 THE METRIC SYSTEM & CONVERSIONS

Introductory Unit

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BY THE END OF THIS LESSON, I WILL BE ABLE TO…

  • Convert numbers using the metric system by the technique called DIMENSIONAL ANALYSIS.

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WHY ARE WE DOING THIS?

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THE METRIC SYSTEM

  • Most countries use the metric system in everyday life. The scientific community throughout the world uses the metric system, thereby providing an easy flow of consistent measurement and information.

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BASE UNITS & DERIVED UNITS

  • There are several basic units used in measurement, for example:
    • length - meter
    • time - second
    • mass - gram
    • temperature - Kelvin
    • amount of substance - mole
    • luminous intensity – candela
    • Volume - liter
  • We will be using meters, kilograms, and seconds for most of the course.
  • Derived units are combinations of base units, like meters per second (m/s).

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PREFIXES

  • The table below shows the symbol, prefix, prefix meaning, and the scientific notation corresponding with the prefix.

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T

Tera

one trillion

1012

G

Giga

one billion

109

M

Mega

one million

106

k

kilo

one thousand

103

h

hecto

one hundred

102

da

deca

ten

101

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Base Unit

Example: gram, metre, litre

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d

deci

one tenth

10-1

c

centi

one hundredth

10-2

m

milli

one thousandth

10-3

μ

micro

one millionth

10-6

n

nano

one billionth

10-9

ρ

pico

one trillionth

10-12

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CONVERTING UNITS EXAMPLES

  • To convert units (like grams to kilograms) use the times sign/straight line method (also called Dimensional Analysis).
  • The times sign means that you multiply.
  • The underline sign is an equivalent ratio
    • i.e. : 1km/1000m. The top part of the ratio equals the bottom.

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EXAMPLE 1: CONVERT 1 KM TO M

  • 1 km x 1000m = 1000m

1 km

  • Notice that the equivalent ratio has km on the bottom so that it cancels km from 1km.

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EXAMPLE 2: CONVERT 1 M TO KM

  • 1 m x 1 km = 0.001km or

1000m

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  • 1 m x .001km = 0.001km

1m

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EXAMPLE 3: CONVERT 1.5 HOURS TO SECONDS

  • 1.5 hours x 3600s = 5400s 1 hr
  • Remember there are 60s in 1 min and 60 min in 1 hr, so 60s x 60 min to get 3600s in 1 hr.

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EXAMPLE 4: CONVERT 60 KM/HOUR TO M/S.

  • 60 km x 1000m x 1hr = 16.7 m/s

hr 1km 3600s

  • Convert km first, then do hr. Notice that the units will cancel so you are left with m/s.

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