This document discusses measurement units and conversions between metric and other systems. It covers:
- The fundamental SI units of mass, length, time, temperature and derived quantities.
- Using prefixes like kilo and centi to indicate multiples of ten in the metric system.
- Converting between metric units by moving the decimal place.
- Converting between metric and other systems like English units using conversion factors and unit cancellation.
- Applying significant figures rules to calculations to preserve measurement precision.
2. What do we measure?
Fundamental properties
mass (weight) kilogram
length meter
time second
temperature Kelvin
Derived quantities
density, velocity, force, etc...
3. Using the metric system
In the metric system, prefixes are used
to identify the multiples of ten.
103 102 101 1 10-1 10-2 10-3
Kilo Hecto Deka BASE Deci Centi Milli
Base units
mass gram(g)
length meter (m)
liquid volume liter (l)
time second (s)
Each multiple is one decimal place.
Move the decimal to convert
4. Moving the decimal
For measurements that are defined by a
single unit such as length, mass, or liquid
volume , etc., simply move the decimal the
number of places indicated by the prefix.
400 m = 40,000 cm
75 mg = 0.075 g
For area measurements, they are the
combination of two dimensions, you move
the decimal twice the number of places.
2.5 m2 = 2,500,000 mm2
5. Converting measurements
Metric Metric
multiples of 10
move decimal or use conversions
English Metric
conversion factors
unit cancellation method
6. Converting Metric English
When converting in the US (English) system or
converting between US and metric units it is
necessary to use proportions.
In the example below, the measurement 12 in.
is converted to cm. The conversion factor 1 in
= 2.54cm is written as a ratio.
12 in. x 2.54 cm = 30.48 cm
1 in.
8. Solution
A rattlesnake is 2.44 m long. How long is the
snake in cm?
2) 244 cm
2.44 m x 100 cm = 244 cm
1 m
9. What is wrong with the following setup?
1.4 day x 1 day x 60 min x 60 sec
24 hr 1 hr 1 min
10. 1.4 day x 1 day x 60 min x 60 sec
24 hr 1 hr 1 min
Units = day2/hr2 Not the final unit needed
11. Steps to Problem Solving
Read problem
Identify data
Write down a unit plan from the
initial unit to the desired unit
Select conversion factors
Change initial unit to desired
unit
Cancel units and check
Do math on calculator
Give an answer using
significant figures
12. If the ski pole is
3.0 feet in length,
how long is the
ski pole in mm?
13. 3.0 ft x 12 in x 2.54 cm x 10 mm =
1 ft 1 in. 1 cm
14. Significant digits
The digits reported in a measured
quantity
Indicate the precision of the
measuring instrument
Calculations should not have more
significant digits than the least
number of significant digits in the
problem.
15. Rules – Significant Digits
1. All nonzero numbers are
significant. Ex: 456 – 3 sig.
2. All zeros between numbers are
significant. Ex: 408 – 3 sig.
3. If decimal present, zero’s to the
left are not significant.
Ex: 0.0078 – 2 sig.
4. If decimal present, zero’s to the
right are significant.
Ex: 0.090 – 2 sig.
5. If no decimal, zero’s on end are
not significant. Ex: 34500 – 3 sig.
16. Adding and Subtracting
In addition and subtraction, round up
your answer to the least precise
measurement or least number of
places behind the decimal.
For example:
24.686 + 2.343 + 3.21 = 30.239 =
30.24
3.21 is the least precise
measurement.
17. Multiplying and Dividing
In multiplication and division,
round it up to the least number
of significant digits.
For example:
3.22 * 2.1 = 6.762 = 6.8
2.1 contains 2 significant digits.
18. Scientific Notation
Used for expressing very large or
very small values
standard form
base x 10 exponent
base is between 1.0 and 9.999…
if exponent is positive the value is greater than 1
if exponent is negative the value is less than 1
convert to decimal by moving the
decimal the number of places
indicated by the exponent