The Metric System
The metric System
 The metric system is an International System of
Units (SI Units) used in measurements.
 All measurements in the metric system are built
from base units.
 The base units are the starting point.
 We can combine multiple bases to create a
larger unit:
km is a symbol
for kilometers (a
measurement of
distance)
km / h
h is a symbol for
hours
(a measurement
of time)
Important base units we will use:
Base Unit
symbol
Measures?
Metre
m
Gram
g
Length and
distance
Mass
Second
s
Time
Litre
L
Volume
Ampere
A
Electric current
Important base units we will use:
Base Unit
symbol
Measures?
Metre
m
Gram
g
Length and
distance
Mass
Second
s
Time
Litre
L
Volume
Ampere
A
Electric current
We use prefixes to make the base unit
bigger or smaller, and we add a symbol to
describe its value:
Prefix
Symbol
Multiplying Factor
kilo
k
1000
hecto
h
100
deca
da
10
---
---
1 (base unit)
deci
d
0.1
centi
c
0.01
milli
m
0.001
Rules for Changing Metric Units
1.
You only move the decimal. The numbers never change.
2.
If you are converting to smaller units, move the decimal to the
right. When converting to larger units, move the decimal to the
left.
3.
You must memorize the order of the prefixes to know how many
decimal places to move!
Ex:
Convert 24 g to kg and mg:
24 𝑔 = 0.024 𝑘𝑔
24 𝑔 = 24000 𝑚𝑔
TIP: Use a number line to help organize
your prefixes:
MOVE DECIMAL RIGHT
MOVE DECIMAL LEFT
Try These
a) 7.6 cm =
76 mm
b) 1.43 km =
1430 m
c) 0.44 m =
44 cm
d) 277 cm =
2.77 m
e) 1200 mm =
1.2 m
f) 2400 mm =
0.0024 km
Note:
1 cm3 = 1 mL
Taking precise measurements
• Always measure to the precision of the instrument
and estimate 1 extra decimal
Given by instrument
estimated
• Ex:
3.24 cm
units
Ruler tips:
Always line the item up at 0 cm
Know what units and scale you are using (ex: cm or inches? Divided into 10ths?)
Measuring Liquids
 When measuring liquids, use a graduated
cylinder, and read the measurement in line with the
bottom of the miniscus
 (still estimate one extra decimal)
To Do…
1. Measurement Stations
2. Metric Conversion Worksheet
3. Measurement Worksheet
Measurement, Scientific Notation
and Significant Figures
Scientific Notation
 Used in science for very _________ and very
________ numbers
 Examples:
 The average distance from the Sun to Earth is
150 000 000 000 m
 The wavelength of red light is 0.000 000 65 m
 Using many zeros is inconvenient and can lead
to mistakes so scientists came up with an
abbreviation called scientific notation
Rules
1.
2.
3.
4.
5.
Start with the first single digit between 1 and 9 in the
number
Place a decimal point ( . ) to the right of it
After the decimal, write all the other significant figures
Multiply the number by 10
Add an exponent to 10 that is equal to the number of
spots the decimal has moved
 Numbers greater than 1 need a positive exponent
 Numbers less than 1 need a negative exponent
Examples
First Single Other Significant
Figure(s)
Digit
• 150 000 000 000 m
= 1.5 X 1011 m
• 0.000 000 65 m
= 6.5 X 10 -7 m
Significant Figures
 No measurement is ever perfect or exact
 Significant figures are all the certain digits plus the
first uncertain one
Given by instrument
estimated
3.24 cm
units
How many
significant
figures?
Rules for Significant Figures
1. Non-zero digits ARE always significant
2. Zeroes between two significant digits ARE
significant (10506: 5 significant figures)
3. Any leading zeroes (0.008 741) ARE NOT
significant
4. If there is no decimal point, all the trailing
zeroes (75 000) ARE NOT significant
5. Zeroes after decimal points, if shown, are all
significant (4.7800 has 5 significant figures)
Determining the number of sig. figs
# of Sig.
Figs
127.3
0.00874o1
0.0050000
3
5
5
Determining the number of sig. figs
# of Sig.
Figs
127.3
0.00874o1
0.0050000
• 7600: 2 sig. dig.
• 0.300: 3 sig. dig.
3
5
5
Hint:
Another way to
determine the
number of
significant digits is
to convert to
scientific notation
first and then count
the digits
Calculations with significant figures
 Multiplication or division
 Round the result to the same number of significant figures
as the measured value with the least number of significant
figures
Ex: 2.10 x 0.5896 = 1.23816
 Round to 1.24 (three significant digits)

 Addition or subtraction
 Round the results to the same number of decimals as the
least precise number
Ex: 1.586 + 2.31 = 3.896
 Round to 3.90 (two decimals)

Scientific Inquiry
Error Analysis
Precision vs. Accuracy
 Precision and accuracy are two ways that scientists




think about error.
Accuracy refers to how close a measurement is to
the true or accepted value.
Precision is about how close measurements of the
same item are to each other.
Precision and Accuracy are independent of each
other.
The best scientific observations are Accurate and
Precise.
Precision vs. Accuracy
 A: neither accuracy nor precision
 B: precise, but not accurate
 C: accurate (because of equal distance from bulls-
eye), but not precise
 D: both accuracy and precision
Safety Symbol and Equipment