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
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
Determining the number of sig. figs
127.3
0.00874o1
0.0050000
# of Sig.
Figs
3
5
5
Determining the number of sig. figs
127.3
0.00874o1
0.0050000
# of Sig.
Figs
4
5
5
Determining the number of sig. figs
127.3
0.00874o1
0.0050000
# of Sig.
Figs
4
5
5
Determining the number of sig. figs
127.3
0.00874o1
0.0050000
# of Sig.
Figs
4
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)
0
