Starter
1. The radius of the moon is 1,737,000 meters. Write this
in scientific notation.
2. The diameter of a carbon atom is 0.000000000154
meters. Write this in scientific notation.
3. Convert the following numbers into standard notation:
a. 6.7 x 106
b. 8.8 x 10-4
Starter
1. The radius of the moon is 1,737,000 meters. Write this
in scientific notation.
6
1.737 x 10 meters
2. The diameter of a carbon atom is 0.000000000154
meters. Write this in scientific notation.
1.54 x 10-10 meters
3. Convert the following numbers into standard notation:
a. 6.7 x 106 6,700,000
b. 8.8 x 10-4 0.00088
Measurement
• A quantity that has both a number and a unit.
• Fundamental to the experimental sciences.
Accuracy, Precision, and Error
• Accuracy- How close a measure comes to the
actual value of whatever is measured.
• Precision- A measure of how close a series of
measurement are to one another.
XXX
XXX
X
Error
X
X
X
If you boil water and the thermometer
reads 99.1 C . You know that the
boiling point is 100. C. What is the
error?
X
X
Error = Experimental Value – Accepted Value
Error
• Accepted Value = 100
• Experimental value = 99.1
Error = 99.1 – 100
= - 0.9 C
Percent Error =
Error
Accepted Value
Significant Figures
Sig Figs
• Measurements must always be reported to
the correct number of significant figures
because calculated answers depend on the
number of sig figs used in the calculations.
Significant Figures
How would you record the volume of liquid in this
graduated cylinder?
Volume = 9.6 mL
Could I have recorded the volume as 9.65 mL?
What about 10 mL?
What are Significant Figures?
Significant figures are the digits in a measurement that
contribute to the precision. I promise this will make more
sense after a few examples!
The number of significant figures in a measurement
represents how precise that measurement is.
For example, a measurement of 3.1 g (2 sig figs) is less
precise than a measurement of 3.12 g (3 sig figs).
Comparison
This graduated cylinder
reads: 42.9 mL
This beaker reads: 23 mL
Which is more precise??
Counting Significant Figures
Scientists need to be able to count the number of significant
figures in a number. There are rules to do this.
Rule 1
Any digit that is not zero is significant.
Examples:
65.2 has 3 sig figs
7.896735 has 7 sig figs
7,324 has 4 sig figs
Rule 2
Zeros that appear between any two non-zero digits are
significant.
Examples:
504.2 has 4 sig figs
3004.28 has 6 sig figs
6.70809 has 6 sig figs
Rule 3
Leading zeros are not significant. These zeros are
sometimes called placeholders.
Examples:
Leading zeros
0.00005 has 1 sig fig
0.0234 has 3 sig figs
0.0000007081 has 4 sig figs
Remember, this zero is significant!
All these numbers
have 2 sig figs!
52
5.2
0.52
0.052
0.0052
0.00052
Rule 4
Trailing zeros in numbers containing decimals are
significant.
Examples:
trailing zeros
0.5100 has 4 sig figs
0.234000 has 6 sig figs
0.0071200 has 5 sig figs
Leading zeros are not significant
Rule 5
Trailing zeros in numbers that do not contain a decimal are
not significant.
Examples:
trailing zeros
5100 has 2 sig figs
232,000 has 3 sig figs
70,000 has 1 sig fig
70,000. has 5 sig figs
Significant Figures in Scientific
Notation
For numbers in scientific notation, determine the number
of sig figs by looking at the decimal number.
Examples:
5.100 x 103 has 4 sig figs
2.3 x 1026 has 2 sig figs
7.0000 x 10-4 has 5 sig fig