Download Significant Figures Notes

SIGNIFICANT FIGURES
 Significant
figures
Numbers known to have some degree of
reliability
 Critical when reporting scientific data
 Tell accuracy of measurement

For example:
Henry is 2 years old.
Henry is 23 months old.
Henry is 23.25 months old.

Rules for significant figures
All non-zero digits are always significant.
(1,2,3,4,5,6,7,8,9)
1.

Examples
632 = 3 sig figs
72 = 2 sig figs
All zeroes between non-zero numbers are always
significant.
2.

Examples:
303 = 3 sig figs
70004 = 5 sig figs
60204 = 5 sig figs
3.
All zeroes which are simultaneously to the right of
the decimal point AND at the end of the number are
always significant.

4.
Leading zeroes to the left of the first nonzero digit
are NOT significant.

5.
Examples
3.40 = 3 sig figs
7.0 = 2 sig figs
Examples
0.005 = 1 sig fig
0.012 = 2 sig figs
When a number ends in zeroes that are to the left of
the decimal, they are not (necessarily) significant.

Examples
600 = 1 sig fig
70 = 1 sig fig

Rules for Addition and Subtraction

To determine the number of sig figs in your answer:
Count the number of DECIMAL PLACES in the numbers
you are adding or subtracting.
 Your answer cannot contain more decimal places than the
smallest number of decimal places in the numbers being
added or subtracted.
 Example
132.45 (2 decimal places)
49.678 (3 decimal places)
+ 90.3 (1 decimal place)
- 8.23 (2 decimal places)
42.15 (calculator answer)
41.448 (calc. answer)

= 42.2 (1 decimal place)
= 41.45 (2 decimal places)

Rules for multiplication and division

To determine the number of sig figs in your answer
Count the number of significant figures in the numbers you
are multiplying or dividing.
 Your answer cannot contain more significant figures than
the number being multiplied or divided with the least
amount of significant figures.
 Example
332.46 (5 sig figs)
70.45 (4 sig figs)
* 8.29 (3 sig figs)
/ 8.2 (2. sig figs)
2,756.0934 (calc. answer)
8.5914634 (calc. answer)

* 2,760
* 8.6

Scientific Notation
Used to write really large or really small numbers
 Instead of writing 4,000,000,000,000, you could write
4.0 x 1012

Examples:
7,200,000,000
42,869,238,001,043
0.000000000008
0.000000045692
7.2 x 109
4.2 x 1013
8.0 x 1012
4.5 x 108

How to write in scientific notation
Place the decimal point such that there is one nonzero digit to the left of the decimal point (ex. 7.2)
 Count the number of decimal places the number has
moved from the original number. This will be the
exponent of 10.

7,200,000 7.2 the decimal moved 6 spaces
 7.2 x 106
 Of the original number was less than zero, the exponent
will be negative
 If the original number was greater than zero, the exponent
will be positive

7.2 x 107 = 72,000,000.
 7.2 x 10-7 = 0.00000072


Rules for adding/subtracting scientific notation:
 The exponents must have like terms!
 Add/subtract the coefficients
 The base and exponent will remain the same
6.2 x 107
coefficient
base
exponent
7.2 x 104 + 1.1 x 104 = 8.3 x 104
9.2 x 107 – 3.1 x 107 = 6.1 x 107
 Rules
for multiplying scientific notation
Exponents do not have to be the same
 Multiply the coefficient
 Add the exponents

3.2 x 104 x 2.4 x 108 = 7.68 x 1012
4.5 x 104 x 6.4 x 107 = 28.8 x 1011
larger than 10
= 2.88 x 1012
= 2.9 x 1012
7.5 x 10-4 x 1.3 x 10-6 = 9.75 x 10-10
 Rules


for dividing scientific notation
Divide coefficients
Subtract exponents
8.2 x 107 / 3.4 x 105 = 2.4 x 102
5.3 x 105 / 3.7 x 107 = 1.4 x 10-2
4.2 x 10-3 / 1.2 x 10-5 = 3.5 x 102
DIMENSIONAL ANALYSIS
A problem solving method used to convert units.
 Conversion factors

Expression for the relationship between units
 Used to convert units
 Ex. 1 hour = 60 minutes

1 hour
60 minutes
or
60 minutes
1 hour

If you want to convert a unit, you set up the
conversion factors so that the units cancel out
90 minutes = ? Hours
90 minutes x
1 hour
60 minutes
90 minutes x
1 hour
60 minutes
=
1.5 hours