Scientific Notation and Significant Figures

Why do we use Scientific Notation?

Why do we use Scientific Notation?

Chemists often use very LARGE and very SMALL numbers

Examples:

Mass of H atom: 0.000 000 000 000 000 000 000 001 67 g

Mole of atoms: 602 000 000 000 000 000 000 000

Scientific Notation Written as a COEFFICIENT and a

POWER OF 10

Example 1:

2300 = 2.3 x 103

Coefficient

≥ 1 AND <10

Number of times coefficient must be multiplied by ten to get original number

Example 2:

0.0052 =

Example 2:

0.0052 = 5.2 x 10-3

Convert to Scientific Notation

526 000

123

0.0176

624 700 000

0.0010987

19.87 x 10-2

563.28 x 1025

Convert to Scientific Notation

526 000 5.26 x 105

123 1.23 x 102

0.0176 1.76 x 10-2

624 700 000 6.247 x 108

0.0010987 1.0987 x 10-3

19.87 x 10-2 1.987 x 10-1

563.28 x 1025 5.6328 x 1027

Convert to Standard Form

1.26 x 107

4.38 x 10-6

5.9 x 1010

8.6 x 10-13

7.2694 x 103

Convert to Standard Form

1.26 x 107 12 600 000

4.38 x 10-6 0.000 004 38

5.9 x 1010 59 000 000 000

8.6 x 10-13 0.000 000 000 000 86

7.2694 x 103 7269.4

Significant Figures

Scientists report measurements using significant figures

SF: a measurement that includes all the precisely known digits plus a last digit that must be estimated

Measuring using Sig Figs

What is the length of each object?

Sig Fig Rules Every nonzero digit is significant

Zeros between nonzero digits are significant

Zeros in front of all nonzero digits are NOT significant

Zeros at the end of a number and to the right of a decimal are significant

Zeros at the end of a measurement and to the left are NOT significant if there is no decimal at the end

How many Sig Figs?

a. 123 m e. 4.5600 mb. 0.123 m f. 0.078 mc. 40506 m g. 0.070 80 md. 9.8000 x 104 h. 98 000 m

How many Sig Figs?

a. 123 m (3) e. 4.5600 m (5)b. 0.123 m (3) f. 0.078 m (2)c. 40506 m (5) g. 0.070 80 m (4)d. 9.8000 x 104 (5) h. 98 000 m (2)

Addition and Subtraction

The answer can have no more digits to the right of the decimal point than the measurement with the least number of digits after the decimal.

ex. 1 12.52 + 349.0 + 8.24 = ex. 2 740626 - 86.34 =

Multiplication and Division

The answer must contain no more significant figures that the measurement with the least number of significant figure

a. 7.44 m x 0.34 m =b. 2.4526 m / 8.4 =

Practice Problems

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