Chemistry NotesSignificant Figures &

Scientific Notation

We can describe and use numbers in several different ways. These include scientific notation and significant figures.

Describing Numbers

In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power.

Scientific Notation

Examples:Convert to or from Scientific Notation:

241 =6015 =0.0162 =0.512 =6.62 x 102 =3.4 x 10-3 =

2.41 x 102

6.015 x 103

1.62 x 10-2

5.12 x 10-1

662.0034

Significant figures are the numbers in a measurement that “matter”.

Significant Figures

Rules for determining Significant Figures

1. All non-zero digits are significant.

1, 2, 3, 4, 5, 6, 7, 8, 9

2. Zeros between non-zero digits are significant.

(AKA captive or trapped zeros)

102 70023 sig figs

4 sig figs

3. Leading zeros (zeros at the beginning of a measurement) are NEVER significant.

0.0152 005423 sig figs

3 sig figs

4. Trailing zeros (zeros after last integer) are significant only if the number contains a decimal point.

210.0

0.860

5240

524000

5240.

5240.0

4

3

3

3

4

5

5. All digits in the coefficient are significant in scientific notation.

2.1 x 10-5 6.02 x 1023

2 3

6. Exact numbers have unlimited Significant Figures

Examples:1 dozen = exactly 12

Examples:How many significant digits do each of the following numbers contain:

a) 1.2 d) 4600

b) 2.0 e) 23.450

c) 3.002 f) 6.02 x 1023

2

2

4

2

5

3

Rounding: 5 round up< 5 round down (don’t change)

Examples:Round 42.63 to 1 significant digit =Round 61.57 to 3 sig. digs. =Round 0.01621 to 2 =Round 65,002 to 2 sig. digs. =

4061.6

0.016 65,000 or 6.5 x104

Addition and Subtraction

– The measurement with the fewest decimal places to the right of the decimal point determines the number of decimal places in the answer.

Examples:

Solve using correct significant figures

45.756 m + 62.1 m =

75.263 m + 1123.93 m =

107.9m

1199.19m

Multiplying and Dividing Measurements

- The measurement with the fewest total significant figures determines the number of significant figures in the answer.

Examples:Solve using correct significant figures:

3.43 m X 6.4253 m =

45.756 m X 1.2 m =

45.01 m / 2.2 m =

22.0 m2

55 m2

20. m2

22.038779 m2

54.9072 m2

20.45909091 m2