Scientific NotationAP Chemistry August 11th, 2015

Scientific Notation To represent very large numerical values

or very small numerical values, we will use scientific notation!

Scientific NotationTo be in proper scientific notation the number must be written with* a coefficient term between 1 and 10* and multiplied by a power of

ten 23 X 105 is not in proper scientific

notation. Why?

Scientific Notation

A positive exponent shows that the decimal point is shifted that number of places to the right. (Number is large aka greater than 1)

A negative exponent shows that the decimal point is shifted that number of places to the left. (Number is small aka less than 1)

Scientific Notation-Powers of Ten

Scientific Notation Using scientific notation, rewrite the following numbers. Or convert back to

standard notation.

347,000.

902,000,000.

61,400.

1.23 X 105

6.806 X 106

Scientific Notation Using scientific notation, rewrite the following

numbers. Or convert back to standard notation. 347,000.

3.47 X 105

902,000,000. 9.02 X 108

61,400. 6.14 X 104

1.23 X 105

123,000 6.806 X 106

6,806,000

Scientific Notation

4,000

2.48 X 103

6.123 X 106

306,000,000

Scientific Notation4,000

4 X 103

2.48 X 103

2,4806.123 X 106

6,123,000306,000,000

3.06 X 108

Scientific Notation

Negative powers of ten:

Scientific NotationUsing Scientific Notation,

rewrite the following numbers.

0.000882

0.00000059

0.00004

Scientific NotationUsing Scientific Notation,

rewrite the following numbers. 0.000882

8.82 X 10-4

0.00000059 5.9 X 10-7

0.00004 4 X 10-5

Scientific Notation

0.0004

1.248 X 10-6

6.123 X 10-5

0.00000306

0.000892

Scientific Notation 0.0004

4 X 10-4

1.248 X 10-6

0.000001248 6.123 X 10-5

0.00006123 0.00000306

3.06 X 10-6

0.000892 8.92 X 10-4

MultiplicationWhen multiplying numbers written in scientific notation…..multiply the first factors and add the exponents.

Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105)

Division

Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator.

Sample Problem: Divide (6.4 x 106) by (1.7 x 102)

Practice1. (3.05 x 106) ÷ (4.55 x 10¯10)

2. (2.68 x 10¯5) x (4.40 x 10¯8)

3. (8.41 x 106) x (5.02 x 1012)

4. (9.21 x 10¯4) ÷ (7.60 x 105)