Practice:

a) 27.68 cm –14.369 cm =b) 6.54 m x 0.37 m =c) 40.8 m2 ¸ 5.050 m =

Practice:

a) 27.68 cm –14.369 cm = 13.311 13.31b) 6.54 m x 0.37 m = 2.4198 2.4c) 40.8 m2 ¸ 5.050 m = 8.07921 8.08

Raw Math Value

Sig. Fig. Value

Scientific

Notation

Thursday, August 13th, 2015

Textbook pages 63 –

65

Scientific Notation

Scientific notation is way of writing numbers that are too big or too small to be conveniently written in decimal form

Rules for Scientific Notation

To be in proper scientific notation the number must be written with

* a number between 1 and 10

* and multiplied by a power of

ten

23 X 105 is not in proper scientific notation. Why?

1. Move the decimal to the right of the first non-zero

number.2. Count how many places the

decimal had to be moved.3. If the decimal had to be moved

to the right, the exponent is negative.

4. If the decimal had to be moved to the left, the exponent is positive.

To write a number in scientific notation:

BIGExamples!

300 = 3 x 102

60,000 = 6 x 104

98,000,000 = 9.8 x 107

8657 = 8.657 x 103

250 =

36,700 =

785,000,000 =

99,000,000,000 =

Try

These

4,000

2.48 X 103

6.123 X 106

306,000,000

5.70 x 105

Convert each from scientific notation into standard/long form or vice versa

small

Examples!

0.02 = 2 x 10-2

0.0065 = 6.5 x 10-3

0.0000708 = 7.08 x 10-5

0.000000001 = 1 x 10-9

0.25 =

0.0036 =

0.00007001 =

0.00000003 =

Why does a Negative Exponent give us a small

number?

10000 = 10 x 10 x 10 x 10 = 104

1000 = 10 x 10 x 10 = 103

100 = 10 x 10 = 102

10 = 101

1 = 100

Do you see a pattern?

Try

These0.00873

3.48 X 10-4

0.156

0.00000099

5.70 x 10-6

Convert each from scientific notation into standard/long form or vice versa

10,003 9.57 x 10-7

1.6 x 103 507,000,000

0.0001 3.301 x 105

6.1 x 1010 1.8 x 10-9

10,000,000,000 0.0045

Convert each from scientific notation into standard/long form or vice versa

Multiplication

When 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)

Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5

Answer: 6.7 x 102

DivisionDivide 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)Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2

Answer: 3.8 x 104

Addition and SubtractionTo add or subtract numbers written in

scientific notation, you must….express them with the same power of ten.

Sample Problem: Add (5.8 x 103) and (2.16 x 104)Solution: Since the two numbers are not

expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other.

5.8 x 103 = .58 x 104 so .58 x 104 + 2.16 x 104 =?Answer: 2.74 x 104