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PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION

ADDITION AND SUBTRACTION

Review

Scientific notation expresses a number in the

form

M x 10n

n is an integer

1 ? M ? 10

IF the exponents are the same, we simply add or

subtract the numbers in front and bring the

exponent down unchanged.

4 x 106

3 x 106

_______________

7

x 106

IF the exponents are the same, we simply add or

subtract the numbers in front and bring the

exponent down unchanged.

4 x 106

3 x 106

_______________

7

x 106

If the exponents are NOT the same, we must move a

decimal to make them the same.

4 x 106

3 x 105

4.00 x 106

4.00 x 106

.30 x 106

3.00 x 105

4.30

x 106

Move the decimal on the smaller number!

A Problem for you

2.37 x 10-6

3.48 x 10-4

Solution

2.37 x 10-6

002.37 x 10-6

3.48 x 10-4

Solution

0.0237 x 10-4

3.48 x 10-4

3.5037 x 10-4

Addition and subtraction Scientific Notation

2.0 x 102 3.0 x 103

1. Make exponents of 10 the same 2. Add 0.2 3

and keep the 103 intact The key to adding or

subtracting numbers in Scientific Notation is to

make sure the exponents are the same.

.2 x 103 3.0 x 103 .23 x 103 3.2 x 103

2.0 x 107 - 6.3 x 105

2.0 x 107 -.063 x 107 2.0-.063 x 107 1.937

x 107

1. Make exponents of 10 the same 2. Subtract 2.0

- .063 and keep the 107 intact

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION

MULTIPLYING AND DIVIDING

- Rule for Multiplication
- When multiplying with scientific notation
- Multiply the coefficients together.
- Add the exponents.
- The base will remain 10.

(2 x 103) (3 x 105)

6 x 108

(9.2 x 105) x (2.3 x 107) 21.16 x 1012

2.116 x 1013

(3.2 x 10-5) x (1.5 x 10-3)

4.8 10-8

- Rule for Division
- When dividing with scientific notation
- Divide the coefficients
- Subtract the exponents.
- The base will remain 10.

(No Transcript)

(8 106) (2 103)

4 x 103

(3.402 x 105) (6.3 x 107)

0.54 x 10-2

Please multiply the following numbers.

(5.76 x 102) x (4.55 x 10-4)

(3 x 105) x (7 x 104)

(5.63 x 108) x (2 x 100)

(4.55 x 10-14) x (3.77 x 1011)

(8.2 x10-6) x (9.4 x 10-3)

Please multiply the following numbers.

(5.76 x 102) x (4.55 x 10-4)

2.62 x 10-1

(3 x 105) x (7 x 104)

2.1 x 1010

(5.63 x 108) x (2 x 100)

1.13 x 109

(4.55 x 10-14) x (3.77 x 1011)

1.72 x 10-2

(8.2 x10-6) x (9.4 x 10-3)

7.71 x 10-8

Please divide the following numbers.

- (5.76 x 102) / (4.55 x 10-4)
- (3 x 105) / (7 x 104)
- (5.63 x 108) / (2)
- (8.2 x 10-6) / (9.4 x 10-3)
- (4.55 x 10-14) / (3.77 x 1011)

Please divide the following numbers.

- (5.76 x 102) / (4.55 x 10-4) 1.27 x 106
- (3 x 105) / (7 x 104) 4.3 x 100 4.3
- (5.63 x 108) / (2 x 100) 2.82 x 108
- (8.2 x 10-6) / (9.4 x 10-3) 8.7 x 10-4
- (4.55 x 10-14) / (3.77 x 1011) 1.2 x 10-25

Scientific Notation Makes These Numbers Easy

9.54x107 miles

1.86x107 miles per second

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