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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

Any number between 1 and 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 NOT the same, we must move a

decimal to make them the same.

4 x 106

3 x 105

- Determine which of the numbers has the smaller

exponent. - Change this number by moving the decimal place to

the left and raising the exponent, until the

exponents of both numbers agree. Note that this

will take the lesser number out of standard form. - Add or subtract the coefficients as needed to get

the new coefficient. - The exponent will be the exponent that both

numbers share. - Put the number in standard form.

4.00 x 106

4.00 x 106

.30 x 106

3.00 x 105

Move the decimal on the smaller number to the

left and raise the exponent !

Note This will take the lesser number out of

standard form.

4.00 x 106

4.00 x 106

.30 x 106

3.00 x 105

4.30

x 106

Add or subtract the coefficients as needed to get

the new coefficient. The exponent will be the

exponent that both numbers share.

Make sure your final answer is in scientific

notation. If it is not, convert is to

scientific notation.!

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

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

(4.6x108) (5.8x106) 26.68x1014 Notice What is

wrong with this example?

Although the answer is correct, the number is not

in scientific notation.

To finish the problem, move the decimal one space

left and increase the exponent by one.

26.68x1014 2.668x1015

((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.

(8 106) (2 103)

4 x 103

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

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION

Raising Numbers in Scientific Notation To A Power

(5 X 104)2 (5 X 104) X (5 X 104) (5 X 5) X

(104 X 104) (25) X 108 2.5 X 109

Try These

- (3.45 X 1010)2
- (4 X 10-5)2
- (9.81 X 1021)2

1.19 X 1021

1.6 X 10-9

9.624 X 1043

- (3.45 X 1010)2 (3.45 X 3.45) X (1010 X 1010)

(11.9) X (1020) 1.19 X 1021 - (4 X 10-5)2 (4 X 4) X (10-5 X 10-5) (16) X

(10-10) 1.6 X 10-9 - (9.81 X 1021)2 (9.81 X 9.81) X (1021 X 1021)

(96.24) X (1042) 9.624 X 1043

Scientific Notation Makes These Numbers Easy

9.54x107 miles

1.86x107 miles per second

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