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Mathematical Operations Using Numbers in Scientific NotationPowerPoint Presentation

Mathematical Operations Using Numbers in Scientific Notation

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### Using Pre-determined Measurements in CalculationsThe value given in your calculation will influence the number of sig figs in your answer.

Adding

All numbers must be expressed in the same power of 10

(A x 10m) + (B x 10m) (A + B) x 10m

(1.234 x 10‾³) + (5.623 x 10‾3) =

1.234

+ 5.623

6.857 = 6.857 x 10‾3 (answer is in correct sig figs)

Adding

All numbers must be expressed in the same power of 10

(A x 10m) + (B x 10m) (A + B) x 10m

(2.2 x 10³) + (4.12 x 103) =

- Line up the decimals and add
2.2 x 10³

+ 4.12 x 103

6.32 x 103 = 6.3 x 103 (round to correct sig figs)

When moving decimals:If you move the decimal to the right, add (-1) to the exponentIf you move the decimal to the left, add (+1) to the exponent

10.85 X 10-2 need to move the decimal to the left so will add a (+1)

= 10.85 X 10-2+1 = 1.085 X 10-1

If your result is:

0.233 x 102 need to move the decimal to the right so will add a (-1)

= 0.233 x 102-1 = 2.33 X 101

Different Exponents

(1.234 x 10‾³) + (5.623 x 10‾²) =

Doesn’t matter which exponent you change

(1.234 x 10‾³)+ (56.23 x 10-2+-1=-3) = 57.464 x 10‾²

1.234

+56.23

57.464 x 10‾³ = 57.46 x 10‾³

= 5.746 x 10‾²

(0.1234 x 10‾²) + (5.623 x 10‾²) = 5.746 x 10‾²

Addition

(0.1234 x 10‾2) + (5.623 x 10‾²) =

Doesn’t matter which exponent you change

(0.1234 x 10‾²) + (5.623 x 10‾²) = 5.7464 x 10‾2

= 5.764 x 10‾2

OR

(1.234 x 10‾³) - (56.23 x 10-2+-1=-3) = 57.464 x 10‾²

1.234

- 56.23

-57.464 x 10‾³ = -5.746 x 10‾²

Check your work!

(1.234 x 10‾³) + (5.623 x 10‾²) =

0.001234 + 0.05623 =

0.001234

+0.05623

0.057464 = 5.746 x 10‾²

Subtracting

2000 X 104 – 5 X 104 = 1995 X 104

Need to round answer to correct sig figs!

1995 X 104 becomes 2000 X 104

Still not done!

2000 X 104 = move the decimal 3 places to the left and add “3” to the exponent 2000 X 104+3 = 2 x 107

Multiplying

Multiply the decimal parts

Add the exponents of 10s

(A x 10m) x (B x 10n) (A x B) x 10(m +n)

(1.23 x 103) x (7.60 x 102) =

(1.23 x 7.60) x 10 (3 + 2)

= 9.348 x 10 5

= 9.35 x 10 5

(ROUND TO CORRECT SIG FIGS)

Example

(4.16 x 103)(2 x 104) =

Dividing

Divide the decimal parts

Subtract the exponents

(A x 10x) (B x 10y) (A B) x 10(x-y)

or

A

B

10(x-y)

x

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