Mathematical operations using numbers in scientific notation
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Mathematical Operations Using Numbers in Scientific Notation. Adding. All numbers must be expressed in the same power of 10 (A x 10 m ) + (B x 10 m )  (A + B) x 10 m (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.

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Adding
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)


Adding1
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
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
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
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
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
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
Example

(4.16 x 103)(2 x 104) =


Dividing
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


Example:

(4.68 x 10-3) ÷ (4.00 x 10-5)

4.68

4.00

10 -3-(-5) = 1.17 x 102

x


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



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