Scientific Notation

I. A number is expressed in scientific notation when it is written as a product of a facor and a power of 10. The factor must be greater than or equal to 1 and less then 10.

Example: 7.23 x 10⁵ = 723,000 ( The decimal is moved 5 places to the right.)

5.64 x 10^{- 6} = 0.00000564 ( The decimal is moved 6 places to the left.)

II. Scientific to standard notation:

6.85 x  10⁵ 

Move the decimal point 5 places to the right.

685,000

7.95 x 10^-6

Move the decimal point 6 places to the left.

0.00000795

III. Standard to scientific:

7,510,000

Move the decimal point to the right of the last significant digit on the left. Count how many places you move the decimal point. That is the power of 10.

7.51 x 10⁶

0.00000682

Move the decimal point to the right of the first non-zero digit to the right.Count how many places you move the decimal point. The negative of that number is the power of 10.

6.82 x 10^{- 6}

IV. Multiplying scientific notation:

When multiplying two terms in scientific notation, multiply the factors, and add the exponents of 10.

(6.5 x 10⁵ )(7.2 x 10⁶  ) = (6.5)(7.2) x 10^{5 + 6}  = (6.5)(7.2) x 10¹¹ = 4.68 x 10¹² 

V. Dividing scientific notation:

When dividing two terms in scientific notation, divide the factors, and subtract the exponent of 10 in the denominator from the exponent of 10 in the numerator.

(6.6 x 10⁵ ) / (3.3 x 10⁶  ) = (6.6 / 3.3) x 10^{5 - 6}  = (6.6/3.3) x 10^{- 1} = 2 x

 

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