Scientific Notation Chemistry

Scientific Notation Expresses numbers as a multiple of two factors: A number between 1- 10 10 raised to a power or exponent 6.23 x 10 23

Scientific Notation When numbers larger than 1 are expressed in scientific notation, the exponent is positive. 2.0 x 10 3 = 2000 When numbers smaller than 1 are expressed in scientific notation, the exponent is negative. 2.0 x 10 -3 = 0.002

Scientific Notation Moving the decimal. The exponent just tells you how many times you had to move the decimal. Positive exponent, we move to the left. + - Negative exponent, we move to the right.

Practice Express the following in scientific notation: 700m 38 000m 4 500 000m 685 000 000 000m

Answers 7 x 10 2 3.8 x 10 4 4.5 x 10 6 6.85 x 10 11

Practice Express the following in scientific notation: 0.0054 kg 0.000 006 kg 0.000 000 076 kg 0.000 000 000 8 kg

Answers 5.4 x10 -3 6 x 10 -6 7.6 x 10 -8 8 x 10 -10

Adding and Subtracting Scientific Notation Chemistry A

We just add 7.35 and 2.43, don’t worry about adding the exponents. Adding & Subtracting When we add or subtract with these numbers the first thing we must do is make sure the exponents are the same for both number. 7.35 x 10 2 + 2.43 x10 2 We just add 7.35 and 2.43, don’t worry about adding the exponents. = 9.78 x10 2

Adding & Subtracting Must make exponents the same before you continue to add or subtract. 5.40 x 10 3 + 6.00 x 10 2 We must move the decimal to make them the same. The decimals must be aligned 5.40 x 10 3 + 0.60 x 10 3 6.00 x 10 3

If the exponents are not the same then we must make them match each other. We will match it to the first number if and only if the first number is between 1-10. 2.50 x 10 4 + 6.50 x10 3 6.50 x 10 3 = .650 x10 4 2.50 x 10 4 + .650 x10 4 3.15 x 10 4

Practice 5 x 10 -5 + 2 x10 -5 7 x 10 -5 4 x 10 -12 + 1 x10 -12

Subtracting Is basically the same thing, except we’re subtracting instead of adding. We still have to make sure that the exponents are the same.

9 x 10 2 - 7 x10 2 2 x 10 2 7 x 10 8 - 4 x10 8 3 x10 8 4.39 x 10 5 – 2.8 x10 4 4.11 x 10 5 5.36 x 10 -1 – 7.40 x10 -2 4.62 x 10 -1

Multiplying & Dividing We multiply or divide the coefficients (decimal numbers) and add or subtract the exponents. 3.0 x 10 4 x 2.0 x 10 2 = (3.0 x 2.0) x 10 (4+2) = 6.0 x 10 6