Scientific NotationScientific NotationChemistryChemistry

Scientific NotationScientific Notation

Expresses numbers as a multiple of two Expresses numbers as a multiple of two factors:factors:

A number between A number between 1- 101- 10

10 raised to a power or 10 raised to a power or exponentexponent

6.236.23 x x 10 10 23 23

Scientific NotationScientific NotationWhen numbers larger than 1 are expressed When numbers larger than 1 are expressed in scientific notation, the exponent is in scientific notation, the exponent is positive.positive.

2.0 x 10 2.0 x 10 33 = 2000= 2000

When numbers smaller than 1 are When numbers smaller than 1 are expressed in scientific notation, the expressed in scientific notation, the exponent is negative.exponent is negative.

2.0 x 10 2.0 x 10 -3 -3 = 0.002= 0.002

Scientific NotationScientific NotationMoving the decimal.Moving the decimal.

The exponent just tells you how many times you The exponent just tells you how many times you had to move the decimal.had to move the decimal.

PositivePositive exponent, we move to the exponent, we move to the left.left.

++ --NegativeNegative exponent, we move to the exponent, we move to the right.right.

PracticePracticeExpress the following in scientific notation:Express the following in scientific notation:

700m700m

38 000m38 000m

4 500 000m4 500 000m

685 000 000 000m685 000 000 000m

AnswersAnswers

7 x 10 7 x 10 22

3.8 x 10 3.8 x 10 44

4.5 x 10 4.5 x 10 66

6.85 x 10 6.85 x 10 1111

PracticePracticeExpress the following in scientific notation:Express the following in scientific notation:

0.0054 kg0.0054 kg

0.000 006 kg0.000 006 kg

0.000 000 076 kg0.000 000 076 kg

0.000 000 000 8 kg0.000 000 000 8 kg

AnswersAnswers

5.4 x10 5.4 x10 -3-3

6 x 10 6 x 10 -6-6

7.6 x 10 7.6 x 10 -8-8

8 x 10 8 x 10 -10-10

Adding and Subtracting

Scientific NotationChemistry AChemistry A

Adding & Adding & SubtractingSubtractingWhen we add or subtract with these When we add or subtract with these

numbers the first thing we must do is make numbers the first thing we must do is make sure the exponents are the same for both sure the exponents are the same for both number.number.

7.357.35 x 10 x 10 22 + + 2.432.43 x10x10 22

We just add We just add 7.357.35 and and 2.432.43, don’t worry about , don’t worry about adding the exponents.adding the exponents.

== 9.789.78 x10x10 22

Adding & Adding & SubtractingSubtracting

Must make exponents the same before you Must make exponents the same before you continue to add or subtract. continue to add or subtract.

5.40 x 10 5.40 x 10 3 3 + 6.00 x 10 + 6.00 x 10 22

We must move the decimal to make them the We must move the decimal to make them the same.same.

The decimals must be alignedThe decimals must be aligned

5.40 x 10 5.40 x 10 33

+ 0.60 x 10 + 0.60 x 10 33

6.00 x 10 6.00 x 10 3 3

If the exponents are not the same then we If the exponents are not the same then we must make them match each other.must make them match each other.

We will match it to the first number if and We will match it to the first number if and only if the first number is between 1-10.only if the first number is between 1-10.

2.502.50 x 10 x 10 44 + + 6.506.50 x10 x10 33

66..50 x 10 50 x 10 33 == ..650 x10 650 x10 44

2.502.50 x 10 x 10 44 + + .650 .650 x10 x10 44

3.153.15 x 10 x 10 44

PracticePractice5 x 10 5 x 10 -5-5 + 2 x10 + 2 x10 -5-5

7 x 10 7 x 10 -5-5

4 x 10 4 x 10 -12-12 + 1 x10 + 1 x10 -12-12

5 x10 5 x10 -12-12

1.26 x 10 1.26 x 10 44 + 2.5 x10 + 2.5 x10 33

1.51 x 10 1.51 x 10 44

7.06 x 10 7.06 x 10 -3-3 + 1.2 x10 + 1.2 x10 -4-4

7.18 x 10 7.18 x 10 -3-3

SubtractingSubtractingIs basically the same thing, except Is basically the same thing, except we’re subtracting instead of adding.we’re subtracting instead of adding.

We still have to make sure that the We still have to make sure that the exponents are the same.exponents are the same.

9 x 10 9 x 10 22 - 7 x10 - 7 x10 22

2 x 10 2 x 10 22

7 x 10 7 x 10 88 - 4 x10 - 4 x10 88

3 x10 3 x10 88

4.39 x 10 4.39 x 10 55 – 2.8 x10 – 2.8 x10 44

4.11 x 10 4.11 x 10 55

5.36 x 10 5.36 x 10 -1-1 – 7.40 x10 – 7.40 x10 -2-2

4.62 x 10 4.62 x 10 -1-1

Multiplying & Multiplying & DividingDividing

We multiply or divide the We multiply or divide the coefficients coefficients (decimal numbers) (decimal numbers) and add or subtract and add or subtract the the exponentsexponents. .

3.03.0 x 10 x 10 44 x x 2.02.0 x 10 x 10 22 = = ((3.0 x 2.03.0 x 2.0) x 10 ) x 10 ((4+24+2) ) = =

6.06.0 x 10 x 10 66