Significant Figures &Scientific Notation

Significant figures are the figures that are known with a degree of certainty.

All measurements have a certain number of significant figures.

Well….we have rules….

What determines whether a digit is significant?

Digits from 1-9 are always significant.

◦ Example: 739

3 Sig figs 83.61

4 Sig Figs

Rule #1

Zeros between nonzero digits are significant.

◦ Example: 2,304

4 Sig Figs 3.009

4 Sig Figs

Rule # 2

Zeros to the right of the decimal and a significant figure are significant.

◦ Example: 2.300

4 Sig Figs 0.470

3 Sig figs

Rule #3

Zeros used for placing the decimal point are not significant.

◦ Example: 0.0082

2 Sig Figs 5400

2 Sig Figs 5400.

4 Sig Figs

Rule #4

When multiplying or dividing, the answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.

Huh????

Multiplication and Division

319 x 4,206

Multiplication and Division

When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

In English please…….

Addition and Subtraction

6.813 + 2.9

Addition and Subtraction

Scientific Notation

How big is the universe?

700,000,000,000,000,000,000,000,000 meters

How big is this number?

Yeah, I don’t have a clue either.

Lets convert this number to scientific notation…

700,000,000,000,000,000,000,000,000 meters

Step 1: Move the decimal point from here◦ To the right of the first non-zero diget.

Step 2: Count the number of spaces you moved the decimal.◦ 26 spaces

..

7.0

Now rewrite the number with one digit to the left of the decimal and a minimum of one digit to the right of the decimal

Then express the number of places the decimal is moved as an exponent of 10

x 1026

Coefficient

Exponent

Scientific Notation works with very small numbers too!

0.00000002067

Step 1: Move the decimal point from here◦ To the right of the first non-zero digit.

Step 2: Count the number of spaces you moved the decimal.◦ 8 spaces

2.067 x 10-8

Because the decimal point was moved to the right, the exponent is negative.

Large numbers◦ Positive exponent

Small numbers◦ Negative exponent

72,000 7.2 x 105

0.0003 3.0 x 10-4

520 5.2 x 102

0.0000040001 4.0001 x 10-6

Multiplying numbers expressed in scientific notation

Multiply (2.4 x 103) x (1.5 x 102) Step 1: Multiply the coefficients

Step 2: Add the exponents

(7.2 x 103) x (3.0 x 105)

(3.2 x 102) x (0.5 x 104)

(2.3 x 104) x (3.1 x 10-2)

Adding numbers expressed in scientific notation.

Exponents must be the same.

Add (5.2 x 105) + (3.7 x 105)

Step 1: Add the coefficients

Step 2: Keep the exponent

(4.027 x 10-4) + (4.872 x 10-4)

(6.3 x 105) + (3.25 x 106)