Significant Figures

Aren’t all numbers Aren’t all numbers important?!?!?!?important?!?!?!?

Yes, but some are more Yes, but some are more significantsignificant than others… than others…

Accuracy / Precision

Accuracy – the agreement between a measured value and a true value.

Precision – agreement between several measurements of the same quantity.

Significant Figures

A measurement can only be as accurate and precise as the instrument that produced it.

A scientist must be able to express the accuracy of a number, not just its numerical value

Significant Figures

We can determine the accuracy of a number by the number of significant figures it contains.

Doing Math with Sig. Figs.

If you add two numbers together the answer is only as precise as your least precise number.

Your answer will have only as many digits after the decimal point as your leastPrecise number.

Example:

5.46 + 2.0 + 3.1111 = 10. 571

The 2.0 has only 1 significant figure past the decimal, so our answer can only have 1 digit pas the decimal.

Answer = 10.6

ADDING AND SUBTRACTING:

Multiplication and Division with Sig. Figs.

Your answer can only be as precise as your least precise number.

This time we are not just worried about after the decimal, but the least precise number as a whole.

You answer should have the same number of significant figures as the number In the problem with the fewest significant figures.

Example:

(3.78 x 4.0001 x 4.5) = 68.041701

The 4.5 only has two significant figures so our answer can only have two.

Answer = 68

Scientific Notation

Helping us write really tiny or

really big numbers

Carelessness when using numbers

I have a million math problems to doI have a trillion things to get done tonight

If you win 1 million dollars and you’re given the prize in 100 dollar bills, your stack of money is….

4 inches high

Rules to Scientific Notation

Parts:

1. Coefficient (mantissa) – must be a number from 1 – 9.9

2. Exponent – a power of 10

3.4 x 106

Easier than writing 3,400,000

Numbers Greater Than 10

1. Find the number by moving the decimal point that is between 1 – 9.9

45,300,000 4.53

2. Write a positive exponent which is equal to the number of places you moved the decimal point to the left.

4.53 x 107

Numbers Less Than 1

1. Find the number by moving the decimal point that is between 1 – 9.9

0.000291 2.91

2. Write a negative exponent which is equal to the number of places you moved the decimal point to the right.

2.91 x 10-4

Math Operations & Sci. Notation

For Multiplication:

multiply coefficients

add exponents

(3.0 x 104) x (2.0 x 102) = 6.0 x 106

3 x 2 = 6 4 + 2 = 6

Math Operations & Sci. Notation

For Division:

divide coefficients

subtract exponents

(6.4 x 106) / (1.7 x 102) = 3.8 x 104

6.4 / 1.7 = 3.8 6 – 2 = 4

Be Careful…

Remember the rule about the coefficient!

Ex. (4.0 x 103) x (3.0 x 104) = 12.0 x 107

WRONG!!!

Answer = 1.2 x 108

Math Operations & Sci. Notation

For Addition and Subtraction:must make the exponents the same

Ex. 5.4 x 103 + 6.0 x 104 =

0.54 x 104

+6.0 x 104

6.5 x 104

Special Note

Sometimes exponents are written differently.

We are used to 3.4 x 105

However, you may see 3.4E5It means the same thing (“E” represents

the exponent and replaces x 10

Write in Scientific Notation and Determine the number of sig.

figs.1. 0.02 _____2. 0.020_____3. 501 _____4. 501.0_____5. 5,000_____6. 5,000. _____7. 6,051.00 _____8. 0.0005 _____9. 0.1020 _____10. 10,001 _____

11. 8040 ______12. 0.0300 ______13. 699.5 ______ 14. 2.000 x 102 ______15. 0.90100 ______16. 90,100 ______17. 4.7 x 10-8 ______18. 10,800,000. ______19. 3.01 x 1021 ______20. 0.000410 ______