SIGNIFICANT FIGURES

SIGNIFICANT FIGURES

Significant Figures ( SigFigs) Measured digits in a reported number. More SigFigs = more confidence Less SigFigs = less confidence

A Laboratory instrument is read as far it can be, and the last number is estimated.

There are Limitations to how confident you can be! Compare 2m vs. 2.00 m Which one seems more confident?

What is the correct mass to report?

Measured Mass is _______________

What is the correct mass to report?

Measured Mass is 500 + 40 + 6.25 g

OR 546.25 g

SIGNIFICANT FIGURES

Rules for recognizing SigFigs: When a number has a decimal: Read Left to Right until you Reach the first nonzero number Then you begin counting SigFigs Until you run out of digits (including any

zeros along the way) Example: 0.003210 g = _______ SigFigs?

SIGNIFICANT FIGURES

Practice: 82.700 K ____sig figs 0.000365 J ____sig figs 3.034 g ____sig figs 3.220 x 105 m ____sig figs

SIGNIFICANT FIGURES Rules for recognizing SigFigs:

When a number has no decimal: Read Right to Left until you Reach the first nonzero number Then you begin counting SigFigs Until you run out of digits (including any

zeros along the way) Example: 450300 m = _______ SigFigs?

SIGNIFICANT FIGURES

Practice: 421 m ____ sig figs 800,890 J ____sig figs 39,059,000 g ____sig figs 523,000 L ____sig figs

SIGNIFICANT FIGURES

Counted Quantites and Constants have absolute values & we don’t count SigFigs Either you counted the number of items right, or you

didn’t!Example:14 bananas

SIGNIFICANT FIGURES

How many significant figures are in each of the following numbers?

1. 5.40 ng ____2. 1.2 x 103 mt ____3. 210 N ____4. 0.00120 mL ____5. 801.5 K ____6. 0.0102 Amp

____7. 1,000 BTU ____8. 9.010 x 10-6 dm ____9. 101.0100 D

____10. 2,370.0 Cal

____

SIGNIFICANT FIGURES

Why are significant figures important when taking data in the laboratory?

When you measure something, you never get 100% accuracy on its measurement, so you need a way to show just how accurate it is.

SIGNIFICANT FIGURES

Why are significant figures NOT important when solving problems in your math class?

In math, we assume that all numbers are either 100% accurate, or that they are constants, and thus have no uncertainty or error involved in their creation.

SIGNIFICANT FIGURES

Using two different instruments, I measured the length of my foot to be 27 centimeters and 27.00 centimeters. Explain the difference between these two measurements.

The second measurement was made with a ruler that had more graduations, giving a higher level of certainty and more Significant Figures

SIGNFICANT FIGURES AND MATH

We will be required to do math with our SigFigs

Two rule sets cover this: Addition/SubtractionAnd Multiplication/Division

ADDITION AND SUBTRACTION SIG FIG RULES

1. line up the decimals2. draw a line to the right of the number with

the least precision (shortest column) 3. answer can’t go past the line4. use the 1st digit past the line to determine

where to round offExample:32.00 m + 48.1 m + 182.213 m = ????

ADDITION AND SUBTRACTION SIG FIG RULES

1. line up the decimals2. draw a line to the right of the number with the least precision

(shortest column) 3. answer can’t go past the line4. use the 1st digit past the line to determine where to round offExample:32.00 m + 48.1 m + 182.213 m = ????

32.00 m48.1 m

182.213 m+____________262.313 m

Must round to: 262.3 m

ADDITION AND SUBTRACTION SIG FIG RULES

1. 210.6 mm + 14.57 mm = ____________

2. 74.000 cm + 8.6 cm =____________

3. 0.0787 m + 0.85 m =____________

4. 84000 cm + 1110 cm =____________

5. 92008 g + 32100 g =____________

6. 8.000 mm + 0.0304 m =____________

7. 84.34 g - 5.2 g =____________

8. 9.81 cm - 3.151 cm =____________

9. 0.0900 n - 0.0094 n =____________

MULTIPLYING AND DIVIDING SIG FIG RULES

Answer can have no more SigFigs than the factor with the fewest number of SigFigs. This means that constants and

quantities do not affect sigfigs in the answer!

Example: 127.3 x 42 = ???

MULTIPLYING AND DIVIDING SIG FIG RULES

1. 500 kg X 32 kg =____________

2. 680.0 n X 100. n =____________

3. 8560.0 g X 1000 g =____________

4. 4560 m X 0.100 m =____________

5. 85 kg X 0.001 kg =____________

6. 9200 L ÷ 873 L =____________

7. 0.85 2 kg2 ÷ 62 kg =____________

8. 985 g2 ÷ 500. g =____________

9. 10000 n2 ÷ 0.10 n =____________

10. 0.0006 g2 ÷ 25 g=____________