Bellringer: Write down the 3 Quick Rules for Sig Fig zeros: Leading zeros are never significant “Sandwiched” zeros are always significant Trailing zeros are only significant when there’s a decimal

Bellringer: Finish the rules by memory Leading zeros ________________ “Sandwiched” zeros ___________ Trailing zeros are _____________ ____________________________

How many Sig Figs? 0.02030 76,000 56.706 7.00 0.0398 9,008,030,000 4 2 5 3 6

Wilson Physics/Chemistry Significant Figures Wilson Physics/Chemistry

What is a significant figure? There are 2 kinds of numbers: Exact: the amount of money in your account. Known with certainty. Approximate: weight, height; anything MEASURED. No measurement is perfect!

Why use Significant figures When a measurement is recorded only those digits that are dependable are written down.

When to use Significant figures If you measured the width of a paper with your ruler you might record 21.7cm. To a mathematician 21.7, 21.70, 21.700 or 21.7000 is the same. 21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm!

But, to a scientist 21.7cm and 21.70cm is NOT the same If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7_cm.

How do I know how many Sig Figs are in a number? All digits are significant starting with the first non-zero digit on the left.

Sig Fig rules for zeros

1st Rule If there is no decimal, zeros at the end of the number are NOT significant

2nd Rule If zeros are sandwiched between non-zero digits, the zeros are significant.

3rd Rule If zeros are at the end of a number that has a decimal, the zeros ARE significant. WHY????

3rd Rule They are showing how accurate the measurement or calculation is!

Quick rules for Sig Fig zeros: Leading zeros are never significant “Sandwiched” zeros are always significant Trailing zeros are only significant when there’s a decimal.

Quick Example: How many of the zeros in the following number are significant? Which ones? 03075.007900

Quick Example: How many of the zeros in the following number are significant? Which ones? 10,720

How many sig figs? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 4 3

How many sig figs here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 6

Everybody’s favorite monster! Scientific Notation Everybody’s favorite monster!

Parts of a “scientific” number

Parts of a “scientific” number

In scientific notation, the coefficient must ALWAYS be a number between 1-10

1. Adding & Subtracting with Sig Figs Video Examples 1. Adding & Subtracting with Sig Figs http://www.youtube.com/watch?v=2eXC6s9X6Wc Multiplying & Dividing with Sig Figs http://www.youtube.com/watch?v=o5BmoMDJLRY Scientific Notation & Sig Figs http://www.youtube.com/watch?v=IIQPHC5gZT8

What about calculations with Sig Figs?

Calculations with sig figs Rule #1: Do the math FIRST, THEN calculate the number of significant figures!

Calculations with sig figs Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

Add/Subtract examples

Add/Subtract examples 2.45cm + 1.2cm = 3.65cm… = ? Round off to = 3.7cm 7.432cm + 2cm = 9.432…= ? Round off to 9 cm

Multiplication and Division Rule #2: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

A couple of examples 56.78 cm x 2.45cm = 139.111 cm2 Round to  139 cm2 75.8cm x 9.6cm = ?

Prepare For A Quiz!!!

Significant Figures Quiz Tell the number of Significant Figures in the following numbers: 4502 6. 050 035.70 7. 76050 5.000 8. 3.05 x 10-7 80,000 9. 2.9 x 103 0.0030 10. 13.070

Significant Figures ANSWERS Tell the number of Significant Figures in the following numbers: 4502 (4) 6. 050 (1) 035.70 (4) 7. 76050 (4) 5.000 (4) 8. 3.05 x 10-7 (3) 80,000 (1) 9. 2.9 x 103 (2) 0.0030 (2) 10. 13.070 (5)