How to determine and use the proper sig. figs. Significant Figures How to determine and use the proper sig. figs.

What is a significant figure? There are 2 kinds of numbers: Exact numbers Measured numbers

What is a significant figure? 1) Exact: don’t come in fractions or decimals!!! Ex: humans Ex: bacterial colonies on a petri dish

What is a significant figure? On the other hand…not everything is so easy…sometimes you have to … Approximate: A close guess that is in the ball park.

When to use Significant figures 2) Measured numbers Using a tool/ device to measure…you must ask yourself what are the limits of the tool/ device. Ex:

When to use Significant figures You could measure Arrow “A” as 3.9cm. But to some mathematicians 3.9cm, or 3.90cm is the same. A

But, to a scientist 3.9cm and 3.90cm is NOT the same Key difference But, to a scientist 3.9cm and 3.90cm is NOT the same

Uncertainty is defined as ½ of the smallest certain unit The limit of the device! Uncertainty is defined as ½ of the smallest certain unit If a Centimeter Ruler was used… Arrow Length ± 0.5cm* Arrow “A” 3.9 Arrow “B” 3.4 A B *You should report the uncertain digit If a Millimeter Ruler was used… Arrow Length ± 0.5mm* Arrow “A” 39.1 Arrow “B” 33.8

Uncertainty is defined as ½ of the smallest certain unit The limit of the device! Uncertainty is defined as ½ of the smallest certain unit What about electronic devices?* Digital Balances: The last digit is uncertain. For example: The mass of the powder is 5.00g ± 0.05 *some electronic devices have published uncertainty, If you have access to the manual, refer to it.

How do I know how many Sig Figs? Basic Decimal Rules If no Decimal, then start counting at the first NON zero, and stop counting at the last NON zero! 30  1 sig fig 303  3 sig figs 3030  3 sig figs

How do I know how many Sig Figs? Basic Decimal Rules If Decimal, then start counting at the first NON zero, and count until the end! 3.1  2 sig fig 3.03  3 sig figs 3.030  4 sig figs 0.303  3 sig figs

How many sig figs? 7 40 0.5 0.00003 7 x 105 7,000,000 1

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

Identify the uncertain digit in each number? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 1.2 2100 56.76 4.00 0.0792 7,083,000,000

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

How would you indicate uncertainty? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 3401 ±5 2100 ±500 2100.0 ±0.5 5.00 ±0.05 0.00412 ±0.00005 8,000,050,000 ±50,000

What about 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 2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm which digit is uncertain? 3.7

Add/Subtract examples 7.432cm + 2cm = 9.432 round to  9cm which digit is uncertain? 9 cm

Multiplication and Division Rule: 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  139cm2 which digit is uncertain? 139 cm2

A couple of examples 75.8cm x 9.6cm = ? Do the math and round to… Which digit is uncertain? How would you record uncertainty?

Sig fig Math!!!