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

What is a significant figure? There are 2 kinds of numbers: 1) Exact numbers 2) 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

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

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

Uncertainty The limit of the device! Uncertainty is defined as ½ of the smallest certain unit 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. What about electronic devices?*

Uncertainty Random Uncertainty: a deviation from the normalized value (as likely to be “too high” or “too low” How can you reduce this uncertainty? More trials!!!!  average Will still need to evaluate the range of the data or the standard deviation of the data…if graph  “Error Bars!” Systematic Uncertainty Results shifted one direction consistently ex: balance weighing 0.8g too little ! Fix: calibrate the equipment Ex: dispense an extra 3 microliters when using micropipette! Fix: use tool properly, don’t use “hard stop”!!!

How do I know how many Sig Figs? Basic Decim al 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 Decim al 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  4 sig figs  3 sig figs

How many sig figs? x ,000,

How many sig figs here? ,083,000,

Identify the uncertain digit in each number? ,083,000, ,083,000,000

How many sig figs here? ,000,050,

How would you indicate uncertainty? ,000,050, ± ± ± ± ± ,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 = 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 cm x 2.45cm = cm 2 Round to  139cm 2 which digit is uncertain? 139 cm 2

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!!!