# How to determine and use the proper sig. figs.

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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  4 sig figs 0.303  3 sig figs

How many sig figs? 7 40 0.5 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 8,000,050,000 4 2 5 3 6

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

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

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 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!!!