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Significant FiguresHow 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 numbersUsing 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
UncertaintyThe 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…
Arrow Length ± 0.5cm*
Arrow “A” 3.9
Arrow “B” 3.4
If a Millimeter Ruler was used…
Arrow Length ± 0.5mm*
Arrow “A” 39.1
Arrow “B” 33.8
A
B
UncertaintyThe 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?*
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?7400.50.000037 x 105
7,000,000
111111
How many sig figs here?
1.2210056.764.000.07927,083,000,000
224334
Identify the uncertain digit in each number?
1.2210056.764.000.07927,083,000,000
1.2 210056.764.000.07927,083,000,000
How many sig figs here?
340121002100.05.000.004128,000,050,000
425336
How would you indicate uncertainty?
340121002100.05.000.004128,000,050,000
3401 ±52100 ±5002100.0 ±0.55.00 ±0.050.00412 ±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 = 3.7cmwhich 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!!!
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