1. Metric System and Significant Figures

2. The Metric System (SI) Meter = length (about 3ft)
Grams = Weight (paperclip)
Liter = Volume (bottle of soda)
SI=System international
M=3.2 ft
Bottle of Soda is 2 liters

3. Significant Figures What is the point of significant figures? Examples
When you are measuring something, significant figures are used to show how precise you measured too.
Examples
0.073
270.
10.0
37,000
Significant figures also called significant digits
You don’t want to over compensate to what you measured to so the result isn’t more precise than what you actually measured to
Looking for digits that tell you how precise your measurement was
the 600 is sig fig (3 sig fig) What about the 1st 2 0s?  measuring in km same as 6 meters and you measured to the cm. The front 0s shift depending what unit you are measuring in but they are still the same number. Whoever wrote down these 0s didn’t have to write them down but since they did, that means they measure that fair. It just happened to be on an exact number.
.073 (2 sig fig) because km is the same as 73 meters which clearly has 2 significant figures
270. Because they wrote the decimal point it means they measured to exactly 270. They did not round up or down (3 sig fig)
10.0 Once again the 0 following the decimal point is telling you that this person measure to the nearest 10th (3 sig fig)
Measure measured to the thousands place so we have 6 sig fig
37000 because there is no decimal point we do not know how exact this measurement is. Could have rounded up or down to the nearest thousandth, so there are only 2 sig fig

4. Rules of Significant Figures
Count any non 0 digits and zeros in between
2005.
Rule out leading 0s (The zeros that come before your non-zero digit
0.006
LEADING 0s NOT SIGNIFICANT
Trailing 0s
If you have a decimal anywhere in your number count the trailing 0s
0.6000
If you do not have a decimal, it is too ambiguous,
67,000
700

5. Identifying Significant Figures
0.001
4.006
500
0.0245
70.
2398
2000
0.870

6. Adding and Subtraction
When adding and subtracting precise measurements significant figures don’t matter as much, as the actual precision of what you are measuring
=3.56
Go by the least precise thing you measured 2.3 (2 sig fig) round to 3.6 =
Precision is the amount of numbers after the decimal point (not the actual significant digits
 103.6
1.26 has two numbers after the decimal point but has 1 so we round to the nearest 10th.

7. Adding and Subtraction
Why do we forget about sig fig and only look at the numbers after the decimal point?
Block 1  2.09 m
Block 2  m
2.09m m =3.991 m
Because we measured to the hundredth on the 1st block and measured to the thousandth on the 2nd block we can only write to the hundredth spot
3.991 rounds to 3.99
If I have two blocks
2.09 meters our meter stick measures to the centimeter
1.901 meters this stick measures to the millimeter

8. Adding and Subtraction
This does not only apply when there is a decimal point
Building 450 ft
Antenna 8 ft
450+8 = 458
However we were only able to measure the building precisely to the tens spot
458 rounds to 460 ft
60 + 6

9. Multiplying and Dividing
Measuring carpet
2.03 m x 3.06 m = m^2
rounds to 6.21m^2 because we were only able to measure to the centimeter.
When multiplying and dividing use the least significant figure out of your two numbers that you are multiplying
Setting down tile in your kitchen
Area of kitchen
12.07 ft x 10.1 ft = ft (Area)
3 sig fig  122
However, we are not done with our math
Tile area (1.07 ft)
Do not round until you are done with your math
/1.07 = …
Now we care about sig fig
 114 ft^2

10. Multiplying and dividing
346.3 x 24.7
10.001x 24.3
80./20.
373 x 2
940/10
24.x35
78./2.01
863.01/24.003
845x2.01
7.0 x 208.