Download Significant Digits

Significant Digits
Why are they important?
-Show precision of instruments used
-We use them ALL THE TIME in Chemistry
-MUST KNOW THE RULES!!
1. Digits other than zero are always significant
96 g.
61.42 g.
0.538 g.
2 significant digits
4 significant digits
3 significant digits
2. One or more trailing zeros after the decimal
point are always significant
4.00000 s.
0.05600 s.
0.002 m.
6 significant digits
4 significant digits
1 significant digits
3. Zeros between two other significant digits are
always significant
5.029 km.
30600 km.
0.050060 km.
4 significant digits
3 significant digits
5 significant digits
4. A zero can be made significant by placing a
bar over it.
We normally write these in scientific notation, but here are
some examples
_
10 mL
2 significant digits
_
1000 mL
4 significant digits
_
100000 mL
3 significant digits
An exception to the rules..
When talking about a value that is absolute,
all digits are significant.
25 apples
10 planes
800 students
2 significant digits
2 significant digits
3 significant digits
Strategy to determine number of significant digits
1. Find the leftmost significant digit
(leftmost nonzero digit)
2. Find your rightmost significant digit
(rightmost nonzero digit, a zero after a decimal, or a
zero with a bar over it)
3. All digits in between are significant
Practice!
1. 70.12 L
2. 0.000800 mg.
3. 82.003 mm.
4. 27.0 km
5. 50 people
6. 1.002 cm
_
7. 200kg
8. -270.8 K
9. 1000 mL
10. 42,729.00 cm
11. 225 beans
12. 99.294 dm
13. 0.06900 m
_
14. 3200000 kL
Using Significant Digits for Calculations
Multiplying and Dividing
1. look at original numbers
2. determine number with least amount
of significant digits
3. answer should contain this amount
of significant digits
Example
When multiplying 22.37 cm x 3.10 cm x 85.75 cm =
5946.50525 cm3.
22.37 shows 4 significant digits
3.10 shows 3 significant digits
85.75 shows 4 significant digits
Answer would have only 3 significant digits: 5950 cm^3.
Practice
1. 24 mm x 31.8 mm =
2. 8.40 g / 4.2 mL =
3. 200 dm x 3.58 dm =
4. 5500 km / 55.0 s =
Adding and Subtracting
1. Look at original numbers
2. Find the one with least number of
decimal places
3. Answer should contain this amount of
decimal places
Example
When we add:
3.76 g + 14.83 g + 2.1 g = 20.69 g
3.76 g
14.83 g
2.1 g
2 decimal places
2 decimal places
1 decimal place
Final answer should have one decimal place: 20.7
Practice
1. 49.1 g + 8.001 g =
2. 81.350 m - 7.35 m =
3. 4.60 s + 3 s =
4. 67.5 cm - 0.009 cm =