1. Unit 1: Matter, Measurement, and unit conversions≈

2. Big Idea
Chemistry, being the science of matter, requires that we have systems for classifying, describing and measuring quantities of matter.

3. Topic 2: significant figures
Learning Goal: You will be able to identify the significant figures in any number and properly perform arithmetic involving significant figures.
Success Criteria: You will know you have met the learning goal when you can truthfully say:
1. I can determine the sig figs in any number.
2. I can multiply, divide, add, and subtract numbers and report the answer with the correct number of sig figs.
3. I can use scientific notation to express numbers.
Materials: none

4. Success Criteria 1: I can determine the sig figs in any number.
Not all numbers are equally precise. While some numbers are exact (Ex: there are 27 people in this room), many quantities have some amount of uncertainty. For example, if you say you are two miles from your house, taking three steps isn’t going to change that. “Two miles” is a number with a lot uncertainty in it.

5. Success Criteria 1: I can determine the sig figs in any number.
Some other examples:
Seattle is 200 miles from Portland, Oregon.
There are centimeters in one mile.
200 x = 32,186,880.
Is Seattle actually 32,186,880 centimeters from Portland?
I added 10 gallons of gas to my car.
There are liters in one gallon.
10 x =
Did I add liters of gas to my car?
Precise or vague/estimate.

6. Success Criteria 1: I can determine the sig figs in any number.
You can see from these examples that the uncertainty of the numbers you use will have an effect on the uncertainty of your answer. The way we determine how certain your answer should be is by looking at the significant figures in a number. The significant figures are all of the digits that add to the certainty of a number. More sig figs means the number is more precise.
Rule: Zeroes that come at the beginning or end of a number that make the number bigger or smaller are the only numbers that are not significant figures.
Ex:
28 has two sig figs
28,000 also has two sig figs
104 has three sig figs
also has three sig figs
has three sig figs
has four sig figs
also has four sig figs
Precise or vague/estimate.

7. Success Criteria 1: I can determine the sig figs in any number.
Another way to determine significant figures:
If it has a decimal, unbound zeroes on the left are not significant,
if it doesn’t have a decimal, unbound zeroes on the right are not significant.
What are unbound zeroes? They are the zeroes that come at the very beginning ( ) or very end (4200) of a number. They are not zeroes in the middle of a number (10.06). A number such as has unbound zeroes on both the left and the right.
5280 feet/mile. 3 miles = feet

8. Success Criteria 1: I can determine the sig figs in any number.
Task 1.2.1: Underline the sig figs in each number, then write how many sig figs it contains below. When you are done, circle the most precise number out of all of them.
,002,700,000
5280 feet/mile. 3 miles = feet

9. Success Criteria 2: I can multiply, divide, add, and subtract numbers and report the answer with the correct number of sig figs.
Consider again this example from earlier:
Seattle is 200 miles from Portland, Oregon. There are centimeters in one mile. 200 miles x cm/mile = 32,186,880 cm.
We wouldn’t say that Seattle is 32,186,880 cm from Portland. So what would we say, if asked how many cm is it from Seattle to Portland? Use sig figs!!!

10. Success Criteria 2: I can multiply, divide, add, and subtract numbers and report the answer with the correct number of sig figs.
Multiplying and dividing numbers and reporting your answer with the correct number of sig figs is easy. Just figure out the number of sig figs in your least precise number (the one with the fewest sig figs) and round your answer to that number of sig figs.
22 x 400 = 8800.
Round to 9000
÷ x 1,297,100 =
Round to 157.3
÷ 3 =
Round to 10
Seattle to Portland example:
200 miles x cm/mile = 32,186,880 cm. Round to 30,000,000 cm.

11. Success Criteria 2: I can multiply, divide, add, and subtract numbers and report the answer with the correct number of sig figs.
Task 1.2.2: Write the unrounded answer to each problem, then round to the correct number of sig figs (csf).
16 x 35 = __________
csf: __________
840 ÷ 22 = ___________
1000 x 62 ÷ 252 = ________
150 x = _________
443 ÷ 5900 = _________
x 9002 ÷ 1145 = ___________
x 300 = _________
÷ = _______
500.0 ÷ 24 ÷ 17 x 29 = _____
52 x 391 x 24 = _________
490 ÷ 38 ÷ 10 = _________
10.00 x 5050 ÷ 2911 = _____

12. Success Criteria 2: I can multiply, divide, add, and subtract numbers and report the answer with the correct number of sig figs.
To add and subtract numbers, then round to the proper number of sig figs, you can’t apply the same rule as for multiplication and division. Here, we can to consider the not the number of sig figs, but rather how large or small the uncertainty is in each number. To do that, we consider what is the smallest sig fig (the furthest sig fig to the right) in each number that we are adding or subtracting, then round based on the largest of those numbers.
For example, if you have a number that has sig figs down to the tens place (ex: 530) and you add to it a number that has sig figs down to the hundredth’s place (62.18), your answer (592.18) would be rounded to the tens place (590).

13. Success Criteria 2: I can multiply, divide, add, and subtract numbers and report the answer with the correct number of sig figs.
An easy way to do this is to line up the numbers vertically.
8800 =
Round to 14300 =
Round to
Greatest uncertainty
Greatest uncertainty

14. Success Criteria 2: I can multiply, divide, add, and subtract numbers and report the answer with the correct number of sig figs.
Task 1.2.3: Write the unrounded answer to each problem, then round to the correct number of sig figs (csf).
= ________
csf: __________
= _________
= _______
= ________
= _________
= _________ csf: _________
= ________
= ______
= _________ csf: _________
= ________
= _________
= ________ csf: __________

15. Success Criteria 3: I can use scientific notation to express numbers.
Often in science, we deal with very large or very small numbers. Sometimes, writing out every placeholding zero is cumbersome or impractical. For example, we will learn later in this course about a number called Avogadro’s number, which has a value of

16. Success Criteria 3: I can use scientific notation to express numbers.
Writing this number out takes too much time, too much space, and can result in errors if you add up the number of zeroes wrong. Instead, we can write it as x Normally, we will just use the first three significant figures, so we’ll write it as 6.02 x 1023.

17. Success Criteria 3: I can use scientific notation to express numbers.
The way you determine the value of the exponent (the 23 in the previous example) is by how many places from the ones place you have to move the decimal. For example, to write 7600 in scientific notation, you would have to move the decimal three places, so it would be 7.6 x 103. Numbers smaller that 1 have a negative exponent would be 2.5 x Notice that numbers written in scientific notation only include the sig figs.

18. Success Criteria 3: I can use scientific notation to express numbers.
In your calculator, (at least in TI calculators) you can input numbers in scientific notation using the EE button. This saves time and reduces math errors later in the course, so I encourage you to get comfortable using this function.
4.32 x 108 = 4.32E8
5.10 x 10-4 = 5.10E-4
Standard
x 10n EE
5600
5.6 x 103
5.6E3
560
5.6 x 102
5.6E2 56
5.6 x 101
5.6E1
5.6
5.6 x 100
5.6E0
0.56
5.6 x 10-1
5.6E-1
0.056
5.6 x 10-2
5.6E-2
0.0056
5.6 x 10-3
5.6E-3
5.6 x 10-4
5.6E-4

19. Success Criteria 3: I can use scientific notation to express numbers.
Task 1.2.4: Convert between scientific and standard notation.
33000
407000
2.9E5
1.006 x 103
6E7
x 1012
4.07E-4
x 10-6
245.3E5
x 10-3

20. Wrap-up
Task 1.2.5: Write in complete sentences eight things that you learned in this topic.