1. UNIT: Chemistry and Measurement
TOPIC: Measurement
Objectives: Lesson 2 of 4
You will learn how to convert extremely large or small numbers into scientific notation
You will learn the difference between the terms Accuracy and Precision
You will be able to solve problems with Significant Figures

2. Quickwrite In 1-2 sentences answer one of the questions below:
What are some measurements you might take in a Chemistry lab?
Why do you think it is important to make accurate and precise measurements?
Finally, in your own words, try to define the term accurate:

3. Scientific Notation
To make large number seem small, scientist use something call scientific notation
Lets look at the speed of light
Light travels 9,500,000,000,000,000 kilometers in one year
9,500,000,000,000,000 written in scientific notation is x 1015
How did I get 9.5 x 1015?
By moving the decimal over 15 places between the 9 and the 5
9,500,000,000,000,000
x 1015

4. Scientific Notation
You have about 50,000,000,000,000, cells in your body!
Let’s write this in scientific notation
x 1016

5. Scientific Notation
Scientific notation is a useful way to represent numbers that are very large or very small
All numbers are written in a form of exponents of ten such as 9.5 x 1015

6. What is Scientific Notation?
A way to represent numbers that are very large or small
Numbers are written in a form of exponents of ten such as 9.5 x 1015

7. Practice:
Try to write 602,300,000,000,000,000,000,000 in scientific notation:
602,300,000,000,000,000,000,000
x 1023

8. Accuracy and Precision
It is important to make measurements that are both accurate and precise
Accuracy is how close a measurement is to the correct or accepted value
Precision is how close a measurement agrees with other measurements of similar value
Lets apply these terms to a dart board, and our bull's-eye is our “Accepted Value” then we can begin to understand the difference between Accuracy and Precision
Precise, Not Accurate
Not Precise or Accurate 
Precise and Accurate 

9. What is the difference between Accuracy and Precision?
Accuracy is how close a measurement is to the correct or accepted value
Precision is how close a measurement agrees with other measurements of similar value

10. Significant Figures
So, which on is it? Is it or 1.56 centimeters?
It is important to realize that the first two numbers are the same and are therefore certain; however, the third estimate (hundredths place) can vary and is therefore uncertain
Measurement always has some level of uncertainty
Significant Figures are numbers recorded in a measurement that include all certain numbers plus the first uncertain number
Whenever a measurement is made with a device such as a ruler or Graduated Cylinder, a certain degree of estimate is required
For example, lets say we want to measure the length of this nail
We can see the that the length of the nail is between 1.5 and 1.6 centimeters
Because no scale exist between 1.5 and 1.6, we must estimate the nails length
Using a visual estimate, we could estimate the nails length as either or 1.56 centimeters
certain
1.54 cm
1.56 cm?
uncertain

11. What are Significant Figures?
The numbers recorded in a measurement that include all certain numbers plus the first uncertain number

12. Significant Figure Rules
Chemistry requires many types of calculations and measurements
To help us obtain accurate and precise results, me must use a set rules known as the Significant Figure Rules; these rules are as follows:
All Nonzero integers or numbers count as significant
For example, in the number below this includes integers 7, 5, and 8
Zeros in front of nonzero numbers or integers are NOT significant
For example, in the number below this includes the first three zeros
Zeros between nonzero integers or numbers are significant
For example, in the number below this includes the zero between 7 and 5
Trailing zeros at the end of a number are only significant if the number contains a decimal
For example, in the number below this includes the zero after 8 because a decimal is present
significant
5 significant figures TOTAL
significant
significant
NOT significant

13. Practice:
Determine the number of significant figures in each measurement below:
A piece of magnesium metal weighs grams
Answer: the number contains 3 significant figures
A piece of hair from a crime lab weighs grams
Answer: The number contains 5 significant figures

14. Rules for Rounding Off
Lets say we want to round the number below to nearest hundredths place
Because the last digit, 3 is less than 5, our answer would be
Now lets say we want to round the number below to the nearest tenths place
Remember, any number greater than or equal to 5, we round up, which gives us an answer of 845.7
It is important to realize that when you are performing calculations on a calculator, only round off until you have arrived at your final answer
Sometimes our calculators give us answers with a very large number of digits, therefore it is important we learn how to round off
Consider the number below, it is made up certain place names
For example, the 8 is located in the thousands place
The 4 is located in the hundreds place
The 5 is located in the tens place
The 6 is located in the tenths place
The 5 is located in the hundredths place
The 3 is located in the thousandths place
hundreds place
tens place
tenths place
hundredths place
thousandths place
thousands place

15. Practice: Round each number below to the nearest “tenths” place:
A piece of magnesium metal weighs 1.58 grams
Answer: Because 8 is greater than or equal to 5, the answer is 1.6 grams
A sample of water has a mass of grams
Answer: Because 1 is less than 5, the answer is 150.1

16. Significant Figure Rules in Calculations
You will often be performing calculations that involve multiplication, division, addition and subtraction
When using significant figures in calculations, there are rules we must consider, these rules are as follows:
For multiplication or division, the number of significant figures in your answer will be the same as the number with the smallest number of significant figures
For example, let’s say you perform the following calculation below:
4.56 x = 6.384, the smallest number 1.4, contains 2 significant figures,
so our answer must contain two significant figures
Therefore our answer will be 6.4
3 significant
figures
2 significant
figures
For addition and subtraction, the number of significant figures in your answer will be the same as the number with the smallest number of decimal places
For example, let’s say you perform the following calculation below:
= 18.28, the number with the smallest number of decimal places is 6.2,
so our answer must contain only one decimal place
Therefore our answer will be 18.3
2 decimal
places
1 decimal
place

17. What are the Significant Figures Rules?
All Nonzero numbers count as significant
Zero's in front of nonzero numbers are NOT significant
Zero's between nonzero numbers are significant
Trailing zero's at the end of a number are only significant if the number contains a decimal
Calculation Rules:
For multiplication/division, the number of significant figures in your answer will be the same as the number with the smallest number of significant figures
For addition/subtraction, the number of significant figures in your answer will be the same as the number with the smallest number of decimal places

18. Practice:
Solve each problem below, make sure your answer contains the correct number of significant figures: (remember to round)
5.18 x x 1.1 = ??????
Answer: 12 Because 1.1 has 2 significant figures, therefore our answer must contain only 2 significant figures
– 4.6= ??????
Answer: 2.7 Because 4.6 has only one decimal place therefore our answer must contain only one decimal place (don’t forget to round up)
(1.33 x 2.8) = ??????
Answer: 12.1 Because x 2.8 = = 3.7, = , notice 3.7 has only one decimal place therefore our answer must contain only one decimal place 12
2.7
12.1

19. Summary (you can always write your own summary)
In the expression (1.33 x 2.8) = 12.1, describe how you were able to determine the answer using significant figures
Imagine you are measuring an object with a ruler, explain the difference between a certain and an uncertain measurement
How many significant figures does contain?
How many significant figures does 22.1 contain?
Summarize the significant figure rules: