1. Unit 1: Matter & Measurement
Section 2: Scientific Notation, Accuracy, Precision & Error

2. A number is expressed in scientific notation when it is in the form
a x 10n
where a is between 1 and 10
and n is an integer

3. Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to make this number be between 1 and 10?
Between the 2 and the 1

4. How many decimal places did you move the decimal? 23
2.10,000,000,000,000,000,000,000.
How many decimal places did you move the decimal? 23
When the original number is more than 1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023

5. Express 0.000 000 0902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10?
9.02
The decimal was moved how many places? 8
When the original number is less than 1, the exponent is negative.
9.02 x 10-8

6. 1) What is 28750.9 in scientific notation?
Let’s Practice!
1) What is in scientific notation?
x 10-5
x 10-4
x 104
x 105

7. 2) Express 1.8 x 10-4 in decimal notation.
Let’s Practice!
2) Express 1.8 x 10-4 in decimal notation.
3) Express 4.58 x 106 in decimal notation.
4,580,000

8. Accuracy and Precision and Error
Accuracy - how close a measurement comes to the actual or true value of whatever is measured.
Precision - how close a series of measurements are to one another.

9. Accuracy and Precision
The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bull’s-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bull’s-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bull’s-eye and from one another.

10. Yes! Yes! Practice Problems
Three students measure the volume of an object to be 10.4 mL, 10.5 mL, and 10.7 mL.
The actual volume is 10.6 mL.
Are the measurements accurate?
Are the measurements precise?
Yes!
Yes!

11. 2. Five students weigh a sample of metal. Here are their measurements:
2.486 g, g, g, g, g
The actual weight of the metal is g.
Are the measurements accurate?
Are the measurements precise?
No!
Yes!

12. experimental value – actual value
Determining Error
The actual (accepted) value is the correct value based on reliable references.
The experimental value is the value measured in the lab.
Percent error tells you how accurate your results are.
experimental value – actual value
actual value
X 100
% error =

13. % Error Example 1:
Determine the % error if the measured temperature of a solution is 99.1˚C and the actual temperature is 100.0˚C
% error = 99.1˚C – 100.0˚C x 100
100.0˚C
= 0.9˚C x 100
100.0˚C
= 0.9%

14. % Error Example 2
A technician experimentally determined the boiling point of octane to be 124.1˚C. The actual boiling point of octane is 125.7˚C. Calculate the percent error.
Percent error = 124.1˚C – 125.7˚C x 100
125.7˚C
= 1.6˚C x 100
125.7˚C
= 1.27%