Download Scientific Notation and Metrics

Scientific Measurement and Significant Figures
Part 1: Scientific Notation

Objective-express large and small numbers in scientific notation
define scientific notation- a method of representing very large or very small numbers
using the format M x10n
M= the number between 1 and 10
n= an integer
Original Number Larger than 1
2 500 000 000
Original Number Smaller than 1
0.0000579
2.5x109
5.79x10-5
* negative exponents are numbers smaller than 1 but larger than 0
Scientific Notation Practice
_______________________________________
A
D
B
C
E
Place the letters on the number line
A. 0
B. 2.38 x10-2
C. 8.75
D. 2.38 x10-4
E. 8.56 x105
Part 2: Significant Figures

Objective-identify significant figures in measurements
Measurement:
All measurements have uncertainty because instruments can’t be read to an infinite number
of decimal places.
All measurements have the last digit as an estimated one.
define significant figuresAny 0 (s) sandwiched between significant figures are
significant
1.) 30.5 ml = 3
2.) 5005 m = 4
3.) 0.207 grams = 3
Trailing 0 (s) in measurements WITH a decimal point are
significant figures
1.) 30.0 ml = 3
2.) 50 m = 1
3.) 0.9050 grams = 4
If you want these to be significant—you can either add a
decimal point, or put a line over the 0 you want to be
significant
1.) 300 m = 1
2.) 300. m =3
3.) 300 m = 2
How can I use measurement, the metric system, and scientific notation
to explain if a 0 is significant?
T. O’Toole
Leading 0 (s) are NOT significant figures-if you change
the unit you can eliminate the 0’s
1.) $.05 = 1
2.) .0052 g = 2
3.) .070 L = 2
To Summarize:
 Do you think the 20,000,000 tons of debris was measured with an instrument?
No--hyperbole

Is there a difference between .005 kg and 5x10-3 kg?
No—use scientific notation to determine they are equivalent.
Your Turn: Identify the number of significant figures in the following:
1.0070 m = 5
17.10 kg = 4
100,890 L = 5
3.29x103 g = 3
0.0054 cm = 2
3,200,000 ml = 2
How do I get from where I am to where I’m going?
The 10 Minute Makeover
Customize your learning by choosing from the following options each night






Complete the appropriate sections on the Portfolio Page
Review the PPT file on the website
Read pages 51-58 in the book
Answer question #5 on page 58. The answers are in Appendix C.
Check out the tutorial resources in the LiveBinder including the
video example
Review the skills from today’s Train Your Brain
How can I use measurement, the metric system, and scientific notation
to explain if a 0 is significant?
T. O’Toole
Calculating with Significant Figures
Part 3: Calculating with Significant Figures

Objective-round answers to significant figures
Calculated Answers: Multiply and Divide
The number of significant figures in the result equals the number in the least precise measurement used
in the calculation.
Example: 6.38 x 2.0 = 13
6.38 has 3, 2.0 has 2 therefore the final answer has 2
Practice
3.24 m x 7.0 m = 23 m
2
710 m / 3.0 s = 240 m/s
100.0 g / 23.7 cm3 = 4.22 g/cm3
1818.2 lb x 3.23 ft = 5870 ftlb
0.02 cm x 2.371 cm = .05 cm2
1.030 g / 2.87 ml = .359 g/ml
Calculated Answers: Add and Subtract
The number of decimal places in the result equals the number of decimal places in the least precise
measurement.
Example: 6.8 + 11.934 = 18.7
6.8 has tenths, 11.934 has thousandths therefore the final answer has tenths
Practice
3.24 m + 7.0 m = 10.2 m
713.1 L – 3.872 L = 709.2 L
100.0 g – 23.73 g = 76.3 g
1818.2 lb + 3.37 lb = 1821.6 lb
0.02 cm + 2.371 cm = 2.39 cm
2.030 ml – 1.870 ml = .160 ml
How can I use measurement, the metric system, and scientific notation
to explain if a 0 is significant?
T. O’Toole
How do I get from where I am to where I’m going?
The 10 Minute Makeover
Customize your learning by choosing from the following options each night







Complete the appropriate sections on the Portfolio Page
Review the PPT file on the website
Read pages 58-62 in the book
Answer questions #7, 9, and 11 in the reading assignment. The answers are in
Appendix C.
Check out the tutorial resources in the LiveBinder including the video
examples
Complete the SYS Assignment “Calculating with Significant Figures”
Review the skills from today’s Train Your Brain
How can I use measurement, the metric system, and scientific notation
to explain if a 0 is significant?
T. O’Toole