measuring & calculating with significant figures
TRANSCRIPT
Measuring & Calculatingwith
Significant Figures
A measurement compares an unknown quantity to a standard
Every measurement must include an estimated digit and units!
Practice:
Significant Figures indicate the precision measurements.
Measurement Techniques to Remember:
Read from eyelevel to
avoid parallax.
Measurement Techniques to Remember:
Use the measurement device that offers the highest precision.
Accuracy = Precision
Precision:Exactness of a measurement
Depends on the measuring tool
Accuracy: Closeness of a measurement to "true" value
Percent error analysis
• 1. A student measures the boiling point of water as 98.9 degrees Celsius at sea level. Determine his percent error.
2. The density of aluminum is known to be 2.70 g/ml. A student calculates the density to be 3.2 g/ml. Determine the percent error.
Percent Error Practice
Significant Figures
Includes all known digits plus one estimated
digit.
More precise measurements have more significant figures.
Which Numbers are Significant?* Non-zero numbers always are!
* Zeroes sometimes are.
So when are zeroes significant?
When they are "trapped" between non-zero #'s
When they are at the end of a number that has a decimal
Remember sometimes numbers are exact...
» Counted objects
» Conversion factors
These have unlimited significant digits!
Digits What Counts? Examples
Nonzero ALL of ‘em1.23 (3 sig figs)
1333 (4 sig figs)
Leading zeros NONE of ‘em0.12 (2 sig figs)
0.004 (1 sig fig)
Trailing zeros Only if to the right of the decimal
100 (1 sig fig)
1.0 (2 sig figs)
Captive zeros ALL of ‘em 1001 (4 sig figs)100.05 (5 sig figs)
Significant Figures
1 2 3 4 5
20050.0 1.50
0.004
20.010
19
0.5
2.00
1.0 x 102100.0
0.10.0400.0750
0.01030
How many significant figures in each number?
Quick Practice:
How many significant digits in the following?
1) 35.5 mL
2) 0.005 g
3) 81.0 m
4) 1900 cm
5) 0.0070500
6) 22 students in class
7) 12 inches per foot
1. 50.3 m (2 sig figs)
2. 3.0025 s (4 sig figs)
3. 0.892 kg (1 sig fig)
4. 0.0008 ms (3 sig figs)
5. 57.00 g (1 sig fig)
6. 2.000 000 kg (3 sig figs)
7. 1000 (2 sig figs)
8. 20 m (2 sig figs)
9. 20.0 m (1 sig fig)
10. 1.0006 kg (3 sig figs)
Round each measurementto the indicated number ofsignificant digits.
Follow the Rules!
When multiplying/dividing: * Report answer using the same number of significant figures as the least precise measurement from which it was calculated.
When adding/subtracting: * Report answer using the same number of decimal places as the measurement with the fewest decimal places.
Calculating with Significant Figures
Add/Subtract
Use the least # of decimal places
Mulitply/Divide
Use the least # of significant figures
Quick Practice:
1) 200/55.5
2) 33.4 x 10
3) 1800 + 33.35
4) 12.002 x 3.57
5) 75.0/10 +2.50
6) (23.3 x 10.07)/14
7) 5.0 x 7
8) 100.00 x 10.000
9) 22.2/11
10) 5.000 +18.3 +14.07
Dimensional Analysis
What are Dimensions?
• Measured quanes such as length, mass, volume, me, etc.
• All dimensions must include units
How will we convert between units?
• Use Dimensional Analysis
• Objecve is to cancel out unwanted units while leaving wanted units
• Uses conversion factors
What are conversion factors?
• Fracons that are equal to 1
What is the conversion factor that would be used to convert between:
1. inches & feet?2. meters & kilometers?3. seconds & hours?4. liters & milliliters?5. grams & pounds?
Dimensional Analysis Steps:1. Determine the unknown (wanted) units.2. Determine the known (unwanted) values.3. Determine conversion factors that are needed.4. Start with the known. Arrange conversion factors to cancel out known units and leave the unknown (wanted) units.5. Mulply all numbers on top.6. Divide by all numbers on boom.7. Check units and significant figures.
Dimensional Analysis Example 1:
How many miles will a person run during a 12.0 kilometer race?
Dimensional Analysis Example 2:
The moon is 250,000 miles away. How many feet is it from Earth?
Dimensional Analysis Example 3:
A family pool holds 10,000 gallons of water. How many cubic meters is this?
Dimensional Analysis Example 4:
The density of gold is 19.3 g/cm3. How many pounds would a 2 gallon container of gold dust weigh?