uncertainty in measurements: using significant figures & scientific notation unit 1 scientific...
TRANSCRIPT
Uncertainty in Measurements:
Using Significant Figures & Scientific Notation
Unit 1 Scientific Processes
Steinbrink
To understand how uncertainty in a
measurement arises.
Goal:
• Every measurement has some degree of uncertainty
• The uncertainty of a measurement depends on the measuring device.
Types of Digits
• Uncertain digit =
the estimated digit in the measurement---the last digit
• Certain digits = the measurements that are the same with each reading
So what is a Significant Figure?
• The numbers recorded in a measurement (all the certain
numbers plus the first uncertain digit) are the
significant figures
Example
• If a measuring device measures out to the tenths of cm then the uncertain digit would be the hundredths.
Rules for Counting Significant Figures
1. Nonzero integers- nonzero integers always count as significant figures.
Example: The number 1483 has four nonzero integers, which means that the number has 4 significant figures
Zeros
Leading Zeros- precede all the nonzero digits. They never count as significant!
0.00034
This number only has 2 sig figs
Captive Zeros- zeros that fall between nonzero digits. They always count as significant!
12.0092
This number has 6 sig figs
• Trailing zeros- zeros at the right end of the number. They are significant only if the number is written with a decimal point.
100
This number has one sig fig
100.
This number has three sig figs
Rules for Sig Figs in Calculations:Division & Multiplication
• The number of significant figures in the answer is the same as that in the measurement with the smallest number of sig figs.
4.56 x 1.4 = 6.384 6.4
8.315/298 = 0.0279027 .0279
*Based on smallest number of sig figs not decimal places
Rules for Using Sig Figs in Calculations
• Addition or Subtraction– The limiting term is the one with the smallest number of
decimal places.
12.1118.0 limiting-- one decimal
place + 1.013 31.123 31.1
**Only count the number of decimal places**
Scientific Notation
• A method of expressing a quantity as a number multiplied by 10 to the appropriate power.
• For Example: – 4.5 x 103 is the same as 4,500
– 6.06 x 10-3 is the same as .00606
– 0.0015 in scientific notation is 1.5 x 10-3
– 800,000. In scientific notation is 8.0 x 105
– Negative superscript # gets smaller
– Positive superscript # gets larger
More on Scientific Notation
• A positive exponent means you move the decimal to the right and the number in standard form will appear larger
• A negative exponent means you move the decimal to the left and the number in standard for will appear smaller