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. 12.11 18.0limiting-- 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 10 3 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 10 5 –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