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Uncertainty in Measurements: Using Significant Figures & Scientific Notation Unit 1 Scientific Processes Steinbrink

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To understand how uncertainty in a measurement arises. Goal:

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Every measurement has some degree of uncertainty The uncertainty of a measurement depends on the measuring device.

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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

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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

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Example If a measuring device measures out to the tenths of cm then the uncertain digit would be the hundredths.

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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

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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

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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

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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

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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**

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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

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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

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