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Significant Figures and working with measurements Science 10 G.Burgess Feb.2007.

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What is a Significant Figure? A number that demonstrates the precision of a measuring tool.

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Rules for Measuring significantly Write out all digits shown by the markings on the measuring tool Make a guessed digit for the space between the markings If you are using a mm ruler, you guess a digit for the space between the mm markings.

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Recognizing Significant Digits in pre-measured numbers Rules: All digits 1-9 are always significant. IE. The number 234 has two S.F.’s. The number 7344.6 has 5 S.F.’s. Zeros to the left of non-zero digits are not significant. IE. The number 0078 has 2 S.F.’s. The number 022 has 2 S.F.’s.

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Recognizing Significant Digits in pre-measured numbers Zeros to the right of a non-zero digit are significant only when a DECIMAL is present. IE.The number 7000 only has 1 S.F. because there is not a decimal in the number. The number 70.00 has 4 S.F.’s because there is a decimal. Zeros between non-zero digits are significant. IE.The number 807 has 3 S.F.’s. The number 70.006 has 5 S.F.’s

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Rounding numbers Round down all digits ending with 4 or less. Round up all digits that are 6 or more. If the digit is a 5; If the digit before is odd, round up If the digit before is even, round down.

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Practice Problems Round the following to 3 Sig. Fig.’s 1.0.9973 2.0.01955 3.6.070 4.809.2 5.875.54 6.0.0019754 7.201.59 8.29.27 9.20.52 10.687.59300 Answers 1.0.997 2.0.0196 3.6.07 4.809 5.876 6.0.00198 7.202 8.29.3 9.20.5 10.688

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Scientific Notation The short hand method for writing very large or very small numbers and showing numeric significance All notation numbers have a non-zero digit followed by a decimal and other significant digits. IE. 87.99 rounded to 2SF would be 8.8 X 102 Check out next slide to find out how.

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How to convert to Scientific Notation Converting 0.97580 to sci.notation. Write first non-zero digit. In this case it is the digit 9 Put a decimal after the 9 Write out all other digits Write X 10 Give the 10 an exponent that represents the number of places the decimal was moved. **minus means decimal was moved to the left **plus means the decimal was moved to the right. Example: 9 9. 9.7580 9.7580 X 10 9.7580 X 10-1

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Using Scientific Notation to show significance The only digits that appear in a sci.notation number are the significant ones. IE. 79,954.094 rounded two significant figures would be; 80,000 Using scientific notation the number would be; 8.0 X 104

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Practice Problems Convert the following numbers to scientific notations having 3 sig figs. 1.0.000207 2.98.256 3.999.999 4.5467.3 5.100809.2 Answers 1.2.07 X 10-4 2.9.82 X 101 3.1.00 X 103 4.5.47 X 103 5.1.00 X 106

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Multiplying and Dividing with significant figures Your answer must be rounded to the same number of significant digits as the number with the least number of significant digits. 75 = 2 SF’s X 1.256 = 4 SF’s 94.200 = 5 SF’s **Answer must be rounded to 2 SF’s. Answer = 94

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Practice Problems Complete the following using Sig figs. 6.25 X 0.3 =___ 78 X 0.345 =___ 2 x 16 = ___ 25.03 5.33 = ___ 0.09465 0.00356 = ___ 1.2 2.27 3.30 4.4.70 5.26.6

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Adding and Subtracting with Significant Figures Your answer must have the same number of place values as the number with the least. 18.509 = 3 SF after Decimal +96.5 = 1 SF after Decimal 115.009 = 3 SF after Decimal **Our answer must have no more than 1 place after the decimal. Answer is 115.0

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Practice Problems Complete the following using Sig figs. 1.13.05 + 6 = ___ 2.120 + 56.5 =___ 3.1209.9 +.1 = ___ 4.0.98 – 0.0567 = ___ 5.0.16458 -.1307 = ___ Answers 1.19 2.176 3.1210.0 4.0.92 5.0.0339

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