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

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

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.

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.

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

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.

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

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.

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

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

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

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

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

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

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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