Significant Figures and working with measurements

Significant Figuresand 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 • 0.9973 • 0.01955 • 6.070 • 809.2 • 875.54 • 0.0019754 • 201.59 • 29.27 • 20.52 • 687.59300 • Answers • 0.997 • 0.0196 • 6.07 • 809 • 876 • 0.00198 • 202 • 29.3 • 20.5 • 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. • 0.000207 • 98.256 • 999.999 • 5467.3 • 100809.2 • Answers • 2.07 X 10-4 • 9.82 X 101 • 1.00 X 103 • 5.47 X 103 • 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 = ___ • 2 • 27 • 30 • 4.70 • 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. • 13.05 + 6 = ___ • 120 + 56.5 =___ • 1209.9 + .1 = ___ • 0.98 – 0.0567 = ___ • 0.16458 - .1307 = ___ • Answers • 19 • 176 • 1210.0 • 0.92 • 0.0339

Significant Figures and working with measurements