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Significant Figures. Integrated Science Dr. May. Significant Figures. Numbers obtained from measurements are never exact values Maximum precision includes all digits that are known plus one estimated The digits used to express a measured quantity are known as significant figures.

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## Significant Figures

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**Significant Figures**Integrated Science Dr. May**Significant Figures**• Numbers obtained from measurements are never exact values • Maximum precision includes all digits that are known plus one estimated • The digits used to express a measured quantity are known as significant figures**Evaluating Zero**• In any measurement all nonzero numbers are significant • 65.6291 grams has six significant figures • Zeros may or may not be significant depending on their position in the number**Zero is Significant When**• It is between nonzero digits • 2.05 has three significant figures • 61.009 has five significant figures**Zero is Significant When**• It is at the end of a number that includes a decimal point • 0.500 has three significant figures • 25.160 has five significant figures • 200. has three significant figures**Zero is Not Significant When**• It comes before the first nonzero digit (These zeros are used to place the decimal) • 0.0025 has two significant figures • 0.00708 has three significant figures**Zero Is Not Significant When**• It comes at the end of a number that contains no decimal point • 1000 has one significant figure • 590 has two significant figures**4.5 inches =**3.025 feet = 125.0 meters = 0.001 miles = 25.0 grams = 100,000 people = 205 birds = 2 4 4 1 3 1 3 Determine Significant Figures**Rounding Off Numbers**Integrated Science Dr. May**Rounding Off Numbers**• When we do calculations we often obtain answers with more digits than are justified • We need to drop the excess digits to express the answer in the proper number of significant figures • This is called rounding off numbers**Rounding Off Numbers - Rule 1**• When the first digit after those you want to retain is 4 or less, that digit and all others to the right are dropped. • The last digit retained is not changed • Round 1.00629 to 4 significant figures • 1.00629 = 1.006**Rounding Off Numbers - Rule 2**• When the first digit after those you want to retain is 5 or greater, that digit and all others to the right are dropped. • The last digit retained is increased by 1 • Round 18.02500 to four significant figures • 18.02500 = 18.03**42.246 (four) =**88.015 (four) = 0.08965 (three) = 0.08965 (two) = 225.3 (three) = 14.150 (three) = 42.25 88.02 0.0897 0.090 225 14.2 Round Off As Indicated**Scientific Notation**Integrated Science Dr. May**Scientific Notation**• Very large and very small numbers can be simplified and conveniently written using a power of 10 • 4,500,000,000 (4.5 billion) can be written 4.5 x 109 • Writing a number as a power of10 is called scientific notation**100 =**101 = 102 = 103 = 104 = 105 = 106 = 1 10 100 1,000 10,000 100,000 1,000,000 Powers of Ten**10 0 =**10 1 = 10 2 = 10 3 = 10 4 = 10 5 = 10 6 = 1 0.1 0.01 0.001 0.0001 0.00001 0.000001 Negative Powers of Ten**Number to Scientific Notation**• Convert 0.000056 to 5.6 x 10 5 • Choose the number between 1 and 10 = 5.6 • Multiply by 10: 5.6 x 10 • If the number is < 1 use a negative exponent 5.6 x 10 • Count the spaces the decimal was moved 5.6 x 10 5**Number to Scientific Notation**• Convert 560,000 to 5.6 x 10 5 • Choose the number between 1 and 10 = 5.6 • Multiply by 10: 5.6 x 10 • If the number is > 1 use a positive exponent 5.6 x 10 • Count the spaces the decimal was moved 5.6 x 10 5**Scientific Notation to Number**• Convert 5.6 x 10 5 to 560,000 • Write the significant figures = 56 • The exponent is positive, the number is > 1 • Add zeros to place the decimal 5 spaces to the right 560,000. 5 **Scientific Notation to Number**• Convert 5.6 x 10 5 to 0.000056 • Write the significant figures = 56 • The exponent is negative, the number is < 1 • Add zeros to place the decimal 5 spaces to the left 0.000056 5 **0.00034 =**0.00145 = 0.0000985 = 0.016856 = 0.0003967 = 0.0000002 = 0.00040 = 0.00600 = 3.4 x 10 4 1.45 x 10 3 9.85 x 10 5 1.6856 x 10 2 3.967 x 10 4 2 x 10 7 4.0 x 10 4 6.00 x 10 3 Convert To Scientific Notation**3400 =**36,000,000 = 367,800,000,000 = 58 = 65789 = 1,000,000,000 = 2,000 = 3.4 x 103 3.6 x 107 3.678 x 1011 5.8 x 101 6.5789 x 104 1 x 109 2 x 103 Convert To Scientific Notation**7.4 x 103 =**5.6 x 105 = 6.674 x 1010 = 5.1 x 104 = 6.5559 x 101 = 3.64186 x 104 = 1 x 103 = 7,400 560,000 66,740,000,000 51,000 65.559 36,418.6 1,000 Convert to Numerical Values**7.4 x 103 =**5.6 x 105 = 6.674 x 108 = 5.1 x 104 = 6.5559 x 101 = 3.641 x 104 = 1 x 103 = 0.0074 0.000056 0.00000006674 0.00051 0.65559 0.0003641 0.001 Convert to Numerical Values**The End**• This presentation was created for the benefit of our students by the Science Department at Howard High School of Technology • Please send suggestions and comments to rmay@nccvt.k12.de.us

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