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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