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Significant Figures and Scientific Notation Math in the Science Classroom

Scientific Notation Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10 -9. So, how does this work?

Scientific Notation 10000 = 1 x 10 4 24327 = 2.4327 x 10 4 1000 = 1 x 10 3 7354 = 7.354 x 10 3 100 = 1 x 10 2 482 = 4.82 x 10 2 10 = 1 x 10 1 89 = 8.9 x 10 1 (not usually done) 1 = 10 0 1/10 = 0.1 = 1 x 10 -1 0.32 = 3.2 x 10 -1 (not usually done) 1/100 = 0.01 = 1 x 10 -2 0.053 = 5.3 x 10 -2 1/1000 = 0.001 = 1 x 10 -3 0.0078 = 7.8 x 10 -3 1/10000 = 0.0001 = 1 x 10 -4 0.00044 = 4.4 x 10 -4

Scientific Notation A positive exponent shows that the decimal point is shifted that number of places to the right. 251 x 10 4 = 2,510,000 A negative exponent shows that the decimal point is shifted that number of places to the left. 251 x 10 -4 =.0251

Scientific Notation Practice 1.Write in scientific notation: 0.000467 2.Write in scientific notation 32000000 3.Express 5.43 x 10 -3 as a number. 4.Express 6.34 x 10 9 as a number.

Significant Figures There are two kinds of numbers in the world: exact: –example: There are exactly 12 eggs in a dozen. –example: Most people have exactly 10 fingers and 10 toes. inexact numbers: –example: any measurement. If I quickly measure the width of a piece of notebook paper, I might get 220 mm (2 significant figures). If I am more precise, I might get 216 mm (3 significant figures). An even more precise measurement would be 215.6 mm (4 significant figures).

PRECISION VS ACCURACY –Accuracy refers to how closely a measured value agrees with the correct value. –Precision refers to how closely individual measurements agree with each other. accurate (the average is accurate) not precise precise not accurate accurate and precise

Significant Figures The number of significant figures is the number of digits believed to be correct by the person doing the measuring. It includes one estimated digit. So, does the concept of significant figures deal with precision or accuracy?

Significant Figures Consider the beaker pictured below: The smallest division is 10 mL, so we can read the volume to 1/10 of 10 mL or 1 mL. We measure 47 mL So, How many significant figures does our volume of 47? Answer - 2! The "4" we know for sure plus the "7" we had to estimate.

Significant Figures Now consider a graduated cylinder. First, note that the surface of the liquid is curved. This is called the meniscus. The smallest division of this graduated cylinder is 1 mL. We measure 36.5mL How many significant figures does our answer have? 3! The "3" and the "6" we know for sure and the "5" we had to estimate a little.

Significant Figures Rules for Working with Significant Figures: 1.Leading zeros are never significant. 2.Imbedded zeros are always significant. 3.Trailing zeros are significant only if the decimal point is specified. Hint: Change the number to scientific notation. It is easier to see.

Significant Figures ExampleNumber of Significant FiguresScientific Notation 0.00682 3 6.82 x 10 -3 1.072 4 1.072 (x 10 0 ) 300 1 3 x 10 2 300. 3 3.00 x 10 2

Significant Figures

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