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**Scientific Measurement**

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Significant Figures Measurements should be reported using the correct number of digits so they do not appear to be more accurate than they actually are Significant figures are the numbers in a measurement that actually mean something 123 three significant figures four significant figures three significant figures

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**Rules: Significant Figures**

All nonzero digits are significant: 1.234 g has 4 significant figures 1.2 g has 2 significant figures Zeroes between nonzero digits are significant: 1002 kg has 4 significant figures mL has 3 significant figures Leading zeros to the left of the first nonzero digits are not significant and merely indicate the position of the decimal point: 0.001o C has only 1 significant figure g has 2 significant figures

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**Rules: Significant Figures**

Trailing zeroes that are also to the right of a decimal point in a number are significant: mL has 3 significant figures g has 2 significant figures When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 190 miles may be 2 or 3 significant figures 50,600 calories may be 3, 4, or 5 significant figures

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**Rules: Mathematical Operations**

In addition and subtraction, the result is rounded off so that it has the same number of digits as the measurement having the fewest decimal places (counting from left to right) 100 (3 sig. figs.) (5 sig. figs.) = This should be rounded to 124 (3 sig. figs.) In multiplication and division, the result should be rounded off so as to have the same number of significant figures as in the component with the least number of significant figures 3.0 (2 sig. figs.) × (4 sig. figs.) = This should be rounded to 38 (2 sig. figs.)

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**Scientific Notation and Exponents**

Science deals with both very large and very small numbers, so scientists often use a "shorthand" way to write these values Bases and Exponents 24 103 10-3 Scientific notation is a tool that uses exponents to simplify handling numbers that are very big or very small 3400 (standard notation) = 3.4 X 103 (scientific notation) 3.4 X 10 X 10 X 10 = 3400

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**Writing a Number in Scientific Notation**

Move the decimal point so that the number is between 1 and 10. Count the number of decimal places moved in Step 1. If the decimal point was moved to the left, the count is positive. If the decimal point was moved to the right, the count is negative. Write as a product of the number (found in Step 1) and 10 raised to the power of the count (found in Step 2). The general format for a number written in scientific notation is N x 10power Practice: Convert the number to scientific notation.

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**The Metric System King Henry Doesn't [Usually] Drink Chocolate Milk **

base giga mega kilo hecto deka meter deci centi milli micro nano gram liter King Henry Doesn't [Usually] Drink Chocolate Milk

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**Practice Problem 1: convert 12.54 km to cm**

Metric Conversions One can move from one prefix to another by moving the decimal point one place, filling in, as necessary, with zeroes. To move to a smaller unit (a unit with a prefix some number of places further to the right in the listing), move the decimal place to the right that same number of places. To move to a larger unit (a unit with a prefix some number of places further to the left in the listing), move the decimal place to the left that same number of places. Practice Problem 1: convert km to cm

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Unit Conversions In many scientific and technical applications, there is a need to change from one type of unit to another. Metric system English system To perform unit conversions, start with the given measure and multiply it by the appropriate conversion factor(s) to yield the desired units in the end. The denominator of the fraction should contain the unit of the original number The numerator of the fraction should contain the unit you want to change to

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**Unit Conversions Practice problem: Convert 105 lb to kg**

Known: 1 kg = 2.2 lb

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