Scientific Measurement

Scientific Measurement

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 123.0 four significant figures 0.0123 three significant figures

Rules: Significant Figures • All nonzero digits are significant: 1.234 g has 4 significant figures1.2 g has 2 significant figures • Zeroes between nonzero digits are significant: 1002 kg has 4 significant figures3.07 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 figure0.012 g has 2 significant figures

Rules: Significant Figures • Trailing zeroes that are also to the right of a decimal point in a number are significant: 0.0230 mL has 3 significant figures0.20 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 figures50,600 calories may be 3, 4, or 5 significant figures

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.) + 23.643 (5 sig. figs.) = 123.643 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.) × 12.60 (4 sig. figs.) = 37.8000 This should be rounded to 38 (2 sig. figs.)

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

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 0.000348 to scientific notation.

The Metric System base giga mega kilo hectodeka meter decicentimilli micro nano 109 106 103 102 101 1.0 10-1 10-2 10-3 10-6 10-9 gram liter King Henry Doesn't [Usually] Drink Chocolate Milk

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 12.54 km to cm

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

Unit Conversions • Practice problem: Convert 105 lb to kg • Known: 1 kg = 2.2 lb

Scientific Measurement