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SCIENTIFIC NOTATION A value written as the product of two numbers: a coefficient and 10 raised to a power. Ex: 602,000,000,000,000,000,000,000 is 6.02 × 10 23 The coefficient in this number is 6.02. (It is always a number equal to or greater than 1, and less than 10.) The power of 10, or exponent, is 23.

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Entering scientific notation correctly in a calculator is important. Here is the procedure for our classroom calculators: 6.02 × 10 23 is entered as 6. 0 2 EE 23 Some calculators may require you to press 2 nd EE, or EXP instead of EE

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Calculations with Scientific Notation: Adding: convert all numbers to the same power of 10, then add coefficients. 6.02 X 10 23 + 3.01 x 10 24 = 0.602 x 10 24 + 3.01 x 10 24 = 3.61 x 10 24 Subtracting: convert all numbers to the same power of 10, then subtract coefficients. 6.02 X 10 24 - 3.01 x 10 23 = 6.02 x 10 24 - 0.301 x 10 24 = 5.72 x 10 24

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Calculations with Scientific Notation: Multiplying: multiply coefficients and add exponents. 6.02 X 10 23 x 3.01 x 10 24 = 18.1 x 10 47 Dividing: divide coefficients and subtract exponents. 6.02 X 10 24 ÷ 3.01 x 10 23 = 2.00 x 10 1

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SIGNIFICANT FIGURES What are they good for? – They tell us how precise a measurement is. The more significant figures, the more precise the measurement. How do you know how many you have? – All known digits that you can read from the ruler, graduated cylinder, etc, plus one estimated digit.

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When is a digit significant? (red ones ARE) 1. Every nonzero digit is significant. 24.7 m, 0.743 m, and 714 m 2. Zeros between nonzero digits are significant. 7003 m, 40.79 m 3. Leftmost zeros appearing in front of nonzero digits are not significant. They are placeholders. 0.000099 meter 4. Zeros at the end and to the right of a decimal point are significant 43.00 m, 1.010 m, 9.000 m 5. Zeros at the rightmost end, left of an understood decimal point are not significant if they serve as placeholders. 300 m, 7000 m, and 27,210 m (If they ARE known measured values, however, then they would be significant. Writing the value 300m in scientific notation as 3.00 x 10 2 m makes it clear that these zeros are significant.) 6. Counting values & exactly defined quantities have an unlimited number of significant figures;. 23 students, 60 min = 1 hr

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When calculating with measurements, how do you know the correct number of significant figures for your answer? An answer cannot be more precise than the least precise measurement from which it was calculated. The answer must be rounded to make it consistent with the measurements from which it was calculated. Density = mass/volume 11.2 g / 2.1 ml = 5.333333333333333 g/ml = 5.3 g/ml

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How do you round the answers? Once you know the number of significant figures your answer should have, round to that many digits, counting from the left. * If the digit immediately to the right of the last significant digit is less than 5, drop it and the last significant digit stays the same. * If the digit in question is 5 or greater, the last significant digit is increased by 1.

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Adding / Subtracting measurements: The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places. 12.52 meters 349.0 meters + 8.24 meters 369.76 meters 369.8 meters

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Multiplication and Division Round the answer to the same number of significant figures as the measurement with the least number of significant figures. 7.55 m x 0.34 m = 2.567 m 2 = 2.6 m 2 (0.34 meter has the least number of significant figures: two.)

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Table 5. SI prefixes Factor Table 5. SI prefixes Factor prefixsymbolvalueexpanded valueEnglish name yottaY10 24 1 000 000 000 000 000 000 000 000U.S. septillion; U.K. quadrillion zettaZ10 21 1 000 000 000 000 000 000 000U.S. sextillion exaE10 18 1 000 000 000 000 000 000U.S. quintillion; U.K. trillion petaP10 15 1 000 000 000 000 000U.S. quadrillion teraT10 12 1 000 000 000 000U.S. trillion; U.K. billion gigaG10 9 1 000 000 000U.S. billion megaM10 6 1 000 000million kilok10 3 1 000thousand hectoh10 2 100hundred decada10 1 10ten 10 0 1one

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decid10 -1 0.1tenth centic10 -2 0.01hundredth millim10 -3 0.001thousandth microu10 -6 0.000 001millionth nanon10 -9 0.000 000 001U.S. billionth picop10 -12 0.000 000 000 001U.S. trillionth; U.K. billionth femt o f10 -15 0.000 000 000 000 001U.S. quadrillionth attoa10 -18 0.000 000 000 000 000 001U.S. quintillionth; U.K. trillionth zeptoz10 -21 0.000 000 000 000 000 000 001U.S. sextillionth yoctoy10 -24 0.000 000 000 000 000 000 000 001 U.S. septillionth; U.K. quadrillionth

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