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Scientific Measurement What is measurement… What is measurement… Measurement is a quantity that has both a number and a unit. Measurement is a quantity that has both a number and a unit. 12 meters or 26 o C or 2 grams

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Numbers in Chemistry can be very large or very small For example…. For example…. A single gram of hydrogen gas contains 602,000,000,000,000,000,000,000 atoms! A single gram of hydrogen gas contains 602,000,000,000,000,000,000,000 atoms! The mass of one atom of gold is 0.000 000 000 000 000 000 000 327 grams! The mass of one atom of gold is 0.000 000 000 000 000 000 000 327 grams! Simplified way to write very large or very small numbers. Simplified way to write very large or very small numbers.

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ALWAYS follows the same format: ALWAYS follows the same format: a coefficient with the first digit in the ones place x 10 raised to a power. 602,000,000,000,000,000,000,000 atoms! Becomes… 6.02 x 10 23 atoms 0.000 000 000 000 000 000 000 327 grams Becomes… 3.27 x 10 -22 grams Scientific Notation

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The exponent tells you how many places you move the decimal to the right or to the left. Positive exponent move decimal to the right (bigger #) Negative exponent move decimal to the left (smaller #) Let’s practice…

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88,000 8.8 x 10 4 0.000341 3.41 x 10 -4 2.41 x 10 5 241,000 6.93 x 10 -3 0.00693 Now try some on your own. Now try some on your own. Check your answers when done. Check your answers when done.

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Measurements are always read to the certain markings AND then estimated one place beyond that marking. cm 1 2 3 4 5 6 cm 1 2 3 4 5 6 This line reads as 3.5 cm 2 significant figures This line reads as 3.55 cm 3 significant figures

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Accuracy and Precision Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is being measured. Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is being measured. Precision is how close a series of measurements are to each other. Precision is how close a series of measurements are to each other.

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Graphic from: http://elchem.kaist.ac.kr/vt/chem-ed/data/acc-prec.htm poor

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Error Error is how far your experimental answer is from the accepted value Error is how far your experimental answer is from the accepted value Error = Experimental value – accepted value Experimental value – accepted value Experimental value – accepted value accepted value accepted value X 100 %Error =

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Significant Digits Significant figures = digits in a measurement we are confident are free from error. Significant figures = digits in a measurement we are confident are free from error. Significant figures include all of the digits that are known for sure, plus a last digit that is estimated. Significant figures include all of the digits that are known for sure, plus a last digit that is estimated.

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Guide to Significant Digits

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Counting Significant Digits 1. Every non-zero digit is significant. 346 3 sig digs 2. Any zeroes between other sig figs are significant. 346007 6 sig digs 3. Zeroes to the left of the first non-zero digit are NOT significant. 0.00028 2 sig digs 4. Zeroes at the end of a number AND to the right of the decimal point ARE significant. 78.400 5 sig digs

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5. Zeroes to the right of a number with no decimal are NOT significant. 34600 3 sig digs 6. For a number in scientific notation, all of the digits to the left of the “x” are significant, and these are the only sig figs in the number. 3.460 x 10 4 4 sig digs

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1. When multiplying or dividing, count the number of sig figs in all the numbers you start with. The number with the fewest sig figs determines the number of sig figs our answer should have. 36 2 sig fig 36 2 sig fig X255 3 sig fig x 3 1 sig fig 27540 30000 1 sig fig 2. When adding or subtracting, look at which place the last sig fig is in for each of the numbers you start with. Whichever place is highest is the last place that answer can have sig digs. 325 (one’s place) + 9.1 (tenth’s place) +20 (ten’s place) 354.1 350 (ten’s place) Calculating with “Sig Figs” How many sig figs should your answer have?

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