Significant Figures Aren’t all numbers important?!?!?!? Yes, but some are more significant than others…

Accuracy / Precision Accuracy – the agreement between a measured value and a true value. Precision – agreement between several measurements of the same quantity.

Significant Figures A measurement can only be as accurate and precise as the instrument that produced it. A scientist must be able to express the accuracy of a number, not just its numerical value

Significant Figures We can determine the accuracy of a number by the number of significant figures it contains.

Doing Math with Sig. Figs. If you add two numbers together the answer is only as precise as your least precise number. Your answer will have only as many digits after the decimal point as your least Precise number. Example: = The 2.0 has only 1 significant figure past the decimal, so our answer can only have 1 digit pas the decimal. Answer = 10.6 ADDING AND SUBTRACTING:

Multiplication and Division with Sig. Figs. Your answer can only be as precise as your least precise number. This time we are not just worried about after the decimal, but the least precise number as a whole. You answer should have the same number of significant figures as the number In the problem with the fewest significant figures. Example: (3.78 x x 4.5) = The 4.5 only has two significant figures so our answer can only have two. Answer = 68

Scientific Notation Helping us write really tiny or really big numbers

Carelessness when using numbers I have a million math problems to do I have a trillion things to get done tonight If you win 1 million dollars and you’re given the prize in 100 dollar bills, your stack of money is…. 4 inches high

Rules to Scientific Notation Parts: 1. Coefficient (mantissa) – must be a number from 1 – Exponent – a power of x 10 6 Easier than writing 3,400,000

Numbers Greater Than Find the number by moving the decimal point that is between 1 – ,300,000  Write a positive exponent which is equal to the number of places you moved the decimal point to the left x 10 7

Numbers Less Than 1 1. Find the number by moving the decimal point that is between 1 –  Write a negative exponent which is equal to the number of places you moved the decimal point to the right x 10 -4

Math Operations & Sci. Notation For Multiplication: multiply coefficients add exponents (3.0 x 10 4 ) x (2.0 x 10 2 ) = 6.0 x x 2 = = 6

Math Operations & Sci. Notation For Division: divide coefficients subtract exponents (6.4 x 10 6) / (1.7 x 10 2 ) = 3.8 x / 1.7 = 3.86 – 2 = 4

Be Careful… Remember the rule about the coefficient! Ex. (4.0 x 10 3 ) x (3.0 x 10 4 ) = 12.0 x 10 7 WRONG!!! Answer = 1.2 x 10 8

Math Operations & Sci. Notation For Addition and Subtraction: must make the exponents the same Ex. 5.4 x x 10 4 = 0.54 x x x 10 4

Special Note Sometimes exponents are written differently. We are used to 3.4 x 10 5 However, you may see 3.4E5 It means the same thing (“E” represents the exponent and replaces x 10

Write in Scientific Notation and Determine the number of sig. figs _____ _____ _____ _____ 5. 5,000_____ 6. 5,000._____ 7. 6,051.00_____ _____ _____ ,001_____ ______ ______ ______ x 10 2 ______ ______ ,100 ______ x ______ ,800,000. ______ x ______ ______