Warm-Up: To be turned in How long (in cm) is this line? What is the volume (in mL) of the liquid?
Using Scientific Measurements Sig Figs and Scientific Notation
Accuracy vs. Precision Accuracy- how close the measurements are to the accepted value Precision- how close the measurements are to each other
Sig Figs The digits in a measured number that indicate the measuring equipment’s degree of precision. All numbers in a measurement are known with certainty, except for the last number
Determining the Number of Sig Figs All non-zeros are always significant Leading zeros are never significant Ex: 0.000056 has 2 sig figs “sandwiched” zeros are always significant 80.009 has 5 sig figs Trailing zeros are significant only if there is a decimal 2000 has 1 sig fig 2000. has 4 sig figs
Practice Put the following numbers in order from the fewest sig figs to most sig figs: 1.02 .000005 2.3 80006 4000.
Solving problems Using Sig Figs Adding/ subtracting- answer will have the same number of digits as the number with the fewest decimal points Ex: 3.4 + 5.68 = 9.08 9.1 Multiplying/ dividing- answer will have the same number of digits as the number with the fewest sig figs Ex: 2.6 x 3.14 = 8.164 8.2
Practice 2.36 + 5.012 + 6.3= 6.258 x 2.56=
Scientific Notation Shorthand for writing really large and really small numbers M x 10n format M is a number greater than 1, but less than 10 N is a whole number whose value is based on how many places the decimal is moved to the left or right Ex: 90,000= 9 x 104 0.00009= 9 x 10-4
Practice Put the following in scientific notation: .0000056 9850000000 Put the following numbers in standard notation: 2.5 x 106 1.36 x 10-4
Solving Problems Using Scientific Notation Addition/ subtraction- can only be done if exponents are the same Add M values, but leave exponent the same Ex: 3.6x104 + 1.8x104 = 5.4x104 Multiplication/ division- multiply M values, add (if multiplying) or subtract (if dividing) exponents Ex: 1.2x103 x 2.0x107 = 2.4x1010
Practice 2.5 x 106 – 1.0 x 106 = 2.5 x 106 = 2.0 x 102