warm-up: to be turned in
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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 - PowerPoint PPT PresentationTRANSCRIPT
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