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