Ch. 3 – Scientific Measurement

Test: Sept. 14th

Workbook Units: 1-3

3.1 – The Importance of Measurement

What types of measurements are made in chemistry?

Length, Temperature, Mass, Volume…

Qualitative v. Quantitative Measurements

Not all measurements give the same amount of info.

Qualitative

•Descriptive

•Non-numerical

•Ex: the basketball is brown, the person feels hot

Quantitative

•Require an instrument

•Have numbers and units

•Ex: the diameter of the basketball is 31 cm, the person’s temperature is 99.7o F

Scientific NotationScientific Notation

In chemistry, we use scientific notation b/c we deal with extreme numbers.

36,000 = 3.6 x 104 and 0.0000073 = 7.3 x 10-6

coefficient exponent

The exponent tells you how many places to move the decimal and in which direction.

Multiplication & Division

Multiply

•Multiply the coefficients

•Add the exponents

Ex: (3.0 x 103)(2.0 x 102) = 6.0 x 105

Divide

•Divide the coefficients

•Subtract the exponents

Ex: 3.0 x 105 / 2.0 x 102 = 1.5 x 103

Addition and Subtraction

Before adding or subtracting in scientific notation you must make the exponents the same.

7.1 x 10-2

-5.0 x 10-3

7.1 x 10-2

-0.50 x 10-2

6.6 x 10-2

Make sure the decimals are aligned.

3.2 - Uncertainty in Measurements

•Accuracy = how close a measurement is to the accepted (true) value

•Precision = how close multiple measurements are to each other

•Error = accepted value – experimental value

•% Error = (|error| / accepted value) x 100%

Let’s visualize a target:

Accuracy

Precision

Accuracy

Precision

Accuracy

Precision

Percent Error Calculations

You measure the boiling point of water to be 99.3oC and the accepted value is 100.0oC… Find the % error.

|0.7| / 100 x 100% = .7%

Note: Error can be negative too so we use the absolute value of it.

You try: Accepted value = 7.5 m; Experimental value = 7.9 m 5.3%

Significant Figures in Measurements

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html

•Rules For Counting, Calculating, and Rounding Sig. Figs:

•Practicing with Sig. Figs:

http://science.widener.edu/svb/tutorial/sigfigures.html

When are Digits Significant?Non-zero digits are always significant.

With zeroes, the situation is more complicated:

a) Zeroes placed before other digits are not significant; 0.046 has two significant digits.

b) Zeroes placed between other digits are always significant; 4009 kg has four significant digits.

c) Zeroes placed after other digits but behind a decimal point are significant; 7.90 has three significant digits.

When are Digits Significant? … continued

d) To avoid uncertainty, use scientific notation to place significant zeroes behind a decimal point:

•8.200 103 has four significant digits •8.20 103 has three significant digits

•8.2 103 has two significant digits

2 Exceptions!!Measurements have unlimited number of

sig figs if..1) COUNTING IS INVOLVED.

*If you count how that there are 23 people in this classroom, then there are exactly 23 people, not 22.9 or 23.1

*This measurement can only be a whole number and has unlimited number of sig figs in the form of zeroes to the right of the decimal.

Measurements have unlimited number of sig figs if…

2) INVOLVES EXACTLY DEFINED QUANTITIES

*Usually associated with a system of measurement

*Ex) 60 minutes = 1 hour

*By definition, there are exactly 60 minutes in an hour.

*Saying “60.0000000” does not change that there are 60 minutes in an hour!

Sig Figs in Calculations

• Addition & Subtraction – the answer should be rounded to the same number of decimal places not digits as the measurement with the least number of dec. places

• EX: Add 12.52m + 349.0m + 8.24m

• What is the correct rounded answer?

369.8 m

Multiplication & Division

• You need to round the number to the same number of sig figs as the measurement with the least number of sig figs.

• EX: 7.55m x 0.34m =

2.6 m2