Unit 1- Units and Measurement Chemistry. Scientific Notation, Measurement, Accuracy, Precision, Error.

Unit 1- Units and Measurement

Chemistry

Scientific Notation, Measurement, Accuracy, Precision, Error

Scientific Notation

M x 10n

M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10 n is positive if number is greater 1 n is negative if number is less 1

Scientific Notation Write the following in scientific notation:

5450000 =

0.0002570 =

Limits of Measurement

Accuracy and PrecisionUncertaintyExact Numbers vs. Inexact

Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

Example: AccuracyWho is more accurate when

measuring a book that has a true length of 17.0cm?

Susan:

17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy:

15.5cm, 15.0cm, 15.2cm, 15.3cm

Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Example: Precision

Who is more precise when measuring the same 17.0cm book?

Susan:

17.0cm, 16.0cm, 18.0cm, 15.0cm

Amy:

15.5cm, 15.0cm, 15.2cm, 15.3cm

Example: Evaluate whether the following are precise, accurate or both.

Error

Error= experimental –accepted value

Percent Error

% Error= |experimental –accepted| x100

accepted value

Significant Figures

The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

Uncertainty-

Centimeters and Millimeters

The last (farthest to the right) significant figure in a measured quantity alwayshas some associated uncertainty. The minimum uncertainty is ± 1 in the last digit

Graduated Cylinder - Meniscus

Reading Scales to the Correct Significant Figures Uncertainty?

Reading Scales to Correct Significant Figures

Reading Scales to Correct Significant Figures Uncertainty?

Rules for Counting Significant Figures

All nonzero digits are significant. (42 has 2 sf’s.) Zeros in the middle of a number are significant. (4.803 cm has 4 sf’s.) Leading zeros are not significant; they are there to locate the decimal point. (0.00123 g has three sf’s.) Trailing zeros are significant if the number contains a decimal point. (55.220 K has five sf’s; 50.0 mg has three sf’s, 5.100 × 10-3 has four sf’s.) Trailing zeros are not significant if the number does not contain a decimal. (34,200 m has three sf’s.)

How many sig figs?100 kg 0.000303 mm

10302.00 cm 92,900,000 km

0.001L 6.02 x 1023 atoms

10302 m 0.0205 m

1.0302x104 ms2.05 x 10-2 m

1010.010 g

Sig Figs in Addition/Subtraction

The result has the same number of decimal places as the number in the operation with the least decimal places.

Ex: 2.33 cm

+3.0 cm

5.3 cm

Sig Figs in Multiplication/Division

The answer has the same sig figs as the factor with the least sig figs.

Ex: 3.22 cm

x 2.0 cm

6.4 cm2

Measured Numbers vs. Exact Numbers Exact numbers are values that are known

exactly (3 atoms = 3.00000…atoms) or that are true by definition: 12 inches = 1foot, 60 s = 1 min, 5280 feet = 1 mile, 100 cm = 1m, 2.54 cm = 1 inch, etc.

All inexact or measured numbers will have some limit to how precisely they are known, and there is a limit to the number of significant digits contained in the number.