How should data be

reported in Chemistry?

There are two kinds of numbers:

• Exact numbers: may be counted or defined (they are absolutely accurate).

Numbers obtained from measurements are not exact.

These measurements involve estimating.

You can report one estimated digit.

• 6.35 or• 6.36 or• 6.37• the last number is the best

estimate for the 3 students.• Two numbers are certain.• One number is uncertain.• three significant figures!

significant figures indicate the uncertainty in measurements

Scientific notation:

How to count significant figures ?

1. 438 g = 4.38 x 102 3 s.f.

2. 2678.42 = 2.67842 x 103 6 s.f.

3. 1.7 2 s.f.

Task 1: Try these! A) Write in scientific notation.B) Determine the number of significant figures

1. 5062. 10.053. 900.434. 60.005. 1.096. 0.067. 0.00470

How do you round off?

• If the numbers to be discarded are less than 50 leave the last significant number unchanged : 23.31 23

• If the numbers to be discarded are more than 50 add one to the last significant digit : 23.54 24

• If the numbers to be discarded are 50 round off so that the last significant number is an even number : 23.5024

TASK 2: Complete these multiplication and division problems

1. 13.7 x 2.5

2. 200. x 3.58

3. 2.3 x 3.45 x 7.42

4. 0.003 / 5

5. 89 / 9.0

6. 5000 / 55

500 = 1 SF 500. = 3 SF 550 = 2 SFOn a measuring device, for example the measurement of 500 ml in a measuring cylinder, for the purposes of accuracy this is assumed to be an absolute value.

TASK 3: Complete these addition and subtraction problems

1. 0.008 + 0.05

2. 4.50 + 3

3. 35.89 + 34.6

4. 200 – 87.3

5. 75.0 – 2.55

6. 10.0 – 9.9

TASK 4: Apply your knowledge

Write:1. 35.270 to 3 significant figures

2. 0.4140 to 2 significant figures

3. 87.257 to 3 significant figures

4. 1.350 to 2 significant figures

5. 62.50 to 2 significant figures

Multiple step problems

• When carrying out multiple step problems keep one extra significant figure throughout the whole problem, to reduce rounding errors.

• The final result should be consistent with the number of significant figures given in the experimental measurements.

• Unit conversions are infinitely accurate. The number of significant figures does not change because conversions are exact values, not measured values.

• Counted numbers are infinitely accurate, such as counting the number of atoms in H2O (there are 3). 3 is an exact value not a measured value. Counting does not need a tool.

• Measuring requires the use of a tool: ruler, scale, balance, graduated cylinder etc… Measured numbers are only as accurate as the tool being used. The number of significant figures should indicate this.

Converted, Measured and Counted Numbers

A great website for practicing Significant figures can be found at:http://www.sciencegeek.net/Chemistry/taters/sigfigs.htm