Chapter 1 “Chemistry and You”

‘Significant Figures and

Scientific Notation’

Scientific NotationNumbers that are very large or

very small are conveniently expressed in scientific notation.

Scientific NotationThere are two parts to scientific

notation:The first part is the number 1 or a

number between 1 and 10 The second part is x 10n

So 54 000 = 5.4 x 104

And 0.000 008 765 = 8.765 x 10-6

Scientific Notation

+

If the decimal point is moved to the left, the exponent is POSITIVE

-

If the decimal point is moved to the right, the exponent is NEGATIVE

Scientific Notation Rules for calculations:

Addition and subtraction: All values must have the SAME

exponent before they can be added or subtracted:

4.5 x 106 – 2.3 x 105 = 45 x 105 – 2.3 x 105 = 42.7 x 105

= 4.27 x 106

Scientific Notation Rules for calculations:

MultiplicationThe numbers are multiplied and

the exponents are ADDED (3.1 x 103) (5.01 x 104) = (3.1 x 5.01) x 104+3

= 16 x 107

= 1.6 x 108

Scientific Notation Rules for Calculations

DivisionThe numbers are divided and the

exponents are SUBTRACTED7.63 x 103 = 7.63 x 103-4

8.6203 x 104 8.6203 = 0.885 x 10-1

= 8.85 x 10-2

The number of significant figures in a measurement depends on the ability of the measuring device.

Significant figures in a measurement include all the known digits plus one that is estimated.

Significant Figures

Calculations with Sig FigsWhen a calculation involves

measurements with numbers that have different numbers of significant figures, the answer should have the same number of significant figures as the number with the LEAST, in the measurement.

Rule 1All non-zero figures are

significant

523 grams

972,366 sec

25.61 moles

3 significant figures

6 significant figures

4 significant figures

Rule 20’s in the MIDDLE of a number are ALWAYS

significant

5082 meters

2.0008 liters

0.00800341 moles

4 significant figures

5 significant figures

6 significant figures

Rule 30’s in the front of a number

are NEVER significant

0.0032 kg

0.00000751 meters

0.00300305 liters

2 significant figures

3 significant figures

6 significant figures

Rule 4 – Part 10’s at the END of a number are SOMETIMES significant** Decimal Point PRESENT,

0’s ARE significant

2.000 Liters

0.000500 grams

0.0070300 moles

4 significant figures

3 significant figures

5 significant figures

Rule 4 – Part 20’s at the END of a number are SOMETIMES significant

** Decimal Point ABSENT, 0’s are NOT significant

2000 L

550 meters

3,005,000 seconds

1 significant figure

2 significant figures

4 significant figures

Scientific notation is the most reliable way of expressing a number to a given number of significant figures.

In scientific notation, the power of ten is insignificant.

For example, if one wishes to express the number 2000 to varying degrees of certainty:

2000 2 x 103 is expressed to one significant figure.2000 2.0 x 103 is expressed to

two significant figures.2000 2.00 x 103 is expressed

to three significant figures2000 2.000 x 103 is

expressed to four significant figures

Rounding Off Significant figuresWhen rounding, examine the figure

following (i.e., to the right of) the figure that is to be last.

This figure you are examining is the first to be dropped.

The Rules1. If it is less than 5, drop it and

all the figures to the right of it.2. If is more than 5, increase by

1 the number to be rounded, that is, the preceding figure.

3. If it is 5, round the number so that is will be even.

Example 1Round 62.5347 to four significant

figures.Look at the 5th figure. It is a 4A number less than 5.Drop every figure after the fourthThe original number rounds to

62.53

Example 2Round 3.78721 to three significant

figuresLook at the 4th figure. It is 7.A number greater than 5.Round the original number up.The original number rounds to 3.79

Example 3Round 726.835 to five significant

figures.Look at the 6th figure. It is 5.Now look at the 5th figure. It is 3.

ODDRound the original number up.The original number rounds to

726.84

Example 4Round 24.85 to three significant

figures.Look at the 4th figure. It is 5.Now look at the 3rd figure. It is 8.

EVENDrop the 5 and all number after it.The original number rounds to 24.8