Cup of coffee = ~ 200 ml Add drop of H

2

O = 0.05 mL New volume: ~200 mL or 200.05 mL??

If you say 200.05 you imply that the volume of the initial cup of coffee was exactly 200 mL and we don’t know that accurately.

New volume: ~200 mL or 200.05 mL??

We convey our uncertainty in measured quantities by abiding by the rules of significant figures.

Definition of Significant figures.

The number of all known digits reported in measurements plus one estimated digits.

We would have to report the coffee measurement as ~200 because that is our least accurate number.

A chain can never be stronger than its weakest link.

An answer can never be more precise than the least precise number you use to get the answer.

Significant Figures

Try These!

1.36

172 3247 3 significant digits 3 significant digits 4 significant digits

Try These!

0.5

0.0053567

0.0008769

1 significant digit 5 significant digits 4 significant digits

Try These!

20.05

1.003

102001 4 significant digits 4 significant digits 6 significant digits

Try These!

9.000000000

85.00

9.98000

10 significant digits 4 significant digits 6 significant digits

Try These!

250 780,000,000 90.

2 significant digits 2 significant digits 2 significant digits

Practice 46800

3 significant figures

Rule:

Trailing zeroes in a number with no decimal are not significant

Practice 126.48

5 significant figures

Rule:

All nonzero integers are significant

Practice 1.0005

5 significant figures

Rule:

Captive zeroes are always significant

Practice 90.0

3 significant figures

Rules:

1. Trailing zeroes in a decimal number are significant.

2. Zeroes at the end of a number count if there is a written decimal point.

Practice 192

3 significant figures

Rule:

All nonzero integers are significant

Practice 0.000004

1 significant figure

Rule:

Leading zeroes are never significant

Practice 0.01006

4 significant figures

Rules:

1. Leading zeroes are never significant 2. Captive zeroes are always significant

Question For Thought

Using two different rulers, I measured the width of my hand to be 4.5 centimeters and 4.54 centimeters. Explain the difference between these two measurements.

The first measurement implies that my hand is somewhere between 4.5 and 4.9 cm long. There is a uncertainty in this number because we have to estimate.

The second measurement implies that my hand is between 4.5 and 4.6 cm long. This measurement is more certain due to its greater precision.

4.5 cm 2 significant figures Uncertain 4.54 cm 3 significant figures More certain due to greater precision

Significant figures are necessary to reduce uncertainty in our measurements.

Significant figures indicate the precision of the measured value!!