Calibration vs. Precision

• If a balance is accurate, it should read 0 when nothing is on it.

• The process for making sure a balance or any equipment is accurate is called CALIBRATION.

• Clocks can measure to the minute, second or fraction of a second.

• This refers to an instrument’s PRECISION.

Need for Sig Figs

• Measurements must reflect the precision of the instrument used, so significant figures become important.

• When measuring, you record all known digits plus you estimate the final digit if possible.

• For example if your ruler measures to the nearest cm, you would estimate how far it is between the 2 cm markings.

Rules for counting sig figs

1. All nonzero numbers ARE significant

Ex: 234.5 = 4 sig figs

2. All zeros between nonzero numbers ARE significant

Ex: 2304.5 = 5 sig figs

Rules for counting sig figs3. Zeros that act as placeholders ARE NOT significant.

Think of how you’d rewrite these numbers as a fraction or in scientific notation – the zeros would disappear.

This includes any zeros left of nonzero digits or any number ending in zero that does NOT include a decimal.

Ex: 0.0234 = 3 sig figs 14320 = 4 sig figs

Rules for counting sig figs

4. All final zeros to the right of the decimal are significant.

Ex: 23.00 = 4 sig figs

5. Counting numbers and defined constants have an infinite number of sig figs.

Ex: 6 molecules, 60 seconds in a minute or 100%

Try It

• Round each figure to 3 sig figs:

219034

25.38

0.08763

119.99

Solutions

• Round each figure to 3 sig figs:

219034 = 219,000

25.38 = 25.4

0.08763 = 0.0876

119.99 = 120.

Counting Sig Figs when adding/subtracting

• Your final answer must have the same number of sig figs to the right of the decimal as the starting value with the fewest digits to the right of the decimal.

Ex: 2.54 + 3.1 + 2.275 = 7.915 BUT your final answer needs to round to 7.9

Counting Sig Figs when multiplying/dividing

• Your final answer must have the same number of sig figs as the starting value with the fewest significant figures.

Ex: A box measures 2.5 on a side, so you find the volume to be 15.625 BUT you must round your answer to 16 cm3 since you only had 2 sig figs in your measurement.

Try It

• Complete the following problems, rounding answers to the correct number of sig figs:

(5.53 x 10-6 km) x (7.64 x 103 km)

(9.33 x 104 mm) / (3.0 x 102 mm)

(4.42 x 10-3kg) – (2.0 x 102 kg)

Solutions

• Complete the following problems, rounding answers to the correct number of sig figs:(5.53 x 10-6 km) x (7.64 x 103 km)

= 4.22 x 10-2 km(9.33 x 104 mm) / (3.0 x 102 mm)

= 3.1 x 102

(4.42 x 10-3kg) – (2.0 x 102 kg)= -2.0 x 102

Try It

• The accepted length of a steel pipe is 5.5 m. Calculate the percent error and round to the correct number of sig figs for these measurements:

5.7 m

5.1 m

Try It

• The accepted length of a steel pipe is 5.5 m. Calculate the percent error and round to the correct number of sig figs for these measurements:

5.7 m = .2/5.5 x 100% = 3.6%

5.1 m = -.4/5.5 x 100% = -7.3%