Advanced Placement Chemistry Significant Figures Review

AP Chemistry

2010 - 2011

Significant Figures

When we use equipment to measure quantities, we are limited in our

ability to report an accurate value of the measurement by the precision of

the equipment used to measure the quantity.

When we report measurements, we want the presented values to have the

precision that is possible but not more than is possible or reasonable.

Thus, we apply rules for reading equipment and using those

measurements in our calculations and reported data (answers).

Significant Figures

For example, look at the burette at right. It is

marked in 1 mL increments. Because the

burette is marked in 1 mL increments, we

can easily read the volume to these markings.

Consider that the volume is at the level

shown and the burette was initially at the

zero mark. What certain volume of solution

has been used?

Although we know for certain that the

volume used is 14 mL, we really know that

the volume used is between 14 and 15 mL.

So, we estimate one additional digit beyond

those that are known for certain. Here, we

estimate the 0.10 mL value because we know

the 1 mL value with certainty.

What estimated volume of liquid has been

used?

Significant Figures

We report measurements to one additional digit beyond those that are

know for certain – these are termed the significant figures of the

measurement.

We do not report beyond one estimated digit because the estimated digit

is just that – estimated; to increase the precision beyond an estimated

digit would add no usefulness to the measurement. In fact, it would report

false information by implying that we know the value to a greater

precision than that which is actually known. For example, we would not

report the volume in the previous example to 14.557839200 mL, as this

implies much more precision than what is really available to us.

Significant Figures

In essence, we report data to one place beyond the place in which the

equipment is marked. So, for a burette marked to the ‘ones’ place, we

report to the ‘tenths’ place. For a pipette marked to the ‘tenths’ place, we

would estimate the ‘hundredths’ place.

Typical laboratory equipment that we use will require estimation to 0.10 or

0.01. Digital equipment is programmed to estimate the last digit – do not

try to estimate beyond those that are shown on the display.

Significant Figures

When reading data, how many significant figures are present?

• All non-zero digits are significant.

This measurement has 3 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Zeros between non-zero digits are significant.

This measurement has 4 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 3 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 3 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 3 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 4 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 4 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 1 significant figure.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 1 significant figure.

Significant Figures

When reading data, how many significant figures are present?

• Zeros are also significant when a decimal point is present and the zeros

are to the right of a non-zero digit. (Ask, “Is this zero a placeholder or does

it add precision to the measured value?”)

This measurement has 4 significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Defined and counted values have an infinite number of significant digits

and are not used in determining the overall precision of a reported value.

This defined value has INFINITE significant figures.

Significant Figures

When reading data, how many significant figures are present?

• Defined and counted values have an infinite number of significant digits

and are not used in determining the overall precision of a reported value.

These counted values have INFINITE significant figures.

Significant Figures

Practice: Indicate the number of significant figures in the following values.

0.056 cm 0.111 g 3.045 x 103 lbs

2 3 41.34 meters 0.0500 hours 4.5 x 10-4 grams

3 3 26.54 g 5260 feet in a mile 6.022 x 1023 atoms

3 infinite 4125.05 grams 2.54 cm 60 minutes in 1 hour

5 3 infinite15.9994 grams 0. 0540 cm3 1.0 x 102 grams

6 3 2

Significant Figures

When calculating with data, how do we represent an answer?

• When adding or subtracting values, we report the answer to contain a

number of DECIMAL places equal to the term with the fewest used to obtain

the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• When adding or subtracting values, we report the answer to contain a

number of DECIMAL places equal to the term with the fewest used to obtain

the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• When adding or subtracting values, we report the answer to contain a

number of DECIMAL places equal to the term with the fewest used to obtain

the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• When adding or subtracting values, we report the answer to contain a

number of DECIMAL places equal to the term with the fewest used to obtain

the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• When multiplying or dividing values, we report the answer to contain a

number of SIGNIFICANT FIGURES equal to the term with the fewest used to

obtain the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• When multiplying or dividing values, we report the answer to contain a

number of SIGNIFICANT FIGURES equal to the term with the fewest used to

obtain the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• When multiplying or dividing values, we report the answer to contain a

number of SIGNIFICANT FIGURES equal to the term with the fewest used to

obtain the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• When multiplying or dividing values, we report the answer to contain a

number of SIGNIFICANT FIGURES equal to the term with the fewest used to

obtain the answer.

Significant Figures

When calculating with data, how do we represent an answer?

• Rounding: consider only the digit that follows the digit to be retained;

round up if it is 5 or greater, round down if it is less than 5.

Significant Figures

When calculating with data, how do we represent an answer?

• Rounding: consider only the digit that follows the digit to be retained;

round up if it is 5 or greater, round down if it is less than 5.

Significant Figures

When calculating with data, how do we represent an answer?

• Rounding: consider only the digit that follows the digit to be retained;

round up if it is 5 or greater, round down if it is less than 5.

Significant Figures

When calculating with data, how do we represent an answer?

• Sometimes, we can only represent data to the correct number of sig figs if

we use scientific notation.

Significant Figures

When calculating with data, how do we represent an answer?

• Sometimes, we can only represent data to the correct number of sig figs if

we include trailing zeros and a decimal point.

Significant Figures

Practice: Perform the following calculations to the correct number of sig

figs

0.05 g + 1.04 g 0.05 – 1.04 g

1.09 g –0.99 g0.05 g + 1.0 g 0.05 g – 1.0 g

1.1 g –1.0 g100.0 grams + 10.0 grams 0. 05 g + 3.222 g

110.0 g 3.27 g5.1 kg + 3.672 kg 6.0944 g + 32.998 g + 22.989 g

8.8 kg 62.081 g

Significant Figures

Practice: Perform the following calculations to the correct number of sig figsAssume all are measured values unless otherwise indicated

6.345 x 0.0025 3.250 ÷ 200

0.016 0.022.50 · 102 x 100 20 x 20

3 x 104 40020 x 20. 20. x 20.

400 4.0 x 102

20.0 x 20.0 20.00 x 20.00

400. 400.019.55 days converted to hours molar mass of PbCO3

469.2 hours 267.2 g

Significant Figures

The following items in your textbook will

provide additional practice:

1.37 to 1.42

You can also try the Skill Activity on this topic online:

AP Chemistry Skill Activities Significant Figures

Significant Figures