Significant FiguresDensity% Error

Significant Figures

The number of digits reported in a measurement.

All the known digits plus one estimated value.

The number of significant figures possible depends upon the piece of equipment used to take the measurement.

Significant Figures

Rules for Significant Figures1. Non-zero numbers are always significant.2. Zeros between non-zeros are always

significant.3. All final zeros to the right of the decimal

place are significant. 4. Zeros that act as placeholders are NOT

significant. 5. Counting numbers and defined constants

have an infinite number of significant figures.

Practicing Significant FiguresDetermine the number of sig figs in the following numbers.

1)0.02

2)70001

3)5600

4)4.100

5)3.1416

(π)

6)2.80 x

105

0.02

70001

5600

4.100

3.1416 (π)

2.80 x 105

1

5

2

4

Infinite

3

Red numbers=significant Black numbers=not significant

Rules for Rounding

If the digit to the immediate right of the last sig fig is 5-9, round up.

If not, leave as is.

Significant Figures and Calculators

When using a calculator, you should do the calculation using the digits allowed by the calculator and round off only at

the end of the problem.

Do not round off in the middle of the problem!

Sig Figs and Addition/Subtraction

+ - + - + - + - + - + - + - +When you add or subtract, you answer must have the same number of digits to

the right of the decimal point as the original value with the fewest digits to

the right of the decimal place.+ - + - + - + - + - + - + - +

Sig Figs and Multiplication/Division

When you multiply or divide, your answer must have the same number of significant figures as the original value

with the least significant figures.

Practicing Significant Figures

3.33 m2

25 m

53 mL

26.6 g

6.7 cm3

Density

Which weighs more, a pound of bricks or a pound of feathers?

Density

When something feels heavy, you are noting its density.

Density—the mass of an object per unit volume

Density

D= The unit for density should always

be some unit for mass over some unit for volume.

Usually it is g/mL, g/L or kg/m3

mv

Practice Problem #1

What is the density of an object that has a mass of 22.5g and a

volume of 30.4 mL?

Practice Problem #2

If a cube has sides that are 8.2 mL each and a total mass of 46.1g,

what is its density?

Practice Problem #3

What is the volume of isopropyl alcohol if its mass is 45.22g and it

has a density of 0.899 g/mL?

Percent Error

A way to evaluate the accuracy of data.

Percent Error=Ratio of the error to the accepted value

│Accepted value – Measured value │Accepted value X 100%

Percent Error

If your measurement of a liquid is 123.4 mL but the actual amount is 125.0 mL, what is the percent error of the

measurement?

125.0 mL – 123.4 mL 1.6 mL________________________________________ _______________

125.0 mL 125.0 mL = X 100% = 1.3%