UNDERSTANDING

SIGNIFICANT

FIGURES

Towson University Academic Achievement Center CK524

HOW MANY SIG FIGS ARE IN A NUMBER?

We’re going to use a map of the United States to

help us.

First question to ask ourselves,

is if a decimal is present or not.

If it’s

Present,

start

counting at

the first

non-zero

from the

Pacific side

and keep

counting

until the

end.

If it’s

Absent, start

counting at

the first

non-zero

number

from the

Atlantic side

and keep

counting

until the

end.

YOUR TURN!!!

23.4 3306 3 4 100 54.20 1 5 54.2 606 3 3

NOW, LET’S DO SOME ADDITION

(OR SUBTRACTION)

1. Count up the decimal places in every number

2. Identify the number with the least amount of

decimal places

3. Solve the problem as normal with all decimal

places 4. Round your number to the same number

of decimal places as the number in step 2

AN EXAMPLE 10.12 + 38.254 + 6.0 + 105.9999 = ?

2 3 1 4

1. Count up the decimal places in every number

2. Identify the number with the least amount of decimal places

3. Solve the problem as normal with all decimal places

4. Round your number to the same number of decimal places

as the number in step 2

160.3739

160.4

YOUR TURN!!!

106.23-48.0+2+28.8756 85.56+62.0-3.869 1.23X10^23-3.3X10^16

LET’S APPLY THIS TO LAB Suppose that a mixture of 8g of sugar, 52.0 g of

salt, and 100.01 g of flour is prepared. What is

the total mass of the mixture expressed in

exponential notion and with proper significant

figures?

1.13 x 102

ALL RIGHT….TIME TO MOVE ON TO

MULTIPLICATION AND DIVISION

1. Count up the sig figs in every number

2. Identify the number with the least amount of

sig figs

3. Solve the problem as normal with all sig figs

4. Round your number to the same number

of sig figs as the number in step 2

BIG PICTURE!!!

Addition/Subtraction – Use Decimals Multiplication/Division – Use Sig Figs

AN EXAMPLE 23 x 38.254 ÷ 6.0 = ?

2 5 2

1. Count up the sig figs in every number

2. Identify the number with the least amount of sig figs

3. Solve the problem as normal with all decimal places

4. Round your number to the same number of sig figs as the

number in step 2

146.640333333333…

150

YYOOUURR TTUURRNN!!!!!!

101.1 X 21 85.56 X 62.0 / 3.869 9.65 X 10^13 / 3.3 X 10^16

LET’S APPLY THIS TO LAB Suppose there are 412 Quercus alba (white oak

trees) and 5563 Rhododendron arborescens

(sweet azalea bushes) in 5.2 acres at a state park.

How many individuals of each species are in one

acre?

79 white oaks 7.9 x 101 white oaks

1100 sweet azalea 1.1 x 103 sweet azaleas

ANOTHER LAB APPLICATION….. A thermometer in lab reads 52.3°C. You are

curious what that is in°F. Use the below equation

to convert °C to°F:

126

°C x 9/5 + 32 = °F

Important Note!!! Constants (such as 9/5, 9.81, etc.) do not “Count” when determining sig figs!!!

OTHER WEIRD THINGS YOU MIGHT

ENCOUNTER…

So we already know that constants don’t “count” for sig figs, but

what about other things?

Exact values i.e.) 7 apples, 12 eggs in one dozen DO NOT

count

Inexact values i.e.) π, c =3.00 m/s, anything you measure

DO count

OTHER WEIRD THINGS YOU MIGHT ENCOUNTER…

Trig functions follow the same rules for sig figs as multiplication

and division

Exponents do not count for sig figs, only the number raised to

the exponent i.e.) 2.364 has 3 sig figs

Lab application: number derived from graphs i.e.) slope or y

intercept only have as many significant figures as the data point with the least amount of significant figures

ALWAYS ASK YOUR PROFESSOR IF YOU’RE UNSURE!

ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION.

OH MY! 1.Use the order of operations to determine

what group of numbers to start with (PEMDAS)

2.While working within one group ie) P, or MD, do not round with

appropriate sig figs until you’ve

finished with that one group

3.Move onto the next group and use the sig fig rules for that group and the number you got from step 2

4.Repeat this process for each group until the end

AN EXAMPLE (10.12 + 85.2 – 100.527) ÷ 6.31 + 10.4 = ?

(-5.2) ÷ 6.31 + 10.4 = ?

(-.82) + 10.4 = 9.6

1. Use the order of operations to determine what group of numbers to start

with (PEMDAS) 2. While working within one group ie) P, or MD, do not round

with appropriate sig figs until you’ve finished with that one

group

3. Move onto the next group and use the sig fig rules for that group

and the number you got from step 2

4. Repeat this process for each group until the end

YOUR TURN!!!

3.6^6 x (1.25 x 10^3 + 3.2 x 10^2 (TAN(43) + .5631)^2 + .5 (100.0 – 21.22 + 6.6) x COS(35) + 7.34^3

MORE LAB APPLICATION

When using digital equipment, always record the exact number

that comes from the machine (including ALL zeros) When doing measurements yourself, always estimate to one

more significant digit than what is shown.

MORE LAB APPLICATION

MORE PRACTICE…

http://www.sciencegeek.net/APchemistry/APtaters/sigfigs.htm

Made for Towson University’s

Academic Achievement Center 2013

Contact us for more information!

achieve@towson.edu

410-704-2291