Significant Digits

Aluminum Foil Investigation

• Your teacher will provide you with a hand out of an investigation in which you will be trying to determine the thickness of a piece of aluminum foil

• You will get into groups of 2 to 3 and complete the investigation

Hints for Investigation

• Does anyone need a few hints to get them started?

• Then density of aluminum is 2.70 g/cm3 • The equation for density is • Is anyone still having trouble?• Here’s another hint:–

Using Measurements In Science

• In the previous activity you were forced to take several measurements such as length, volume, and mass

• We take measurements like this every day of our lives and often take them for granted

• In science we use a standard system of measurements called the International System of Units (SI units) so that everyone is using the same system

Quantity Definition SI units or their derived equivalents

Equipment used to measure

mass Amount of matter in an object

Kilogram (kg)Gram (g)Milligram (mg)

Balance

length Distance between 2 points

Metre (m)Centimeter (cm)Millimetre (mm)

ruler

temperature Hotness or coldness of a substance

Kelvin (K)Degrees Celsius (◦C)

thermometer

volume Amount of space object occupies

Cubic metre (m3)Litre (L)

Breaker, graduated cylinder …

mole Amount of a substance

Mole (mol) Calculated not measured

density Mass per unit of volume

Kilograms per cubic metre (kg/m3)Grams per cubic centimetre (g/cm3)

Calculated or measured

energy Ability to do work Joule (J) Calculated not measured

Measurement and Uncertainty

• When you were doing your calculations in the previous activity how accurate where your answers?

• How accurate did you measure the aluminum with your ruler?

• When working in science you need to know how much you can depend on measurements

• You need to know when something was just an approximation

Measurement and Uncertainty

• An example: How many great lakes are there?• There are 5 great lakes• What about the amount of millilitres in 1 L?• Number of seconds in 1 minute?• These are numbers that you can count or that

are true by definition (exact numbers)• Now think about the numbers you were using

in the activity, were they exact numbers?

Measurements and Uncertainty

• In this course you will be using equipment such as rulers, balances and other scales to measure

• You will be calculating most of your results with a calculator

• These pieces of equipment as well as your ability to use them will affect your ability to record and communicate measurements and calculations

Significant Digits, Certainty, and Measurements

• All measurements involve uncertainty• You cannot measure anything with complete

certainty• The last (farthest right) digit in any

measurement is always an estimate• Significant digits: are the digits that you record

when you measure something (include digits that you are certain about and a final uncertain digit that you estimated

Example

• 4.28 g has three significant digits:– The first two digits (the 4 and the 2) are certain– The last digit (the 8) is an estimate and therefore it

is uncertain• The value 4.3 has two significant digits• Which digits are certain and which are

uncertain?

Rules for Determining Significant Digits

1. All non-zero numbers are significant

Examples:• 7.886 has four significant digits• 19.4 has three significant digits• 527.266 992 has significant digitsnine

Rules for Determining Significant Digits

2. Zeros placed between other digits are always significant.

Examples:• 408 has three significant digits• 25 074 has significant digits• 7003 has how many significant digits?

five

Rules for Determining Significant Digits

3. In a measurement with a decimal point, zeros placed before other digits are not significant.

Examples:• 0.0907 has three significant digits. • 0.000 000 000 06 has .• 0.0056 has how many significant digits?

one significant digit

Rules for Determining Significant Digits4. Zeros that are located to the right of a value may or may not

be significant

– Zeros placed after nonzero digits after a decimal are significant

Examples: • 9.100 has 4 significant digits• 802.0 has significant digits.• 7400.0 has how many significant digits?

• If there is no decimal place then it becomes a bit more difficult to identify if the zeros to the right are significant

4

Rules for Determining Significant Digits4. Zeros that are located to the right of a value may or may not

be significant

– If a decimal is not present, zeros to the right of the last non-zero digit are not significant.

Examples:• 1200 has two significant digits• 520 has significant digits• 30 400 000 has how many significant digits?• What if you used a measuring tape to measure the length of a

box and the length was exactly 200cm, how would you report this answer so that people know there are three significant digits?

2

Rules for Determining Significant Digits• Scientific notation is used to indicate whether zeroes at the

end of a measurement are significant• Instead of reporting our length measurement as 200cm we

would report it as 2.00xcm• When a measurement is written in scientific notation all digits

in the coefficient are significant

Examples:• has three significant digits• has significant digits• has how many significant digits?

5

Practice Problems (as a class)

• Write the following quantities in your notebook. Beside each record the number of significant digits.

a) 24.7 kgb) 247.7 mLc) 247.701 mgd) 0.247 01 L

3 significant digits4 significant digits

6 significant digits5 significant digits

Practice Problems (on your own)

• Write the following quantities in your notebook. Beside each record the number of significant digits.

e) 8.9300x kmf) 2.5 gg) 0.0003 mLh) 923.2g

5 significant digits

2 significant digits

1 significant digits4 significant digits

Homework!!!

• Complete worksheet “How many significant digits for each number?”• Complete questions 1 and 2 on worksheet “Significant Digits and

Rounding”

BOOHOO!!!