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

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

QuantityDefinitionSI units or their derived equivalents Equipment used to measure massAmount of matter in an object Kilogram (kg) Gram (g) Milligram (mg) Balance lengthDistance between 2 points Metre (m) Centimeter (cm) Millimetre (mm) ruler temperatureHotness or coldness of a substance Kelvin (K) Degrees Celsius ( ◦ C) thermometer volumeAmount of space object occupies Cubic metre (m 3 ) Litre (L) Breaker, graduated cylinder … moleAmount of a substance Mole (mol)Calculated not measured densityMass per unit of volume Kilograms per cubic metre (kg/m 3 ) Grams per cubic centimetre (g/cm 3 ) Calculated or measured energyAbility to do workJoule (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: has four significant digits 19.4 has three significant digits has significant digits nine

Rules for Determining Significant Digits 2.Zeros placed between other digits are always significant. Examples: 408 has three significant digits 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: has three significant digits has has how many significant digits? one significant digit

Rules for Determining Significant Digits 4.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: has 4 significant digits hassignificant digits 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 Digits 4.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 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 5

Practice Problems (as a class) Write the following quantities in your notebook. Beside each record the number of significant digits. a)24.7 kg b)247.7 mL c) mg d) L 3 significant digits 4 significant digits 6 significant digits 5 significant digits

Practice Problems (on your own) 5 significant digits 2 significant digits 1 significant digits 4 significant digits

Homework!!! Complete worksheet “How many significant digits for each number?” Complete questions 1 and 2 on worksheet “Significant Digits and Rounding” BOOHOO!!!