When adding or subtracting measured quantities, there should be the same number of decimal places in the answer as there are in the measurement with the least number of decimal places. For addition and subtraction the number of significant figures is NOT important.

Look at the left most digit to be dropped

• If this digit is '5' or greater, or is '5' followed by nonzero digits, add '1' to the last digit to be retained and drop all the digits further to the right.

• If this digit is less than '5', drop it and all digits further to the right.

So lets try some examples where we report a calculation to the correct number of significant figures.

These are the easy problems. Lets try something a little more interesting. Now this is a harder problem and requires that we apply all the rules we've been discussing these past several days.

Check out the next Self-Test to try your skill at these kind of problems.

Throughout this semester and next semester it will be necessary to convert from one unit to another. Later this semester we will learn how to use a balanced chemical equation to perform conversion of a differnt type. Conversions generally involve the re–expression of a physical quantity expressed in one form of units into another form of unit. For example converting 2 yards to inches. We know that each yard has three feet and each foot has twelve inches, therefore 2 yards is the same as 72 inches. We used two relationships to convert yards to inches. The two relations were;

1 yard = 3 feet and 1 foot = 12 inches

The most useful approach to these types of problems is to use dimensional analysis or unit analysis where equivalences are expressed as ratios and used to convert from one unit to another. Given the two equivalence above we can write two ratios,

We can use these ratios to convert from yards to inches;

Another example can be selected from the metric system;

1 meter = 100 centimeters

The unit conversion factor for this definition is;

Either can be used depending on the direction of conversion. Given the number of centimeters the first unit conversion factor can be used to convert centimeters to meters. Given the number of meters the second unit conversion factor can be used to convert meters to centimeters. For example;

The unit conversions in this case are exact numbers. We do not have to worry about the number of significant figures in the unit conversion. However, there are conversion factors which are not exact and we must use more care. The conversion of yards to meters is an example. We know that

The number of significant figures in the given quantity will determine the correct number of significant figures in the unit conversion. You may wish to use all of significant figures in the calculation and than round the answer to the correct number of significant figures. There is a useful list of important relationships which can be used a conversion factors inside the back cover of your textbook.

Some other exact unit conversions include;

Lets try some problems;

Quantities expressed in compound units are a little more interesting. Density is a good examples of a compound unit. For example the density of gold is;

this compound unit say that for gold 19.3 gram equals 1 cubic centimeter.

Temperature is a measure of the degrees of hotness and coldness. Temperature is also the quantity measured with a thermometer. Three systems for measuring temperature are often used: the Fahrenheit scale, the Celsius scale and the Kelvin scale. The second and third are used in most scientific calculations, while Fahrenheit is used in many engineering applications. The Fahrenheit scale, named after the Dutch instrument maker Daniel Gabriel Fahrenheit, defined 0 degrees F as the temperature of a particular mixture of ice and salt and defined body temperature as 96 degrees F. On this scale the freezing point of water as 32 degrees F and the boiling point as 212 degrees F. The Celsius scale, named after the Swedish astronomer Anders Celsius defines 0 degrees C as the freezing point of water and 100 degrees C as the boiling point of water. Both Fahrenheit and Celsius are relative temperature scales. They define two reference points, divide the range of temperature between the two points into degrees and compare all other teperatures to the arbitrary references.

There is a relationship between the Fahrenheit scale and the Celsius scale which is given as,

If you would like to see the derivation of this equation check this link.

Here are some sample calculations

The relationship between the Celsius scale and the Kelvin scale is more straight forward,

K = 273.15 + C

So to determine the temperature in Kelvins we need to add 273.15 to the temperature in degrees Celsius. Kelvin is called the absolute temperature scale because 0 Kelvins is the lowest temperature possible. While we can have a negative temperature in degrees Celsius and degrees Fahrenheit, we do not have a negative temperature in Kelvins.