1. All data and results in your lab reports must be reported using scientific notation. Scientific Notation makes it easy to report extremely small and large numbers, and to report numbers using the correct number of significant digits. Here is an example: SCIENTIFIC NOTATION, SIGNIFICANT FIGURES, AND READING ERRORS 300250 350 By convention, any number reported without a decimal place is agreed to have an uncertainty of half a digit smaller than the smallest digit reported. The number 300 really means anything between 250 and 350. 295 305299.5 300.5 In Scientific Notation this would be written as 3 X 10 2 Now if the first zero in 300 was significant, the the uncertainty range would be as follows: In Scientific Notation this would be written as 3.0 X 10 2 If the second zero in 300 was significant, the the uncertainty range would be as follows: In Scientific Notation this would be written as 3.00 X 10 2

2. X 103.00 2 This is called the mantissa 10 2 This is called the base This is called the exponent, or characteristic

3. This determines the decimal place of the least significant digit in the answer. In this example, the 1/1000th place. SIGNIFICANT DIGITS: Rules for ADDING and MULTIPLYING 6.843 +0.001 6.844 In this number there are four significant digits. The least significant digit is the ‘3’ which is in the third decimal place In this number there is one significant digit. The only significant digit is the ‘1’ which is in the third decimal place 3131 Find the decimal place of the least significant digit shared by both numbers. 6.843 8 +1 Once again, there are four significant digits in this number. The least significant digit is the ‘3’ which is in the third decimal place. The only, and therefore significant digit here is the ‘1’. Find the decimal place of the least significant digit shared by both numbers. 6161 This determines the decimal place of the least significant digit in the answer. In this example, the one’s place.

4. SIGNIFICANT DIGITS: Rules for ADDING and MULTIPLYING 5.2 x 3.1 16 In this number there are two significant digits. In this number there are two significant digits. This determines the number of significant figures in the answer: In this example, two. Find the number with the least number of significant digits. In this example both numbers have the same number of significant digits. 5.243 16 x 3.1 In this number there are four significant digits In this number there are two significant digits Find the number with the least number of significant digits. 5.2 3.1 The final answer should also have the same number of significant digits (two).

5. SIGNIFICANT DIGITS: Rules for ADDING and MULTIPLYING When reporting measured values you must include an estimate of the uncertainty in every measurement. Here is an example... Here you are to measure the distance between two points on a piece of paper. The dots represent the position of an air puck at different times. The dots are formed by an electric spark which leaves a burn mark on the paper. Here’s a close up of what they look like... Using the ruler, you measure the distance between these dots and claim it is 1.7cm. How good is the measurement? Is it 1.6 to 1.8? Is it 1.699 to 1.701? You must explicitly state the range of values you think are acceptable for the measurement. As you look even closer you can begin to realize how how important it is to include a range of values. Here are some factors to consider when finding an acceptable range: How well can you estimate the center of a dot? Does the thickness of the ruler lines affect how well you line up the ruler with the dot? How well can you estimate a fraction of the space between ruler markings? There are no hard and fast rules for estimating reading errors. You must learn to make the best measurements using the measuring devices available under the conditions existing where and when you take the measurements. And remember, measurements with too large an uncertainty are almost as useless as no measurement at all, while too small an uncertainty suggest that the data itself is not credible. A reasonable estimate for the distance would likely be 1.6+/-.3

6. You have completed the tutorial. To return to the main lab site click here.here. Presentation created by: Craig Fraser