Teacher Resources Needed for Lesson Copies of the following worksheets: – Rounding with Addition and Subtraction – Rounding with Multiplication and Division – Scientific Notation – Significant Digit Worksheet

Rounding Answers and Scientific Notation

Calculating with Significant Digits In this course you will often take measurements and use them to calculate other quantities Must be careful to keep track of which digits in your calculations and results are significant We do this because your results of your calculations should not imply more certainty than your measured quantities justify

Example

Rules for Reporting Significant Digits in Calculations Rule 1: Multiplying and Dividing The value with the fewest number of significant digits, going into the calculation, determines the number of significant digits that you should report in your answer. Rule 2: Adding and Subtracting: The value with the fewest number of decimal places, going into the calculation, determines the number of decimal places that you should report in your answer.

Rules for Reporting Significant Digits in Calculations Rule 3: Rounding To get the appropriate number of significant digits (rule 1) or decimal places (rule 2), you may need to round your answer.  If the first digit to be dropped is 4 or less, the preceding digit is not changed. (example: is rounded to 8.67)  If the first digit to be dropped is 5, the preceding digit is increased by 1. (example: is rounded up to 8.68)  If the first digit to be dropped is a lone 5 or a 5 followed by zeros, the preceding digit is not changed if it is even, but is increased if it is odd. (example: is rounded up to 8.68, but is rounded down to 8.66)  When solving multistep problems record all the digits until the final answer to avoid rounding error

Practice Problem (as a class) A student measured a rectangular shaped sample of iron and found it to be 6.78 cm long, cm wide, and 11 cm tall. Determine its volume to the correct number of significant digits.

Practice Problem (as a class) Suppose that you measure the masses of four objects as 12.5 g, g, 79.0 g, and g. What is the total mass of the objects?

Homework!!! Complete the following worksheets: – Rounding with addition and subtraction – Rounding with multiplication and division

Scientific Notation

Converting Numbers into Scientific Notation

Practice Problems Copy the following into your notes and convert them into scientific notation: a) b) c) d) e)15 f)0.23

Practice Problems

Calculations Involving Scientific Notation

Homework!!! Complete the following worksheets: – Scientific Notation – Significant Digit Worksheet