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Presentation transcript:

You will need your own paper for notes. Math with Sig Digs You will need your own paper for notes.

When measured numbers are used in mathematical calculations, you cannot be more exact than the worst number you have to start with. To determine where to round to reflect your worst number depends on if you are adding and subtracting or multiplying and dividing.

Rule for rounding to the proper amount of sig digs when adding and/or subtracting: Round your answer to the decimal place the farthest to the right that each starting number had a significant digit in that decimal place.

Example: 1.23 + 87.654 + 9.0 = ?

Example: 1.23 + 87.654 + 9.0 = ? Line up the decimal points….

Example: 1.23 + 87.654 + 9.0 = ? Line up the decimal points…. 1.23 87.654 9.0

Example: 1.23 + 87.654 + 9.0 = ? Line up the decimal points…. 1.23 87.654 9.0 Do the math…

Example: 1.23 + 87.654 + 9.0 = ? Line up the decimal points…. 1.23 87.654 + 9.0 Do the math… 97.884

Example: 1.23 + 87.654 + 9.0 = ? Line up the decimal points…. 1.23 87.654 + 9.0 97.884 Find the column with Sig Digs for every number - farthest to the right

Example: 1.23 + 87.654 + 9.0 = ? Line up the decimal points…. 1.23 87.654 + 9.0 97.884 Find the column with Sig Digs for every number - farthest to the right

Example: 1.23 + 87.654 + 9.0 = ? Line up the decimal points…. 1.23 87.654 + 9.0 97.884 Round there

Example:1.23 m + 87.654 m + 9.0 m = ? Line up the decimal points…. 1.23 m 87.654 m + 9.0 m 97.884 m Your final answer is 97.9 m

Try this: 4000 g - 0.0004 g = ?

Try this: 4000 g - 0.0004 g = ? 4000 g 0.0004 g 3999.9996 g

Try this: 4000 g - 0.0004 g = ? 4000 g 0.0004 g 3999.9996 g The final answer is 4000 g, why?

Rule for rounding to the proper amount of sig digs when multiplying and/or dividing: Round your answer to the amount of sig digs that matches the smallest amount of sig digs in the starting numbers.

Example: 9.87 x 65.432 ÷ 1.090 = ?

Example: 9.87 x 65.432 ÷ 1.090 = ? Do the math: 9.87 x 65.432 ÷ 1.090 = 592.49

Example: 9.87 x 65.432 ÷ 1.090 = ? Do the math: 9.87 x 65.432 ÷ 1.090 = 592.49 How many sig digs in each number?

Example: 9.87 x 65.432 ÷ 1.090 = ? Do the math: 9.87 x 65.432 ÷ 1.090 = 592.49 3 5 4 How many sig digs in each number?

Example: 9.87 x 65.432 ÷ 1.090 = ? Do the math: 9.87 x 65.432 ÷ 1.090 = 592 3 5 4 3 Round to match lowest

Please Note! Defined numbers and counted objects are considered to have unlimited significant digits. If I count 3 donuts, that is 3 donuts and 3.000000000000000000000 donuts, because I counted it! There are 100 cm in a m, and 100.0000000000000000000000 cm in m!