Significant Figures

Who cares? Sig Figs measure the degree of precision of a measurement.

But first: What’s the difference between accuracy and precision? Do they mean the same thing?

Important definitions: accuracy: a measure of how closely a measurement agrees with the correct or true value precision: a measure of how closely individual measurements agree with one another

Example question: Two students measured the mass of a small pebble, which had an actual mass of 2.35 grams. Sally’s measurements were 2.78 grams, 2.82 grams, and 2.81 grams. Madison’s measurements were 2.30 grams, 2.34 grams, and 2.41 grams. Which student was more accurate? Which student was more precise?

A correctly precise measurement includes all digits that are known for sure, PLUS a digit that is estimated.

For example: To what decimal place should your answer be?

Another example:

Rules for counting sig figs: There are ONLY two rules to remember when counting the # of Sig Figs.

Rule #1: Don’t start counting till you get to a number that isn’t a zero. Rule #2: Once you start counting, don’t stop till you’ve counted all the digits, including zeroes.

And you need to remember a little geography: Where is the Atlantic Ocean, and where is the Pacific Ocean?

How many sig figs are in this number: ? Ask yourself: Is the decimal point present or absent?

Answer: Present Count from first non-zero number starting at the Pacific side Once you start counting, you don’t stop!

Examples S.F S.F S.F.

Examples

The first step is always to ask yourself: Is the decimal point present or absent? 18,000,000

Answer: Absent Count from first non-zero number moving from the Atlantic side. 18,000,000

Examples 1353 S.F S.F S.F.

Examples ,

Rounding Starting from the left find the 1 st nonzero number….this is the MOST significant digit, then round accordingly –Numbers BEFORE decimal = convert to zero –Numbers AFTER decimal = Drop EXAMPLE: round to 2 sig figs –120,320 – –

Using sig figs in calculations

For multiplication and division:

Your answer can should have the fewest number of significant figures from the problem

x 200 = S.F.1 S.F.4 S.F.? Answer must be recorded as 50,000 cm 2 It can have only one sig fig.

610 x 6.20 = S.F.3 S.F. What is the correct answer? 3800

Example: You calculate the density of an object with mass of grams, and volume of 62.5 ml. How many sig figs in your answer? D=M/V /62.5 = Correct Sig. Figs. = 0.389

For addition and subtraction

Your answer can not contain more decimal places than the least precise measurement.

Line up the decimal points in the numbers =????

Answer stops here

Calculations Recap Multiplication & Division –Fewest Number of Significant figures Addition & Subtraction –Fewest Numbers after the decimal (least precise)

Scientific notation

The number of sig figs comes from the number written before the times sign.

Examples 3.50 x S.F. 5.0 x S.F. 3 x S.F.

Standard Notation to Scientific Notation Positive exponent: Number ≥ 1 Negative exponent: Number ≤ 1 Exponent = Number of times the decimal is moved Only 1 number in front of decimal Ex: 1,

Scientific Notation to Standard Notation Positive exponent: move decimal to the right Negative exponent: move decimal to the left Ex: 3.65 x x 10 -3

Practice