Significant Figures

Non-zero digits are significant.

Ex: 453 kg All non-zero digits are always significant # of Sig Fig’s?

3!

Rule 1:

Zeros between non-zero digits are significant.

Ex: 5057 L Zeros between 2 Sig. Fig’s. are significant # of Sig. Fig’s??

4

Rule 2:

Zeros at the end of a decimal number are

significant. Ex: 5.00 Additional zeros to the right of decimal and a

sig. fig. are significant # of sig. fig.’s

3

Rule 3:

Zeros in front of a decimal number are not

significant. Ex: 0.007 Placeholders are not significant # of sig. fig.’s??

1

Rule 4:

Zeros at the end of a non-decimal number

are not significant. Ex: 42000 # of sig. fig.’s??

2

Rule 5:

This is called the Ocean Rule. You really should use this for the purpose of

checking your work. First you need to see whether it has a decimal or

not. If it does not have a decimal point, then think A for

Absent. If it does have a decimal point, then think P for

Present The letters ‘A’ and ‘P’ correspond to the ‘Atlantic’

and ‘Pacific’ ocean.

The “Trick”

With a decimal point the decimal is “Present” so start on the Pacific Side (left) and

don’t start counting until you hit a whole number and then the rest count. 100.0 has ?

4 0010. has ?

2 1.010 has ?

4 0.010 has ?

2 If the decimal is “Absent” start on the Atlantic side (right) and move from right to left.

Don’t start counting until you hit a whole number  and the rest count. 1000 has ?

1 12050 has ?

4 12001 has ?

5 125000 has ?

3

Ocean Rule

How many significant digits are shown in the

number 20,400? There is no decimal, so we think A for Absent So imagine we have an arrow coming in from

the atlantic ocean 20,400

The first nonzero digit that the arrow hits would be the 4 making it, and all digits to the left of it significant 3 sig. fig.’s

Examples:

How many significant digits are shown in the

number 0.090 ? Well, there is a decimal, so we think of "P" for

"Present".  This means that we imagine an arrow coming in from the Pacific ocean, as shown below 0.090

The first nonzero digit that the arrow will pass in the 9, making it, and any digit to the right of it significant. 2 sig. fig.’s

Examples:

When multiplying or dividing, your answer may only

show as many significant digits as the multiplied or divided measurement showing the least number of significant digits. When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525

cm3

We look to the original problem and check the number of significant digits in each of the original measurements: 22.37 shows 4 significant digits. 3.10 shows 3 significant digits. 85.75 shows 4 significant digits.

Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem.

5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm3.

Multiplying and Dividing:

When adding or subtracting your answer can

only show as many decimal places as the measurement having the fewest number of decimal places. Example: When we add 3.76 g + 14.83 g + 2.1 g =

20.69 g We look to the original problem to see the number of

decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places. We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 g

Adding and Subtracting