Significant Figures

1. Significant Figures

2. Rule 1: • Non-zero digits are significant. • Ex: 453 kg • All non-zero digits are always significant • # of Sig Fig’s? • 3!

3. Rule 2: • Zeros between non-zero digits are significant. • Ex: 5057 L • Zeros between 2 Sig. Fig’s. are significant • # of Sig. Fig’s?? • 4

4. Rule 3: • 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

5. Rule 4: • Zeros in front of a decimal number are not significant. • Ex: 0.007 • Placeholders are not significant • # of sig. fig.’s?? • 1

6. Rule 5: • Zeros at the end of a non-decimal number are not significant. • Ex: 42000 • # of sig. fig.’s?? • 2

7. The “Trick” • 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.

8. Ocean Rule • 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

9. Examples: • 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

10. 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

11. Multiplying and Dividing: • 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.

12. Adding and Subtracting • 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