University:
Everett Community College
Course:
CHEM 121 | Introduction to Chemistry
Academic year:

2012
Views:

423

Pages:

2
Author:

Bryanna Downs

Significant Figures 1) Multiplication/ Division Rules: The number that has “the fewest number of Significant Figures” decides the number of significant figures in the final answer. Example: 2.711 x 6.3 = 17.0793 => 17 4 SF 2 SF 2 SF in the final answer (Choose the fewest SF) 2) Addition/ Subtraction Rules: When two numbers are added or subtracted the final answer should not have greater certainty than the original measurements. Round the result of addition/subtraction to the same decimal place as the measurement with the highest/biggest uncertainty. Example: 2.042 + 3.2 – 0.123 = 5.365 => 1000ths 10ths 1000ths 5.4 The final answer rounds to the tenths place The highest uncertainty is in the tenths place  Addition/ Subtraction of Scientific Numbers with the SAME Exponents: Step 1: If exponents are the same, then proceed with the addition/ subtraction operations immediately. Example: (2.661 x 103) + (3.01 x 103) = 5.671 x 103 => 1000ths 5.67 x 103 100ths The final answer rounds to the hundredths place The highest uncertainty is in the hundredths place.  Addition/ Subtraction of Scientific Numbers with DIFFERENT Exponents: Step 1: Make exponents the same. Step 2: Perform the addition or subtraction operation. Step 3: After the exponents have been made the same, round answer to the same decimal place as the measurement with the highest/biggest uncertainty. Step 4: Make sure the final answer is in standard scientific notation. Example: (9.98 x 10-3) + (8.04 x 10-5) =? Step 1: 8.04 x 10 –5 becomes 0.0804 x 10-3 Step 2 and 3: (9.98 x 10-3) + (0.0804 x 10-3) =10.0604 x 10-3 = 100ths 10.06 x 10 -3 10,000ths The highest uncertainty is in the hundredths place. Step 4: The correct scientific notation adjustment must be made! Final answer => Special Cases: Internal Zeros are ALWAYS Significant Example: 4.001 => 4 Significant Figures Leading Zeros are NEVER Significant Example: 0.000007 => 1 Significant Figure Trailing Zeros are Significant ONLY IF the decimal point is specified Example: 200000 => 1 Significant Figure 200. => 3 Significant Figures 200.1 => 4 Significant Figures Practice Problems: 1. 414 + 7750 + 2500 = 4. (2.66 x 104) – (1.03 x 103) = 2. 0.254 – 0.367 + 5.4892 = 5. 5.905 / 14.0 = 3. 24.8 x 6.4 x 301 = 6. (112 x 0.456) / (3.2 x 120) = Solutions: (1) 10700, (2) 5.376, (3) 48000 or 4.8 X 104, (4) 2.56 x 104, (5) 0.422, (6) 0.13 (1.) 10700 (2.) 5.376 (3.) 48000 or 4.8 X 104 (4.) 2.54 x 104 (5.) 0.422 (6.) 0.13 1.006 x 10 -2