Unit 2 notes LT 4: Calculations, Significant Figures, and Dimensional Analysis

Percent Error and Percent Yield

The accuracy of a measurement is found by calculating the percent error. The error of a measurement is the \n difference between the accepted value and the experimental measurement. If the error is divided by the true value and then multiplied by 100, it’s called percent error.

Percent Error = (|Real Answer - Measured| / Real Answer) * 100

In chemistry, yield is the amount of a substance produced in chemical reaction. The amount is \n often measured in grams. The percent yield is calculated by dividing the actual yield (the amount of substance produced in the lab) by the theoretical yield (the amount that should have been created according to a mathematical calculation) multiplied by 100%.

Percent Error = ( Real Answer / Measured) * 100

Scientific Notation

• is used to write very large or very small numbers.
• is used to give the width of a human hair (0.000 008 m) as 8 x 10-6 m.
• for a large number such as 100,000 hairs is written as 1 x 105 hairs.
• Moving the decimal to the left increased the power, moving it to the right decreases the power

Writing numbers in scientific notation:

• A number in scientific notation contains a coefficient between 1 and 10, a power of 10, and a unit.

• For numbers larger than 1, the power of is positive. For numbers smaller than 1, the power of 10 is \n negative.

  Examples of Scientific Notation Conversion

Significant Figures

Rules~~~~ \n It is the Atlantic-Pacific rule. Here is how it works. \n If the decimal point is ==present== start on the ==Pacific side of the number (far left)==, and if it is %%absent%% then start \n on the %%Atlantic side of the number (far right)%%. From there you move through the number stopping at the \n ^^first nonzero^^ number and counting that as the first significant number, then continue moving through the \n number counting ALL (even zeros) other numbers.

@@Examples:@@

100,001,000,000 has 6 significant numbers

0.00012500 has 5 significant numbers \n 210,000,000 has 2 significant numbers

0.02003800 has 7 significant numbers \n 800,000,000 has 1 significant number

1.00250 has 6 significant numbers

Significant Figures in Calculations

\n Multiplication & Division: when multiplying & dividing, round the final answer to the ==least number of significant figures.==

Addition & Subtraction: when adding or subtracting measurements, round the ==final answer to the least number of decimal places.==

Dimensional Analysis (==Do not memorize chart==)

1 mile = 5,280 feet

1 ton = 2000 lbs

1 gallon = 3.79L

1 L = 1000 mL
2.54 cm = 1 inch

20 drops = 1 mL

1 yard = 36 inches

1L =1000 cm3
12 inches = 1 foot

1 lb = 16 oz

1 kg = 2.2 lbs

1cm3 = 1 mL
1 km = 0.621 miles