Math Outline

Math Concepts Important to ChemistryA. Significant Figures and Rounding

B. Scientific Notation

C. Unit Conversions & Conversion Factors

A. Significant Figures• A measurement always has some degree of uncertainty.

• Different people estimate differently.

• Record all certain numbers and one estimated number.

A. Significant Figures

• Some numbers are exact; others are not.– Exact numbers can be counted or defined.

i.e.-the no. of people in the class, eggs in a dozen– Numbers from measurements are not exact.

i.e.-volume of 53.5 mL…

• Significant digits are used to demonstrate what was actually counted in a measurement and to what degree it was estimated.

(includes all measured + 1 estimated digits)• All non-zero numbers you see in a recorded

measurement are significant.

Significant Figures: the tricky parts…

There are several rules to tell if a zero is significant:1. All zeroes between non-zero numbers ARE

significant.2. Zeroes used to position the decimal ARE NOT

significant.3. Zeroes to the right of numerical digits AND to the

right of a decimal ARE significant.4. Use scientific notation OR a decimal to eliminate

confusion about multiple zeroes at the end of a number.

Sumup1. Nonzero integers always count as significant figures.

1457 4 significant figures 2. Zeros

a. Leading zeros - never significant0.0025 2 significant figures

b. Captive zeros - always significant

1.008 4 significant figures

a. Trailing zeros - significant only if the number is written with a decimal point 100 1 significant figure 100. 3 significant figures 120.0 4 significant figures

3. Exact numbers - unlimited significant figures • Not obtained by measurement • Determined by counting OR Determined by definition

3 apples 1 in. = 2.54 cm

Math and Significant Figures

The first thing to remember:

…the answer in your calculator

is NOT “THE ANSWER!”

The Rounding Rules

• Sometimes you have to round in order to have a desired number of significant figures:

• If the last significant digit place is followed by a number less than 5 ……………… LEAVE IT!

(fill with placeholders as needed)

• If the last significant digit place is followed by a 5 or a number greater than 5 ………… ROUND UP!

(fill with placeholders as needed)

Practice Rounding• 456,500 (round to 2 sig figs) = _________________• 76,822 (round to 2 sig figs) = _________________• 9,985 (round to 3 sig figs) = _________________• 125,475 (round to 5 sig figs) = _________________• 90,044 (round to 2 sig figs) = _________________• 45,988,335 (round to 4 sig figs) = _______________• 449,589 (round to 4 sig figs) = _________________• 120,045 (round to 3 sig figs) = _________________• 26,645 (round to 4 sig figs) = _________________• 980 (round to 1 sig fig) = _________________

Math and Significant FiguresIn multiplication and division:

• The answer must contain no more significant figures than the LEAST number of significant figures used in the problem.

Math and Significant FiguresIn addition and subtraction:

• When reading left to right, the last digit of the answer is in the same position of the FIRST ESTIMATED digit used in the problem.

B. Scientific NotationChanging a standard number into sci. not.:• Move the decimal to the place after the first non-zero

number. (Count places; that will be the exponent.)• If you are moving the decimal to the left, your exponent

will be positive. (Every space the decimal moves to the left, the exponent increases by one)

34, 500 3.45 x 104

• If you are moving the decimal to the right, your exponent will be negative. (Every space the decimal moves to the right, the exponent decreases by one)

0.00761 7.61 x 10-3

Scientific Notation (cont’d)

Changing sci. not. number into standard:1. If the exponent is positive, move the decimal to

the right (make the number “bigger”) and fill with zeros:

3.67 x 104 36,7002. If the exponent is negative, move the decimal to

the left (make the number “smaller”) and fill with zeros:

5.908 x 10-2 0.05908

Math Operations with Scientific Notation

Multiplication:1. Multiply the base numbers2. Add the exponents3. Adjust to correct scientific notation format

Division:1. Divide the base numbers2. Subtract the exponents3. Adjust to correct scientific notation format

Addition and Subtraction:

1. Change the members of the problem so that they all have the same exponent.

2. Add or subtract the base numbers.

3. DO NOT CHANGE THE EXPONENT!

4. Adjust to correct scientific notation format.

More Math with Scientific Notation