Lab 2: Background information

Ways of expressing data

Numerical figures can be very large or very small

Scientists use SCIENTIFIC NOTATION to express numbers

B X 10^E   E = exponent

B = base

1< number < 10

The metric system is based on 10

10³ = 1000

10^-2 = 0.01 = 1/100

If there is a positive exponent, then you add that number of 0s.
You move the decimal point to the right.

If there is a negative exponent, then that is how many decimal places there are before the number. 
You have moved the decimal point to the left that many of places.

7.23 X 10³ = 7230
7.23 X 10^-3 = .00723

Look at section 2.2, question 2 and convert the numbers to scientific notation

Numbers can also be expressed in decimal notation.

9.83 X 10^-3 = 0.00983

Look at section 2.2, question 3 and convert the numbers to decimal notation

 

Multiplication of numbers

Multiply the bases and add the exponents.

(2.1 X 10⁹) X (4.3 X 10¹²)

= 2.1 x 4.3 = 9.03

10(^{9 + 12}) = 10²¹

Answer = 9.03 X 10²¹
 

If the base > 10, you need to express it in a form that is less than 10 to be using CORRECT
scientific notation.

(2.3 X 10⁸) X (5.8 X 10⁶) = 13.34 X 10¹⁴ = 1.334 X 10¹⁵

Remember, multiply the bases and add the exponents but you must express the base <10.

Move the decimal to the left and add one to the exponent.

If the number is <1, you must make it greater than 1.
You would move the decimal to the right one place and subtract the exponent by 1.

Look at section 2.2, question 4 and do the calculation requiring multiplying numbers (adding exponents).

Division of numbers

Divide the bases and subtract the exponents.

8 X 10³  = 8  X  10³ = 8 X 10^(3-8) = 2 X 10^-5
4 X 10⁸     4       10⁸    4  

If the answer results with the base is <1 or >10, you must correct it to get the answer
in correct scientific notation.

4 X 10³ = 0.5 X 10^-5 = 5 X 10^-6
8 x 10⁸

Look at section 2.2, question 5 and do the calculation requiring dividing numbers (subtracting the exponents).

Section 2.3  Look at other document showing how to convert between different units in the metric system.

Standard units in the metric system:

    meter = m = length
    gram = g = mass (weight)
    liter = l = volume
    degree celcius = °C = temperature

can combine these different standard units with prefixes and suffixes

milli, centi, kilo, etc.

If you go from smaller to larger, you move the decimal point to the left or decrease the exponent.
If you go from larger to smaller, you move the decimal point to the right or increase the exponent.

You will always have more of the smaller units than the larger units.

ng        10³       mg        10³       mg       10        cg        10    dg   10    g     10³         kg

 Examples:

Going from smaller to larger

10³ ng = 10^{3 - 3} = 10⁰ = 1 mg

 10 mg = 1 cg

 10³ g = 1 kg

1g = 10^-3kg

1 ng = 10¹² kg
 

Going from larger to smaller

1 kg = 10³ g

Look at section 2.3, question 6 and do the problems requiring you to convert between different units.

You will also need the following formulas to do the temperature conversion.

°C = (°F - 32) X 5/9
°F = (°C X 9/5) + 32

Graphing

You should have a title on each graph and label the X and Y axes.

Line graph:

each value represented by one point

points represented by a straight line

    continuous variables

the points are related to each other

for example:  how long student held breath after different times of exercise

can have more than one line in a graph - from last week, each line would
represent a different student

This is a graph of the results from last week.  I have only shown one person.

Each person who did the experiment should have a line.

Bar graph

Discrete variables

No intermediate values

The points are not related

For example:  if we take 4 different students and take the values for how long each held
his/her breath after1 minute of exercise.

Look at section 2.4 and answer the questions on graphs.