Lecture 17 – Review of Scientific Notation

In preparation for an intense study of bone structure, bone density, and the significance of the body’s minerals, I promised a review of scientific notation.  Scientific notation is a simple way of writing and keeping track of large and small numbers without a lot of zeros.  It also provides a shortcut to recording results and doing calculations.

Example 1- Large Numbers:

100 equals  (10)(10)                                                  or 102                  or one hundred

1,000 equals  (10)(10)(10)                                            or 103                  or one thousand

10,000 equals  (10)(10)(10)(10)                                     or 104                  or ten thousand

100,000 equals  (10)(10) (10)(10)(10)                                 or 105                    or one hundred

thousand

1,000,000 equals  (10)(10)(10)(10)(10)(10)                        or 106                     or one million

1,000,000,000 equals  (10)(10)(10)(10)(10)(10)(10)(10)(10)   or 109                   or one billion

The best technique is to just commit this to memory.  Use Post-It notes attached to your bathroom mirrors if you have to.  I am constantly reviewing as I apply my make-up.  Pick up a hand held recording device and read this information aloud.  Hearing information in your own voice is quite effective.

Example 2 – Small Numbers:

1/10                 equals 10-1                                                                                                   or one tenth

1/100               equals 1/(10)(10)                                                      or 10-2                     or one hundredth

1/1,000            equals 1/(10)(10)(10)(10)                                         or 10-4                   or one ten thousandth

1/1,000,000     equals 1/(10)(10)(10)(10)(10)(10)                            or 10-6               or one millionth

1/100,000,000 equals 1/(10)(10)(10)(10)(10)(10)(10)(10)(10)        or 10-9               one billionth

Here are some everyday metric measurements. Metric measurements can describe different scale objects.

Sample                                                                                               Measurements (Meters)

Diameter of Uranium Nucleus                                                            10-13

H2O Molecule                                                                                          10-10

Protozoa                                                                                                   10-5

Earthworm                                                                                              10-2

Human                                                                                                     2

Mount Everest                                                                                        103

Diameter of the Earth                                                                           107

Distance from Pluto into Sun                                                              1013

Significant Figures

Measurements may not be exact, but as medical scientists, we try to record the answers with the least amount of uncertainty.  The idea of scientific notation was set up to standardize measurements with the least uncertainty.  Significant figures were used in order to write numbers either in whole units or to the highest level of confidence.

Significant figures are the number of digits written after the decimal point to measure quantity.

A counted significant figure cannot be divided into sub-parts.  These are recorded in whole numbers such as 10 tubes of lipstick, 9 containers of eye shadow, or 7 bottles of foundation.  (Does anybody still use Fashion Fair?  I like Warm Honey.  Fashion Fair and Clinique were the most popular department store cosmetics of my teen years.  I think MAC or Prescriptives might hold that title now.)  Bear with us, Gentlemen.  So many careers have been boys’ clubs for so long, I have to make this fun for the girls!

Now, just relax as we do a few examples.  If you know this well, re-read for good measure.  Over-learning is also a good technique.  Your eyes can never look at good information too many times!  If this is a weak area for you, do not rush through it.  Your future patients need you to grasp each intricate concept.  Medication errors do not have to happen!

How many significant figures are in the following?  Check out the bold hints!

  1.  9.107   (4, because zeros in the middle are significant.)
  2. 401       (3, because the zero in the middle is significant.)
  3. 0.006    (1, because leading zeros are never significant.)
  4. 800 km (3, zeros are significant in measurements unless otherwise indicated.  Note: These zeros follow a non-zero number.)
  5. 3.002 m (4, because zeros in the middle of non-zero digits are significant.)

More Tips:

When finding out the number of significant figures, the easiest shortcut is to look at the zeros acting as placeholders.

Leading zeros at the beginning (or the left-hand side) of a number are never significant.  Start at the left and count to the right of the decimal point.  The measurement 0.096 m has two significant figures.  The measurement 13.42 cm has four significant figures.  The mass 0.0027 has two significant figures.  (Remember to leave off the leading zeros.)

Zeros sandwiched in the middle of non-zero numbers are always significant.  The number 26,304 has five significant figures.  The measurement 0.000001002 m has four significant figures.

In summary, scientific notation gets rid of the guessing and helps to keep track of zeros in very large and very small numbers.  If the diameter of Earth is 10,000,000 m, it is more practical to write 1 X 107 m.  Or, if the length of a virus is 0.000000004 m, it is easier to write 4 X 10-8 m.  Remember to ‘go through the hard parts’.  It will get easier.  It is necessary to review measurements before moving on to bone density and other anatomic slides that reference complex measurements.  You will need a command of measurements as you progress in your career.  Do well with this information.  We are building a solid foundation.

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