# SCIENTIFIC NOTATION

adapted from Taber's Cyclopedic Medical Dictionary, 1973

Sometimes it is necessary to use very large or very small numbers. These can best be handled in calculations by the use of scientific notation or exponents. To use scientific notation, transform the number so that it becomes a number between 1 and 10, then multiply this number by the appropriate power of 10.

EXAMPLES:

1234 = 1.234 X 103

0.01234 = 1.234 X 1/100 = 1.234 X 10-2

0.001234 = 1.234 X 1/1000 = 1.234 X 10-3

To convert a number to its equivalent in scientific notation:

Place the decimal point to the right of the first non-zero digit. This will now be a number between 1 and 10.:

(a.) 1234 goes to 1.234

or

(b.) 0.01234 goes to 1.234

Multiply this number by a power of 10, the exponent of which is equal to the number of places the decimal point was moved. The exponent is positive if the decimal point was moved to the left, and negative if it was moved to the right.:

(a.) 1.234 x 103

or

(b.) 1.234 x 10-2

EXAMPLE:

1,234,000 x 0.000072/6000 = 1.234 x 106 x 7.2 x 10-5/6.0 x 103

Now by simply adding the exponents of 10, and remembering that moving an exponent from the denominator of the fraction to the numerator changes its sign:

= 1.234 x 106 x 10-5 x 10-3 x 7.2/6 = 1.234 x 7.2 x 10-2/6

= 8.8848 x 10-2/6 = 1.4808 x 10-2 or 0.014808

## THE METRIC SYSTEM

• Length = meter (m); = 39.37 inches
• Volume = liter (l); = 1.0567 US quart
also, the length unit cubed also measures volume: 1000 cm3 = 1 liter
• Weight = gram (g); approx 454 g = 1 US pound

Common prefixes:

• (k) kilo = 1000 = 103
• (d) deci = 0.1 = 10-1
• (c) centi = 0.01 = 10-2
• (m) milli = 0.001 = 10-3
• (u) micro = 0.000001 = 10-6
• (n) nano = 0.000000001 = 10-9
• (p) pico = 0.000000000001 = 10-12
• (f) femto = 0.000000000000001 = 10-15

Interesting fact: 1g H2O = 1 ml H2O = 1 cm3 H2O

Problems:

1.) How many mg in 100 g salt?

2.) How many ug in 20 mg of sugar?

3.) How many mm in 30 cm?

4.) How many um in 1 mm? ( a typical bacterium is 1 um long. How many bacteria can you lay end to end to form a straight line 1 mm long?)

5.) Assume bacteria that are 1 um2, how many would fit onto 1 mm2?

6.) How much does 1 m3 of water weigh?

7.) How many mg in 1 g? in 10 g? in 1000 g? in 1 kg?

8.) How many mm in 1 cm? in 10 cm? in 100 cm? in 1 m?

9.) How many ml in 1 l? in 10 l? in 100 l? in 1000 l?

10.) If 1 cc of water weighs 1 g, how much does 1 liter of water weigh? How much does 100 cm3 of water weigh?

11.) How many mg in 0.1 g? in 0.01 g? in 0.001 g? in 0.0001 g?

12.) How many ug in 1 g? in 1 mg? in 0.001 g? in 0.001 mg?

13.) How many ul in 1 l? in 0.001 l? in 1 ml? in 0.000001 l? in 0.001 ml?

14.) How many um in 1 m? 1 cm? 1 mm? in 0.01 m? 0.001 m? 0.01 mm?

15.) How many mm2 in 1 cm2? in 10 cm2? in 100 cm2? inh 10000 cm2?

16.) How many mm3 in 1 cm3? in 10 cm3? in 10000 cm3? 1000000 cm3?