SCIENTIFIC NOTATION

I. WRITING NUMBERS IN SCIENTIFIC NOTATION

Scientists often need to use measurements that are extremely large or small. An example from Dobson, Holman and Rogers (Science Spectrum, 2001) shows how the time for light to travel from Earth to Neptune can be calculated.

t = ___distance from Earth to Neptune (m)______
distance light travels in 1 second (m/s)

t = 4600000000000m
300000 m/s This problem shows the need for a method to decrease the number of zeros without losing track of place value.

Scientists and mathematicians have developed scientific notation that expresses values as a simple number multiplied by a power of 10.

Some examples: 104 = 1000, 103 = 1000, 102 = 100, 101 = 10

100 = 1, 10-1 = 0.1, 10-2 = 0.01, 10-3 = 0.001.

A shortcut for scientific notation involves moving the decimal point and counting the number of places it is moved.

To change 18000 to 1.8, the decimal place is moved 4 places to the left which becomes the correct power of 10. 18000 = 1.8 x 104.

If a number is smaller than 1, the decimal point is moved to the right and the power of 10 ,is negative. An Eschericia coli bacterium is 0.0000021m long. 0.0000021m = 2.1 x 10-6m.

Using scientific notation to perform calculations involves the rules of algebra for the powers of 10. When you multiply 2 numbers, you add exponents and when you divide you subtract exponents.

So, the Earth-Neptune problem becomes:

t = 4.6 x 1012m
3.0 x 108

t = 1.5 x 1012-8 = 1.5 x 104 (15000 s)

PRACTICE PROBLEMS:

1. Write the following measurements in scientific notation:

a. 600000000m
b. .0032kg
c. 20220cm
d. 0.00063m
e. 7003000kg
f. 0.00000000002g

2. Convert the following to long form

a. 4.5 x 103
b. 6.05 x 10-3
c. 3.115 x 106
d. 1.99 x 10-8

BONUS: AVAGADRO’S NUMBER IS AN IMPORTANT NUMBER IN CHEMISTRY FOR A NUMBER OF REASONS.
Expand this number 6.02 x 1023.

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(TEACHER’S NOTE: Science Spectrum, Dobson, Holman, Roberts, 2001, provide several scientific notation problems as part of a Problem Bank appendix. Additionnal text material and problems are also available in an additional appendix. Publisher-- holt, Rinehart, Winston.