Scientific Notation and Logarithms

I. Scientific Notation

Scientists usually express very large or very small numbers in scientific notation or exponential notation. Numbers expressed in scientific notation have 1 digit to the left of the decimal point multiplied by 10 raised to the appropriate exponent.

A mass of 1,254 grams would be expressed as 1.254 x 10³ grams.

Since this is based units of ten the exponent equals the number of places to the right or left the decimal point has been moved.

A volume of 0.000345 mL would be expressed as 3.45 x 10^-4 mL.

Try the following online examples yourself.

This makes comparing numbers much easier because the exponents can be compared quickly to see which is bigger.

Do this  comparing examples.

II. Logarithms

Many biological processes or concepts, such as pH, and population growth, involve logarithmic scales. In any logarithmic scale a number equals the logarithmic base raised to an exponent.

Number = base ^logarithm

In science the most commonly used logarithmic base is 10. This means that scale very similar to scientific notation.

Example 1
10,000 = 10⁴
So the log of 10,000 in the base 10 is 4

Example 2
100 = 10²
The log of 100 in the base 10 is 2.

Try some online examples yourself

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