Scientific Notation

Pre-Algebra Tutorial

Scientific Notation

Intro

Scientific Notation is another way of saying a number to the power of 10 to simplify very large or very small numbers, like the population of the world or the number water molecules in the ocean. It is written as follows:

scientific notation

There are the 3 key points to this: the coefficient, the base of 10, and the exponent. The base will always remain the same unless instructed otherwise. The coefficient will always be greater than 1 but less than 10 and the exponent will generally be an integer, although we will use only rational numbers in this tutorial. The trickiest part is exponent’s sign: positive or negative. A positive exponent means it is really big while the negative exponent means it is really small.

exponent signs

The example above displays the difference between a positive and negative exponent sign; the top represents positive and the bottom negative. For example: 6.02×10^7= 60200000. Another example: 5.11×10^-4= .000511. Sometimes a number will be given and must be reduced to scientific notation: 125000000= 1.25×10^8.

Sample Problem

Simplify

1. 52300000

2. 250

3. .00025

Expand

4. 4.11×10^-5

5. 1.2×10^6

6. 2.556789×10^5

Solution

1. 5.23×10^7
Since this is a large number, we move the decimal left 7 times

2. 2.5×10^2
Since this is a large number, we move the decimal left 2 times

3. 2.5×10^-4
Since this is a small number, we move the decimal right 4 times and make the exponent negative so we know the number is actually less than 1

4. .0000411
Since the exponent is -5, the number is less than 1 and move the decimal left 5 times

5. 1200000
The exponent is 6, so move the decimal right 6 times

6. 255678.9
The exponent is 5, so move the decimal right 5 times



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