Scientific Notation

Why Scientific Notation?

In science, we deal with massive numbers (like the distance to stars) or tiny numbers (like the size of bacteria). Writing 20 zeroes is prone to error.

Scientific Notation (or Standard Form) writes a number as:

Where:

• $1 \le k < 10$ (A number between 1 and 10)
• $n$ is an integer.

Examples

Large Numbers

• Distance to Sun: $149,600,000,000$ m
• Move decimal left 11 places to get 1.496.
• Standard Form: $1.496 \times 10^{11}$ m.

Converting to Standard Form

1. 5900 $\rightarrow$ $5.9 \times 1000 = 5.9 \times 10^3$
2. 80,00,000 $\rightarrow$ $8.0 \times 1000000 = 8 \times 10^6$

Comparisons in Space

To compare, look at the exponent first. $10^{12}$ is 10 times larger than $10^{11}$. So Saturn is roughly 10 times further from the Sun than Earth is.