Scientific Notation
When dealing with very large or very small numbers, it is helpful to use scientific notation.
A number is in scientific notation if it is written in the form
𝑎 × 10𝑛 ,
where 𝑛 is an integer and 1 ≤ |𝑎| < 10
Examples: 3.4 × 106 , 5.43 × 1013 ,
9 × 10−10
1. We use powers of 10 to write numbers in scientific notation. Complete the following table:
Power of 10
Standard Notation
1,000,000
Unit Name
millions
1
0.001
ones
103
millionths
What patterns do you notice in the table?
2. Order the data in the table from least to greatest mass.
Jupiter
1.9 × 1027
Masses of Planets (kg)
Saturn
Uranus
5.7 × 1026
8.7 × 1025
Neptune
1.0 × 1026
3. The mass of Earth’s atmosphere is 5,700,000,000,000,000 tons. Write this in scientific
notation.
4. The mass of the smallest insect, a parasitic wasp, is 0.000 004 92 grams. Write this in
scientific notation.
5. The temperature at the Sun’s core is 1.55 × 106 K. Write this in standard notation.
6. The lowest temperature ever in a lab is 2 × 10−11 K. Write this in standard notation.