CHE 120/140/170 Handout – Scientific Notation
Scientific Notation
Numbers in chemistry can be very large or very small, so it is not always convenient to write a
number out in its full form. Take Avogadro’s number, for instance:
602,200,000,000,000,000,000,000. In these cases, we use scientific notation. In scientific
notation, Avogadro’s number would be written 6.022×1023.
How is a number converted into scientific notation form?
Let’s work through an example with:
295. First, rewrite the number with one number to the left of a decimal and the rest of the
numbers to the right of the decimal: 2.95. Now, does 295 = 2.95? No! So, we must now
multiply our decimal by ten raised to whatever power will make it equal to the original number:
2.95×102. Numbers less than one will be multiplied by ten raised to a negative power.
Now try some problems.
Convert the following numbers into scientific notation.
1. 1,289,409
1.289409×106
4. 10.0064
1.00064×101
2. 0.006798
6.798×10–3
5. 0.14059
1.4059×10–1
3. 465,841.2
4.658412×105
6. 89,416
8.9416×104
We must also be able to convert a number in scientific notation back to a normal notation.
To
do this, simply complete the multiplication!
7. 2.497×108
249,700,000
8. 9.406×10–3
0.009406
9. 4.8915×102
489.15
10. 1.000×104
11. 3.4×10–7
12. 2.750×10–2
10,000
0.00000034
0.02750
It is also imperative to know how to type a number in scientific notation into a calculator.
First,
look for a button with either “EE” on it for TI calculators or “EXP” for Casio calculators; it may
be a shift function. This button means “×10 raised to the x power.” Now, follow these steps to
type in 2.95×102. First, type in the 2.95. Next, push the button that means “×10 raised to the x
power.” Finally, type 2 which is the number, or x, we are raising the ten to.
Computers and calculators do not always represent scientific notation the way we do on paper.
Instead of writing 2.95×102, they might write 2.95E2 or 2.95E2. Some calculators have a special
place where the “2” would be put that is extra small. No matter how a computer or a calculator
represents scientific notation, we need to understand what is meant.
Be sure to practice with your calculator so that you are comfortable with it and scientific
notation.
Scientific Notation key.docx
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