1. Aim: How can we express a large or small number?
Do Now:
Take out a calculator.
How many significant figures are in the following numbers?
200
200.0
200.01
2,000,000,000,000,000

2. Answer to Do Now
200
200.0
200.01
2,000,000,000,000,000
Is there another way to express 2,000,000,000,000,000?

3. Scientific Notation
A way of writing large or small numbers without writing all of its digits.
There are two parts to scientific notation.
A number between 1 and 10.
That number x10 to some power.
If both parts are not present, it is not scientific notation.

4. Using Scientific Notation to Express Large Numbers
Step 1. Take the large number and put a decimal point after the first digit in that number.
Step 2. Count the number of digits (including zeros) that come after that first digit. That will become the exponent to add to the 10.
Step 3. Add x10 and the exponent to the digit.

5. Example: Change 2,000,000,000,000,000 into scientific notation.
Step 1 –
Step 2 – There are 15 zeros.
Step 3 – 2.0 x 1015

6. More Examples: Change the following numbers into scientific notation.
1500 days
2450 years
765,000,000 minutes

7. Using Scientific Notation to Express Small Numbers
Step 1 – Put the decimal after the first nonzero digit.
Step 2 – Count how many places you had to move the decimal and that will become your exponent.
Step 3 – Add x10 to the exponent to the digit.

8. Change 0.000722 into scientific notation.
Example:
Change into scientific notation.
Step 1 –
Step 2 – The decimal was moved 4 times.
Step 3 – 7.22 x 10-4
Notice that the exponent has a negative sign in front of it.
If the decimal is moved to the right, the exponent will be negative. If the decimal is moved to the left, the exponent will be positive.

9. More Examples: Change the following numbers into scientific notation.
0.0039

10. Activity/Homework # Convert the following into scientific notation:
1,900,000
280
1300