1. Objectives
Convert between standard notation and scientific notation.

2. Scientific notation is a method of writing numbers that are very large or very small.
The first part is a number that is greater than or equal to 1 and less than 10.
The second part is a power of 10.

3. Multiplying by Powers of 10

4. If you do not see a decimal point in a number, it is understood to be at the end of the number.
Reading Math
You may need to add zeros to the right or left of a number in order to move the decimal point in that direction.
Writing Math

5. Example 3: Multiplying by Powers of 10
Find the value of each expression.
A  108
Move the decimal point 8 places to the right.
2,389,000,000
B. 467  10–3
4 6 7
Move the decimal point 3 places to the left.
0.467

6. Check It Out! Example 3
Find the value of each expression.
a  105
Move the decimal point 5 places to the right.
85,340,000
b  10–2
Move the decimal point 2 places to the left.

7. Example 4A: Astronomy Application
Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km.
Write Saturn’s diameter in standard form.
Move the decimal point 5 places to the right.
120,000 km

8. Example 4B: Astronomy Application
Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km.
Write Saturn’s distance from the Sun in scientific notation.
Count the number of places you need to move the decimal point to get a number between 1 and 10.
1,427,000,000
1,4 2 7,0 0 0,0 0 0
9 places
Use that number as the exponent of 10.
1.427  109 km

9. Standard form refers to the usual way that numbers are written—not in scientific notation.
Reading Math

10. Example 1
Use the information above to write Jupiter’s diameter in scientific notation.
143,000 km
Count the number of places you need to move the decimal point to get a number between 1 and 10.
5 places
Use that number as the exponent of 10.
1.43  105 km

11. Check It Out! Example 4b
Use the information above to write Jupiter’s orbital speed in standard form.
Move the decimal point 4 places to the right.
13,000 m/s

12. Lesson Quiz: Part I
Find the value of each expression. 1. 2.
3. The Pacific Ocean has an area of about 6.4 х 107 square miles. Its volume is about 170,000,000 cubic miles.
a. Write the area of the Pacific Ocean in standard
3,745,000
form.
b. Write the volume of the Pacific Ocean in scientific notation.
1.7  108 mi3