1. Scientific Notation

2. (base)exponent Exponent
Exponent – a number that shows repeated multiplication. Base – a number that is multiplied repeatedly.
(base)exponent

3. Scientific Notation
Earth is roughly spherical in shape and its volume is extremely large. Both numbers below indicate the Earth’s volume in cubic miles 2.59 X 1011 Or 259,000,000,000
Both quantities are the same. The first is the scientific notation and the second is the standard notation. Scientific notation is a brief way to write very large or very small numbers.

4. A number is in scientific notation if
The first number is greater than 1 or equal to 1 and less than 10.
The first number is a power of base 10.
Examples
1 X 108
1.54 X 107
9.99 X 104

5. Is each number written in scientific notation? If not, explain.
56.29 X 1012 No, is greater than X 10-3 No, 0.84 is less than X 105 Yes, 6.11 is greater than 1, and less than 10.
No, is greater than 10.
No, 0.84 is less than 1.
Yes

6. Writing in Scientific Notation
Place the decimal point so there is one number to the left of it, that is greater than 1 but less than 10.
Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on base 10.
If the original number was less than 1, then the exponent is negative.
If the original was greater than 1, then the exponent is positive.

7. Scientific Notation – original number is greater than 1.
Move the point to get a
number between 1 and 10
The point moved 7 places . .
Add the
decimal point
Between 1 and 10

8. Scientific Notation – Original number is not greater than 1
The decimal needs to be moved from its current position to a position where the number to the left of the decimal is greater than 1, but less than 10.
Move between the 5 and 6.
How many spaces were moved?
4 spaces. Since the original number was less
than 1, the exponent is negative.
Answer: 5.67 x 10-4

9. Standard Notation Example: 1.55 X 106
For a positive exponent
of base 10, move the
decimal point to the right.
Example: 1.55 X 106
(move 6 spaces to the right from where the decimal is, and use zeros to fill in the places.)
1,550,000
For a negative exponent of
base 10, move the decimal
point to the left.
Example: 2.55 X 10 -4
(move 4 spaces to the left from where the decimal is, and use zeros to fill in the places.)

10. What is 0.000932 written in scientific notation?
9.32 X 10-6
9.32 X 10-5
9.32 X 10-4
9.32 X 10-3

11. The population of the Tokyo metropolitan area is estimated as 3
The population of the Tokyo metropolitan area is estimated as X 107 when written in scientific notation. What is the number written in standard form?
3,445,000
34,450,000
344,500,000
3,445,000,000

12. Ordering Numbers in Scientific Notation
To order numbers in scientific notation
First look at the exponent.
If the exponents are the same, you must look at the decimal factor.
Order them by the exponents (or decimal factor if exponents are the same), in ASCENDING (least to greatest) or DESCENDING (greatest to least) order.

13. Order this set of numbers from least to greatest. 5. 6 X 1010 5
Order this set of numbers from least to greatest. 5.6 X X X X 1015
Let’s order the exponents from least to greatest For the 1010, which one is smaller, 5.6 or 6.2? 5.6 It should go first.
Plug in the values, and here’s the order: 5.6 X X X X 1021 Question, why is 5.6 X 1021 larger than 9.2 X 1015? The exponent of base 10 is greater.

14. Which list below orders the numbers in scientific notation from least to greatest?
7.35 X 103, 6.21 X 10-2, 4.37 X 10-3
3.91 X 104, 4.37 X 10-3, 7.35 X 103
4.37 X 10-3, 6.21 X 10-2, 7.35 X 103
3.91 X 104, 7.35 X 103, 6.21 X 10-2

15. Now let’s play a game! Click on the link below to practice converting numbers to scientific notation. Once you finish, please complete the practice problems on Power-school. If the link to the game does not work, call the instructor over!