1. Standard Form (also referred to as "scientific notation“)

2. Standard Form In science, we deal with some very LARGE numbers:
1 mole =
In science, we deal with some very SMALL numbers:
Mass of an electron = kg

3. Imagine the difficulty of calculating the mass of 1 mole of electrons!kg x
???????????????????????????????????

4. Standard Form:
A method of representing very large or very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is an integer
For very large numbers and very small numbers, standard form is more concise.

5. . 9 8 7 6 5 4 3 2 1
Step 1: Insert an understood decimal point
Step 2: Decide where the decimal must end
up so that one number is to its left
Step 3: Count how many places you bounce
the decimal point
Step 4: Re-write in the form M x 10n

6. 2.5 x 109
The exponent is the number of places we moved the decimal.

7. 0.0000579 1 2 3 4 5 Step 2: Decide where the decimal must end
up so that one number is to its left
Step 3: Count how many places you bounce
the decimal point
Step 4: Re-write in the form M x 10n

8. 5.79 x 10-5
The exponent is negative because the number we started with was less than 1.

9. More Examples Use: 2.898 (moved 8 places to the left)
Given: 289,800,000
Use: (moved 8 places to the left)
Answer: x 108
Given:
Use: 5.67 (moved 4 places to the right)
Answer: 5.67 x 10–4
Timberlake lecture plus

10. Learning Check
Express these numbers in standard form: 1) 2) 3)
4) 2 5)
Timberlake lecture plus

11. Solution
Express these numbers in standard form:
1) x 105
2) x 10–3
3) 3 x 109
4) 2 x 100
5) x 10–1
Timberlake lecture plus

12. Coming out of Standard Form
Move the decimal place to the right for a positive exponent 10.
Move the decimal place to the left for a negative exponent 10.
Use zeros to fill in places.

13. Examples Use: 5,093,000 (moved 6 places to the right)
Given: x 106
Use: 5,093, (moved 6 places to the right)
Given: x 10–4
Use: (moved 4 places to the left)
Timberlake lecture plus

14. PERFORMING CALCULATIONS IN STANDARD FORM
ADDITION AND SUBTRACTION

15. Review: M x 10n Standard form expresses a number in the form:
n is an integer
1  M  10

16. IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.
4 x 106
+ 3 x 106 7
x 106

17. The same holds true for subtraction in standard form.
4 x 106
- 3 x 106 1
x 106

18. If the exponents are NOT the same, we must move a decimal to make them the same.

19. 4.00 x 106
4.00 x 106
x 105
+ .30 x 106
4.30
x 106
Move the decimal on the smaller number!

20. A Problem for you…
2.37 x 10-6
x 10-4

21. Solution…
x 10-6
2.37 x 10-6
x 10-4

22. Solution…
x 10-4
x 10-4
x 10-4