1. Unit 3. Day 22.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Operations with numbers in scientific notation
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used...

3. Let’s now turn scientific notation numbers into standard numbers
We just (yesterday) turned really big & really small numbers into scientific notation.
Let’s now turn scientific notation numbers into standard numbers

4. Example A:
1.78× Kg
1 78 . Kg

5. Example B:
3.691× 10 −8 m
3 691 . m

6. Example C:
8.004× sec
Example D:
2.0105× 10 −4 km

7. Example C:
8.004× sec
8 004 .
sec

8. Example D:
2.0105× 10 −4 km
2 0105 . km

10. OPERATIONS SCIENTIFIC NOTATION Now onto the main idea for today:
+, −, ×, ÷ + − × ÷
with numbers expressed in
SCIENTIFIC NOTATION
3.72× 10 19
8.111× 10 −3

11. [Add, Subtract, Multiply, Divide]
8.EE.3 Perform operations
with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology
[Add, Subtract, Multiply, Divide]

12. Adding & Subtracting

13. Example A: Add the scientific numbers
3.56× × 10 3
3560
3.56× 10 3
2.345× 10 3
2345
This means that we can add our scientific numbers like so:
3.4× × 10 75 1
8.6
× 10 75 + 5 . 9 5 1
× 10 3 + 5 9 5
5905

14. Example B: Subtract the scientific numbers
8.111× 10 9 −6.987× 10 9
× 10 9 7 1 1 1 −
1.124 1 . 1 2 4

15. Example C: Subtract the scientific numbers
5.6× 10 8 −3.2× 10 7
52.8× 10 7
× 10 ?
5.28× 10 8
5.6× 10 1 × 10 7
−3.2× 10 7
−3.2× 10 7
5.6× × 10 7
5 . 6
56 × 10 7
−3.2× 10 7 −
3 . 2 2
2.4 . 4
56−3.2 × 10 7
52.8 × 10 7

16. 3.198× 10 26 Example D: Add the scientific numbers
4.8× × 10 26
4.8× 10 24
+ 3.15× 10 2 × 10 24
4.8× 10 24
× × 10 24
4.8× 10 24
× 10 24
× 10 24
319.8 × 10 24
319.8× 10 24
3.198× 10 26

17. Multiplying & Dividing

18. Example E: Subtract the scientific numbers
1.2× × 10 4
1.2× 10 3 ×1.3× 10 4
1200
13000
1.2×1.3× 10 3 × 10 4
1.2×1.3 × 10 3 × 10 4
13000
1.56 × 10 3 × 10 4 ×
1200
1.56 × 10 7

19. Example F: Subtract the scientific numbers
6.4× 10 8 ÷3.2× 10 4
6.4× × 10 4
6.4× × 10 4 2 ×
10 4
20000
20000

20. Add/Subtract
1.5× × 10 8
1.5× × 10 8
1.5× × 10 1 × 10 7
Remember how we needed a common denominator to add/subtract fractions (but not required for multiplication/division) … the same idea works with scientific notation. We need “common exponents” to add/subtract but not to multiply/divide.
3.8× 10 8
3.8× 10 7
1.5× × × 10 7
1.5× × 10 7
× 10 7
24.5 × 10 7
Multiply/Divide
4.5× × 10 5
4.5× × 10 23 3 ×
10 0 1 3 ×
10 68