Lesson 4: Adding and Subtracting Numbers Written in Scientific Notation

To add or subtract numbers in scientific notation:

1. The powers of 10 must be the same.
2. If they are not the same, rewrite one number so that the exponents match.
3. Then add or subtract the first factors (the numbers in front).

Think of it like combining like terms in algebra: 3x + 2x = 5x. Here, the x is like the power of 10. We can only add when the powers match.

Recap

1. Make sure exponents match before adding or subtracting.
2. If not, rewrite one number so powers of 10 are the same.
3. Add or subtract the first factors.
4. Write the final answer in proper scientific notation (first factor between 1 and 10).

Examples

1. Add: 3 thousands + 2 thousands + 4 thousands.
(3 + 2 + 4) thousands = 9 thousands.
Answer: 9 × 10³.

2. Add: 3 fifths + 2 fifths + 4 fifths.
(3 + 2 + 4) fifths = 9 fifths.
Answer: 9/5.

3. Add: 3m + 2m + 4m.
(3 + 2 + 4)m = 9m.

4. Add: 3m² + 2m² + 4m².
(3 + 2 + 4)m² = 9m².

5. Add: 3 × 100 + 2 × 100 + 4 × 100.
(3 + 2 + 4) × 100 = 9 × 100 = 900.

6. Add: 3 × 10² + 2 × 10² + 4 × 10².
(3 + 2 + 4) × 10² = 9 × 10² = 900.

7. Add: 3 × 10¹³ + 2 × 10¹² + 4 × 10¹².
Rewrite 3 × 10¹³ = 30 × 10¹².
Now add: (30 + 2 + 4) × 10¹² = 36 × 10¹².
Rewrite: 36 × 10¹² = 3.6 × 10¹³.
Answer: 3.6 × 10¹³.

8. Add/Subtract: 3 × 10⁸ + 2 × 10⁸ − 4 × 10⁸.
(3 + 2 − 4) × 10⁸ = 1 × 10⁸.
Answer: 1 × 10⁸.

9. Add/Subtract: 3.6 × 10⁹ − 2.1 × 10⁹ + 4.4 × 10⁹.
(3.6 − 2.1 + 4.4) × 10⁹ = 5.9 × 10⁹.
Answer: 5.9 × 10⁹.

10. A cat video has 55,000,000 views. A baby video has 1.1 × 10⁷ views. A science video has 23,000,000 views. How many total views?
55,000,000 = 5.5 × 10⁷, 23,000,000 = 2.3 × 10⁷.
Add: (5.5 + 1.1 + 2.3) × 10⁷ = 8.9 × 10⁷.
Answer: 8.9 × 10⁷ views.

11. Add: 6 × 10³ + 7 × 10³ + 8 × 10³.
(6 + 7 + 8) × 10³ = 21 × 10³.
Rewrite: 21 × 10³ = 2.1 × 10⁴.
Answer: 2.1 × 10⁴.

12. Add: 9.25 × 10³ + 9.8 × 10².
Rewrite: 9.8 × 10² = 0.98 × 10³.
Add: (9.25 + 0.98) × 10³ = 10.23 × 10³.
Rewrite: 1.023 × 10⁴.
Answer: 1.023 × 10⁴.

13. Add/Subtract: 5 × 10⁶ + 9 × 10⁶ − 2 × 10⁶ + 8 × 10⁶.
(5 + 9 − 2 + 8) × 10⁶ = 20 × 10⁶.
Rewrite: 2 × 10⁷.
Answer: 2 × 10⁷.

14. Add: 4 × 10⁵ + 3 × 10⁶.
Rewrite: 4 × 10⁵ = 0.4 × 10⁶.
Add: (0.4 + 3) × 10⁶ = 3.4 × 10⁶.
Answer: 3.4 × 10⁶.

15. Subtract: 7.2 × 10⁵ − 4 × 10⁴.
Rewrite: 4 × 10⁴ = 0.4 × 10⁵.
Subtract: (7.2 − 0.4) × 10⁵ = 6.8 × 10⁵.
Answer: 6.8 × 10⁵.

16. Galaxy Stars Table

Galaxy	Estimated Stars
Milky Way	2.5 × 10¹¹
Whirlpool	1.0 × 10¹¹
Sunflower	4.0 × 10¹¹
Antennae	3.0 × 10¹¹

Total = (2.5 + 1.0 + 4.0 + 3.0) × 10¹¹ = 10.5 × 10¹¹.
Rewrite = 1.05 × 10¹².
Answer: 1.05 × 10¹² stars.