Grade 8 Mathematics
SCIENTIFIC NOTATION is a way to write very large or very small numbers in a compact form.
The form is always: a x 10^n where 1 ≤ a < 10
Large numbers have POSITIVE exponents | Small numbers have NEGATIVE exponents
a = coefficient: A number from 1 to less than 10 (one digit before decimal)
10 = base: Always 10 in scientific notation
n = exponent: Shows how many places the decimal moved
Convert 93,000,000 (distance to Sun in miles) to scientific notation
Place the decimal after the first non-zero digit: 93,000,000 becomes 9.3
Count how many places you moved the decimal: 9.3000000 - moved 7 places LEFT
Write with power of 10: Since we moved LEFT and the number is LARGE, use POSITIVE exponent
Final Answer: 93,000,000 = 9.3 x 10^7
Convert 0.000047 (size of a human hair in meters) to scientific notation
Place the decimal after the first non-zero digit: 0.000047 becomes 4.7
Count how many places you moved the decimal: 0.00004.7 - moved 5 places RIGHT
Write with power of 10: Since we moved RIGHT and the number is SMALL, use NEGATIVE exponent
Final Answer: 0.000047 = 4.7 x 10^-5
WRONG: Writing 45 x 10^6 for 45,000,000. The coefficient (45) is NOT between 1 and 10!
RIGHT: 45,000,000 = 4.5 x 10^7. The coefficient (4.5) IS between 1 and 10. Remember: exactly ONE non-zero digit before the decimal!
Multiplication: Multiply coefficients, ADD exponents
(3 x 10^4) x (2 x 10^5) = (3 x 2) x 10^(4+5) = 6 x 10^9
Division: Divide coefficients, SUBTRACT exponents
(8 x 10^7) / (4 x 10^3) = (8 / 4) x 10^(7-3) = 2 x 10^4
Addition/Subtraction: Must have SAME exponent first!
5.2 x 10^6 + 3.1 x 10^6 = (5.2 + 3.1) x 10^6 = 8.3 x 10^6
If exponents differ, rewrite one to match before adding!
Which is larger: 6.2 x 10^8 or 8.5 x 10^7?
| Number | Exponent | Coefficient |
|---|---|---|
| 6.2 x 10^8 | 8 | 6.2 |
| 8.5 x 10^7 | 7 | 8.5 |
Step 1: Compare exponents first. 8 > 7
Answer: 6.2 x 10^8 is larger (higher exponent wins!)
Note: Only compare coefficients if the exponents are equal.
1. Write in scientific notation: 7,500,000,000
Answer: x 10^
2. Write in scientific notation: 0.00000082
Answer: x 10^
3. Multiply: (4 x 10^3) x (3 x 10^5)
Answer: x 10^
4. Which is larger? Circle your answer.
3.4 x 10^9 OR 9.1 x 10^8