Lesson 3: Time to Be More Precise

What is Scientific Notation?

Scientific notation is a way to write numbers that are very large or very small in a shorter form. A number is in scientific notation when it is written as:

a × 10ⁿ

where:

• a is the first factor, a number greater than or equal to 1 but less than 10.
• 10ⁿ is a power of 10, called the order of magnitude.

Example:
8.86 × 10⁶ is in scientific notation because 8.86 is between 1 and 10, and 10⁶ means 1,000,000.

Recap

• A number is in scientific notation if it looks like a × 10ⁿ.
• a must be at least 1 but less than 10.
• Large numbers use positive exponents.
• Small numbers use negative exponents.

Examples

1. Fill in the blanks:
A number is written in scientific notation when it is represented as a number a multiplied by a power of 10.
The general expression is a × 10ⁿ.

2. Identify the first factor and the order of magnitude in 8.86 × 10⁶.
First factor = 8.86. Order of magnitude = 6.

3. Decide if each is an example of scientific notation.

• 3 × 10² → Example
• 0.38 × 10² → Not example
• 715.39 × 10⁶ → Not example
• 4.8 × 10³ → Example
• 19.04 × 10⁷ → Not example
• −6.75 × 10⁵ → Example
• 1 × 10⁹ → Example
• 10 × 10¹⁰ → Not example

4. Write 3 × 10² in standard form.
3 × 10² = 300.

5. Write 4.8 × 10³ in standard form.
4.8 × 1,000 = 4,800.

6. Write 6.75 × 10⁶ in standard form.
6.75 × 1,000,000 = 6,750,000.

7. Write 9.1 × 10³ in standard form.
9.1 × 1,000 = 9,100.

8. Write 2.05 × 10⁶ in standard form.
2.05 × 1,000,000 = 2,050,000.

9. Logan writes 6.7 × 10⁵ = 67,000. Is he correct?
No. 6.7 × 100,000 = 670,000.

10. Write 200,000 in scientific notation.
200,000 → 2.0 × 10⁵.

11. Write 47,500,000 in scientific notation.
47,500,000 → 4.75 × 10⁷.

12. Write 750,000 in scientific notation.
750,000 → 7.5 × 10⁵.

13. Write 6,040,000 in scientific notation.
6,040,000 → 6.04 × 10⁶.

14. Write 36,360 in scientific notation.
36,360 → 3.636 × 10⁴.

15. Write 0.00045 in scientific notation.
0.00045 → 4.5 × 10⁻⁴.

16. Write 0.0032 in scientific notation.
0.0032 → 3.2 × 10⁻³.

17. Write 52,000,000 in scientific notation.
52,000,000 → 5.2 × 10⁷.

18. Write 98,000 in scientific notation.
98,000 → 9.8 × 10⁴.

19. Write 0.00000072 in scientific notation.
0.00000072 → 7.2 × 10⁻⁷.

20. Write 0.00009 in scientific notation.
0.00009 → 9 × 10⁻⁵.