Scientific Notation Worksheets - Free Printable

Problem: Convert numbers between scientific notation and standard form.

#### Part 1: Write each exponent in standard form.

1. a. \(10^7\)
- \(10^7\) means \(1\) followed by \(7\) zeros.
- Standard form: 10,000,000

2. b. \(10^9\)
- \(10^9\) means \(1\) followed by \(9\) zeros.
- Standard form: 1,000,000,000

3. c. \(10^5\)
- \(10^5\) means \(1\) followed by \(5\) zeros.
- Standard form: 100,000

4. d. \(10^{-2}\)
- \(10^{-2}\) means \(1\) divided by \(10^2\), which is \(1 / 100\).
- Standard form: 0.01

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#### Part 2: Write each number in standard form.

5. e. \(6 \times 10^8\)
- Move the decimal point \(8\) places to the right from \(6\).
- Standard form: 600,000,000

6. f. \(1.8 \times 10^5\)
- Move the decimal point \(5\) places to the right from \(1.8\).
- Standard form: 180,000

7. g. \(4.7 \times 10^9\)
- Move the decimal point \(9\) places to the right from \(4.7\).
- Standard form: 4,700,000,000

8. h. \(7.8 \times 10^3\)
- Move the decimal point \(3\) places to the right from \(7.8\).
- Standard form: 7,800

9. i. \(3.14 \times 10^{-2}\)
- Move the decimal point \(2\) places to the left from \(3.14\).
- Standard form: 0.0314

10. j. \(7.11 \times 10^2\)
- Move the decimal point \(2\) places to the right from \(7.11\).
- Standard form: 711

11. k. \(4 \times 10^6\)
- Move the decimal point \(6\) places to the right from \(4\).
- Standard form: 4,000,000

12. l. \(9.8087 \times 10^{10}\)
- Move the decimal point \(10\) places to the right from \(9.8087\).
- Standard form: 98,087,000,000

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#### Part 3: Write each number in scientific notation.

13. m. \(30,000\)
- Move the decimal point \(4\) places to the left to get \(3.0\).
- Scientific notation: \(3.0 \times 10^4\)

14. n. \(0.00012\)
- Move the decimal point \(4\) places to the right to get \(1.2\).
- Scientific notation: \(1.2 \times 10^{-4}\)

15. o. \(0.000099\)
- Move the decimal point \(5\) places to the right to get \(9.9\).
- Scientific notation: \(9.9 \times 10^{-5}\)

16. p. \(40,000,000,000\)
- Move the decimal point \(10\) places to the left to get \(4.0\).
- Scientific notation: \(4.0 \times 10^{10}\)

17. q. \(840,700,000\)
- Move the decimal point \(8\) places to the left to get \(8.407\).
- Scientific notation: \(8.407 \times 10^8\)

18. r. \(0.000000144\)
- Move the decimal point \(7\) places to the right to get \(1.44\).
- Scientific notation: \(1.44 \times 10^{-7}\)

19. s. \(0.00667\)
- Move the decimal point \(3\) places to the right to get \(6.67\).
- Scientific notation: \(6.67 \times 10^{-3}\)

20. t. \(501,000,000,000,000\)
- Move the decimal point \(14\) places to the left to get \(5.01\).
- Scientific notation: \(5.01 \times 10^{14}\)

21. u. \(6\) thousand
- Six thousand is \(6,000\). Move the decimal point \(3\) places to the left to get \(6.0\).
- Scientific notation: \(6.0 \times 10^3\)

22. v. \(600\) thousand
- Six hundred thousand is \(600,000\). Move the decimal point \(5\) places to the left to get \(6.0\).
- Scientific notation: \(6.0 \times 10^5\)

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Final Answers:

1. a. \(10,000,000\)
2. b. \(1,000,000,000\)
3. c. \(100,000\)
4. d. \(0.01\)
5. e. \(600,000,000\)
6. f. \(180,000\)
7. g. \(4,700,000,000\)
8. h. \(7,800\)
9. i. \(0.0314\)
10. j. \(711\)
11. k. \(4,000,000\)
12. l. \(98,087,000,000\)
13. m. \(3.0 \times 10^4\)
14. n. \(1.2 \times 10^{-4}\)
15. o. \(9.9 \times 10^{-5}\)
16. p. \(4.0 \times 10^{10}\)
17. q. \(8.407 \times 10^8\)
18. r. \(1.44 \times 10^{-7}\)
19. s. \(6.67 \times 10^{-3}\)
20. t. \(5.01 \times 10^{14}\)
21. u. \(6.0 \times 10^3\)
22. v. \(6.0 \times 10^5\)

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
\text{a. } 10,000,000 & \text{m. } 3.0 \times 10^4 \\
\text{b. } 1,000,000,000 & \text{n. } 1.2 \times 10^{-4} \\
\text{c. } 100,000 & \text{o. } 9.9 \times 10^{-5} \\
\text{d. } 0.01 & \text{p. } 4.0 \times 10^{10} \\
\text{e. } 600,000,000 & \text{q. } 8.407 \times 10^8 \\
\text{f. } 180,000 & \text{r. } 1.44 \times 10^{-7} \\
\text{g. } 4,700,000,000 & \text{s. } 6.67 \times 10^{-3} \\
\text{h. } 7,800 & \text{t. } 5.01 \times 10^{14} \\
\text{i. } 0.0314 & \text{u. } 6.0 \times 10^3 \\
\text{j. } 711 & \text{v. } 6.0 \times 10^5 \\
\text{k. } 4,000,000 & \\
\text{l. } 98,087,000,000 & \\
\end{array}
}
\]