Scientific Notation Worksheet - Free Printable

Problem Overview:

The task involves converting numbers into scientific notation and converting numbers from scientific notation back to standard notation. Let's solve each part step by step.

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Part 1: Convert the following numbers into scientific notation

#### Scientific Notation Rules:
- A number in scientific notation is written as \( a \times 10^n \), where:
- \( a \) is a number between 1 and 10 (inclusive of 1 but exclusive of 10).
- \( n \) is an integer that indicates how many places the decimal point has been moved.

#### Solutions:

1. 3,400
- Move the decimal point 3 places to the left to get \( 3.4 \).
- The exponent \( n \) is +3 because the decimal was moved 3 places to the left.
- Answer: \( 3.4 \times 10^3 \)

2. 0.000023
- Move the decimal point 5 places to the right to get \( 2.3 \).
- The exponent \( n \) is -5 because the decimal was moved 5 places to the right.
- Answer: \( 2.3 \times 10^{-5} \)

3. 101,000
- Move the decimal point 5 places to the left to get \( 1.01 \).
- The exponent \( n \) is +5 because the decimal was moved 5 places to the left.
- Answer: \( 1.01 \times 10^5 \)

4. 0.010
- Move the decimal point 2 places to the right to get \( 1.0 \).
- The exponent \( n \) is -2 because the decimal was moved 2 places to the right.
- Answer: \( 1.0 \times 10^{-2} \)

5. 48.01
- Move the decimal point 1 place to the left to get \( 4.801 \).
- The exponent \( n \) is +1 because the decimal was moved 1 place to the left.
- Answer: \( 4.801 \times 10^1 \)

6. 1,000,000
- Move the decimal point 6 places to the left to get \( 1.0 \).
- The exponent \( n \) is +6 because the decimal was moved 6 places to the left.
- Answer: \( 1.0 \times 10^6 \)

7. 0.008671
- Move the decimal point 3 places to the right to get \( 8.671 \).
- The exponent \( n \) is -3 because the decimal was moved 3 places to the right.
- Answer: \( 8.671 \times 10^{-3} \)

8. 4.50
- The number is already between 1 and 10, so no need to move the decimal.
- The exponent \( n \) is 0.
- Answer: \( 4.50 \times 10^0 \)

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Part 2: Convert the following numbers into standard notation

#### Standard Notation Rules:
- To convert from scientific notation \( a \times 10^n \) to standard notation:
- If \( n > 0 \), move the decimal point \( n \) places to the right.
- If \( n < 0 \), move the decimal point \( |n| \) places to the left.

#### Solutions:

9. 2.30 × 10⁴
- Move the decimal point 4 places to the right.
- Answer: 23,000

10. 1.76 × 10⁻³
- Move the decimal point 3 places to the left.
- Answer: 0.00176

11. 1.901 × 10⁷
- Move the decimal point 7 places to the right.
- Answer: 19,010,000

12. 8.65 × 10⁻¹
- Move the decimal point 1 place to the left.
- Answer: 0.865

13. 9.11 × 10³
- Move the decimal point 3 places to the right.
- Answer: 9,110

14. 5.40 × 10¹
- Move the decimal point 1 place to the right.
- Answer: 54.0

15. 1.76 × 10⁸
- Move the decimal point 8 places to the right.
- Answer: 176,000,000

16. 7.4 × 10⁻⁵
- Move the decimal point 5 places to the left.
- Answer: 0.000074

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Final Answers:

1. \( 3.4 \times 10^3 \)
2. \( 2.3 \times 10^{-5} \)
3. \( 1.01 \times 10^5 \)
4. \( 1.0 \times 10^{-2} \)
5. \( 4.801 \times 10^1 \)
6. \( 1.0 \times 10^6 \)
7. \( 8.671 \times 10^{-3} \)
8. \( 4.50 \times 10^0 \)
9. 23,000
10. 0.00176
11. 19,010,000
12. 0.865
13. 9,110
14. 54.0
15. 176,000,000
16. 0.000074

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & 3.4 \times 10^3 \\
2. & 2.3 \times 10^{-5} \\
3. & 1.01 \times 10^5 \\
4. & 1.0 \times 10^{-2} \\
5. & 4.801 \times 10^1 \\
6. & 1.0 \times 10^6 \\
7. & 8.671 \times 10^{-3} \\
8. & 4.50 \times 10^0 \\
9. & 23,000 \\
10. & 0.00176 \\
11. & 19,010,000 \\
12. & 0.865 \\
13. & 9,110 \\
14. & 54.0 \\
15. & 176,000,000 \\
16. & 0.000074 \\
\end{array}
}
\]