Scientific Notation Worksheets - Math Monks - Free Printable

To solve the problem of writing numbers in scientific notation, we need to express each number in the form \( a \times 10^n \), where \( 1 \leq a < 10 \) and \( n \) is an integer.

Steps to Convert to Scientific Notation:

1. Move the decimal point so that there is only one non-zero digit to the left of the decimal point.
2. Count the number of places you moved the decimal point.
- If you moved the decimal point to the right, \( n \) is negative.
- If you moved the decimal point to the left, \( n \) is positive.
3. Write the number in the form \( a \times 10^n \).

Solutions:

#### 1) \( 0.000075 \)
- Move the decimal point 5 places to the right.
- \( n = -5 \).
- Scientific notation: \( 7.5 \times 10^{-5} \).

#### 2) \( 0.00005 \)
- Move the decimal point 5 places to the right.
- \( n = -5 \).
- Scientific notation: \( 5 \times 10^{-5} \).

#### 3) \( 0.000022 \)
- Move the decimal point 5 places to the right.
- \( n = -5 \).
- Scientific notation: \( 2.2 \times 10^{-5} \).

#### 4) \( 0.017 \)
- Move the decimal point 2 places to the right.
- \( n = -2 \).
- Scientific notation: \( 1.7 \times 10^{-2} \).

#### 5) \( 4,523,000 \)
- Move the decimal point 6 places to the left.
- \( n = 6 \).
- Scientific notation: \( 4.523 \times 10^6 \).

#### 6) \( 83.6 \)
- Move the decimal point 1 place to the left.
- \( n = 1 \).
- Scientific notation: \( 8.36 \times 10^1 \).

#### 7) \( 990 \)
- Move the decimal point 2 places to the left.
- \( n = 2 \).
- Scientific notation: \( 9.9 \times 10^2 \).

#### 8) \( 325 \)
- Move the decimal point 2 places to the left.
- \( n = 2 \).
- Scientific notation: \( 3.25 \times 10^2 \).

#### 9) \( 8,600 \)
- Move the decimal point 3 places to the left.
- \( n = 3 \).
- Scientific notation: \( 8.6 \times 10^3 \).

#### 10) \( 75,000 \)
- Move the decimal point 4 places to the left.
- \( n = 4 \).
- Scientific notation: \( 7.5 \times 10^4 \).

#### 11) \( 127.8 \)
- Move the decimal point 2 places to the left.
- \( n = 2 \).
- Scientific notation: \( 1.278 \times 10^2 \).

#### 12) \( 5,962 \)
- Move the decimal point 3 places to the left.
- \( n = 3 \).
- Scientific notation: \( 5.962 \times 10^3 \).

#### 13) \( 1.76 \)
- The decimal point is already in the correct position.
- \( n = 0 \).
- Scientific notation: \( 1.76 \times 10^0 \).

#### 14) \( 0.0000001901 \)
- Move the decimal point 7 places to the right.
- \( n = -7 \).
- Scientific notation: \( 1.901 \times 10^{-7} \).

#### 15) \( 9,110 \)
- Move the decimal point 3 places to the left.
- \( n = 3 \).
- Scientific notation: \( 9.11 \times 10^3 \).

#### 16) \( 3,800 \)
- Move the decimal point 3 places to the left.
- \( n = 3 \).
- Scientific notation: \( 3.8 \times 10^3 \).

#### 17) \( 80,400 \)
- Move the decimal point 4 places to the left.
- \( n = 4 \).
- Scientific notation: \( 8.04 \times 10^4 \).

#### 18) \( 4.8 \)
- The decimal point is already in the correct position.
- \( n = 0 \).
- Scientific notation: \( 4.8 \times 10^0 \).

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 7.5 \times 10^{-5} \\
2) & 5 \times 10^{-5} \\
3) & 2.2 \times 10^{-5} \\
4) & 1.7 \times 10^{-2} \\
5) & 4.523 \times 10^6 \\
6) & 8.36 \times 10^1 \\
7) & 9.9 \times 10^2 \\
8) & 3.25 \times 10^2 \\
9) & 8.6 \times 10^3 \\
10) & 7.5 \times 10^4 \\
11) & 1.278 \times 10^2 \\
12) & 5.962 \times 10^3 \\
13) & 1.76 \times 10^0 \\
14) & 1.901 \times 10^{-7} \\
15) & 9.11 \times 10^3 \\
16) & 3.8 \times 10^3 \\
17) & 8.04 \times 10^4 \\
18) & 4.8 \times 10^0 \\
\end{array}
}
\]