“How do I convert numbers from standard notation to scientific notation?”


To convert numbers from standard notation to scientific notation, follow these steps:

1. **Identify the significant digits**: Find the non-zero digits in the number and note them down. These will be the *significant digits* in scientific notation.
   
2. **Place the decimal point**: Move the decimal point so that only one non-zero digit is to the left of the decimal point. This forms the *coefficient* in scientific notation.

3. **Count the decimal places moved**: Determine how many places you moved the decimal point. This count will be the *exponent* of 10 in scientific notation.

4. **Apply the exponent**: 
   - If the decimal point is moved to the left, the exponent is positive.
   - If the decimal point is moved to the right, the exponent is negative.

5. **Write the final result**: Combine the coefficient and the exponent in the form of \( a \times 10^n \), where \( a \) is the coefficient and \( n \) is the exponent.

### Example:
Convert 45,000 to scientific notation:

1. The significant digits are 4.5.
2. Move the decimal point four places to the left to get 4.5.
3. Since you moved the decimal four places to the left, the exponent is +4.
4. The final answer is \( 4.5 \times 10^4 \).

#### Example with a small number:
Convert 0.0056 to scientific notation:

1. The significant digits are 5.6.
2. Move the decimal point three places to the right to get 5.6.
3. Since you moved the decimal three places to the right, the exponent is -3.
4. The final answer is \( 5.6 \times 10^{-3} \).

Would you like more examples or details on any step?

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### Related questions:
1. How do you convert numbers from scientific notation back to standard notation?
2. What are the key differences between standard notation and scientific notation?
3. How do you handle converting very large or very small numbers to scientific notation?
4. How does scientific notation help in simplifying multiplication and division of large numbers?
5. What are common mistakes made when converting between standard and scientific notation?

#### Tip:
When dealing with scientific notation on a calculator, check whether it uses "E" notation (e.g., \( 3.2E4 \)) to represent powers of 10.

How do I convert numbers from standard notation to scientific notation?

Learn the step-by-step process of converting numbers from standard notation to scientific notation. Understand how to identify significant digits, place the decimal point, and determine the exponent. This guide includes examples for large and small numbers, making it ideal for students in Grades 6-8.

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