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

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

### **Steps for Conversion:**

1. **Identify the Decimal Position**: For a given number, find where the decimal point is (even if it’s not explicitly written, for example in whole numbers).

2. **Move the Decimal**: Move the decimal point to the right or left so that only one non-zero digit remains to the left of the decimal point. This new number will be between 1 and 10.

3. **Count the Moves**: Count how many places you moved the decimal point. This number will be the exponent of 10.

   - **Positive Exponent**: If you moved the decimal to the left (for numbers larger than 1), the exponent is positive.
   - **Negative Exponent**: If you moved the decimal to the right (for numbers smaller than 1), the exponent is negative.

4. **Write the Number**: The final form is \( A \times 10^n \), where:
   - \( A \) is the number between 1 and 10.
   - \( n \) is the exponent indicating how many places you moved the decimal.

### **Example 1**: Converting 25,000 to scientific notation
- The decimal point in 25,000 is at the end (25,000.0).
- Move the decimal point 4 places to the left to get 2.5.
- Since we moved 4 places to the left, the exponent is \( +4 \).

**Result**: \( 2.5 \times 10^4 \)

### **Example 2**: Converting 0.0036 to scientific notation
- The decimal point is already in place (0.0036).
- Move the decimal point 3 places to the right to get 3.6.
- Since we moved 3 places to the right, the exponent is \( -3 \).

**Result**: \( 3.6 \times 10^{-3} \)

Would you like more details or do you have any specific numbers in mind?

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Here are 5 related questions to explore further:
1. How do you convert numbers from scientific notation back to standard notation?
2. How do you handle very large numbers in scientific notation?
3. Can you multiply and divide numbers in scientific notation?
4. What are the rules for adding and subtracting numbers in scientific notation?
5. How do significant figures affect scientific notation?

**Tip**: When dealing with scientific notation, always make sure the coefficient (the number before \( \times 10^n \)) is between 1 and 10 for proper notation.

Learn how to convert numbers from standard notation to scientific notation with this comprehensive guide. This tutorial walks through key mathematical concepts such as moving the decimal point and using exponents, suitable for students in Grades 7-9.

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