Identify the number of significant figures in the following number:

1.)  0.00450
2.) 3050
3.) 123.450
4.) 100
5.) 5,600

Express the following in scientific notation:

1.) 0.000456
2.) 123,000
3.) 7,890,000
4.) 0.0000123
5.) 20,000

### Identifying Significant Figures

The number of significant figures in a number is determined by counting all digits except:

1. Leading zeros (zeros before the first non-zero digit).
2. Trailing zeros (zeros at the end of a number) unless there is a decimal point.

Let's analyze each case:

1. **0.00450**  
   - Leading zeros are not significant.  
   - The digits "450" are significant.  
   - **Significant figures: 3**

2. **3050**  
   - The digits "305" are significant.  
   - The trailing zero is not significant (since there is no decimal point).  
   - **Significant figures: 3**

3. **123.450**  
   - All digits, including trailing zeros after the decimal point, are significant.  
   - **Significant figures: 6**

4. **100**  
   - The digits "1" are significant.  
   - The two trailing zeros are not significant (since there is no decimal point).  
   - **Significant figures: 1**

5. **5,600**  
   - The digits "56" are significant.  
   - The two trailing zeros are not significant (since there is no decimal point).  
   - **Significant figures: 2**

### Scientific Notation

Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.

1. **0.000456**  
   - Move the decimal point 4 places to the right: \(4.56 \times 10^{-4}\).

2. **123,000**  
   - Move the decimal point 5 places to the left: \(1.23 \times 10^5\).

3. **7,890,000**  
   - Move the decimal point 6 places to the left: \(7.89 \times 10^6\).

4. **0.0000123**  
   - Move the decimal point 5 places to the right: \(1.23 \times 10^{-5}\).

5. **20,000**  
   - Move the decimal point 4 places to the left: \(2.0 \times 10^4\).

### Summary:

1. Significant Figures:
   - 0.00450: 3 significant figures
   - 3050: 3 significant figures
   - 123.450: 6 significant figures
   - 100: 1 significant figure
   - 5,600: 2 significant figures

2. Scientific Notation:
   - 0.000456: \(4.56 \times 10^{-4}\)
   - 123,000: \(1.23 \times 10^5\)
   - 7,890,000: \(7.89 \times 10^6\)
   - 0.0000123: \(1.23 \times 10^{-5}\)
   - 20,000: \(2.0 \times 10^4\)

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do trailing zeros affect the number of significant figures when a decimal point is present?
2. What is the significance of significant figures in scientific measurements?
3. How does scientific notation simplify the expression of very large or very small numbers?
4. How would you determine significant figures for a number expressed in scientific notation?
5. What are the rules for rounding numbers to a specific number of significant figures?

**Tip:** Always remember that zeros between non-zero digits are significant, and trailing zeros are significant only when there is a decimal point!

Identify the number of significant figures in the following numbers: 0.00450, 3050, 123.450, 100, 5,600. Express the following in scientific notation: 0.000456, 123,000, 7,890,000, 0.0000123, 20,000.

Learn how to identify significant figures and express numbers in scientific notation with examples such as 0.00450, 3050, 123.450, and 100. This guide explains the core rules for significant figures and shows step-by-step conversions to scientific notation for numbers like 0.000456 and 123,000. Suitable for students in Grades 6-8.

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