Alright! Let's convert each of these decimal numbers to their correct scientific notation. Scientific notation expresses numbers as a product of a coefficient and a power of 10. The coefficient is usually in a form that has one non-zero digit to the left of the decimal point.
1. 30700:
- Identify the significant digits which are 3, 0, 7.
- Place the decimal right after the first significant digit: 3.0700.
- Count the number of places the decimal point was moved to the left to place it after the first digit (3). In this case, it was moved 4 places.
- Express it as [tex]\( 3.07 \times 10^4 \)[/tex].
2. 0.000307:
- Identify the significant digits which are 3, 0, 7.
- Place the decimal right after the first significant digit: 3.07.
- Count the number of places the decimal point was moved to the right to place it after the first digit. In this case, it was moved 4 places.
- Express it as [tex]\( 3.070 \times 10^{-4} \)[/tex].
3. 0.00000307:
- Identify the significant digits which are 3, 0, 7.
- Place the decimal right after the first significant digit: 3.07.
- Count the number of places the decimal point was moved to the right to place it after the first digit. In this case, it was moved 6 places.
- Express it as [tex]\( 3.07 \times 10^{-6} \)[/tex].
4. 3,070,000:
- Identify the significant digits which are 3, 0, 7.
- Place the decimal right after the first significant digit: 3.070000.
- Count the number of places the decimal point was moved to the left to place it after the first digit (3). In this case, it was moved 6 places.
- Express it as [tex]\( 3.07 \times 10^6 \)[/tex].
So, here are the decimal numbers converted to scientific notation:
- 30700 ➔ [tex]\( 3.07 \times 10^4 \)[/tex]
- 0.000307 ➔ [tex]\( 3.070 \times 10^{-4} \)[/tex]
- 0.00000307 ➔ [tex]\( 3.07 \times 10^{-6} \)[/tex]
- 3,070,000 ➔ [tex]\( 3.07 \times 10^6 \)[/tex]
This should give a clear understanding of how to convert the given decimal numbers into their scientific notation form.
