Sure, I can guide you through matching each decimal number to its correct scientific notation. Here's the step-by-step solution:
1. The number 30,700 needs to be written in scientific notation. It can be expressed as [tex]\( 3.07 \times 10^4 \)[/tex]:
[tex]\[ 3.07 \times 10^4 \longrightarrow 30,700 \][/tex]
2. The number 0.000307 should be matched with [tex]\( 3.07 \times 10^{-4} \)[/tex]:
[tex]\[ 3.07 \times 10^{-4} \longrightarrow 0.000307 \][/tex]
3. The number 0.00000307 corresponds to [tex]\( 3.07 \times 10^{-6} \)[/tex]:
[tex]\[ 3.07 \times 10^{-6} \longrightarrow 0.00000307 \][/tex]
4. Finally, the number 3,070,000 is expressed as [tex]\( 3.07 \times 10^6 \)[/tex]:
[tex]\[ 3.07 \times 10^6 \longrightarrow 3,070,000 \][/tex]
Putting it all together, the pairs should be as follows:
- [tex]\( 3.07 \times 10^4 \)[/tex] → 30,700
- [tex]\( 3.07 \times 10^{-4} \)[/tex] → 0.000307
- [tex]\( 3.07 \times 10^{-6} \)[/tex] → 0.00000307
- [tex]\( 3.07 \times 10^6 \)[/tex] → 3,070,000
So the final pairs will look like this:
[tex]\[ 3.07 \times 10^4 \longrightarrow 30,700 \][/tex]
[tex]\[ 3.07 \times 10^{-4} \longrightarrow 0.000307 \][/tex]
[tex]\[ 3.07 \times 10^{-6} \longrightarrow 0.00000307 \][/tex]
[tex]\[ 3.07 \times 10^6 \longrightarrow 3,070,000 \][/tex]
These are the correct matches for the given decimal numbers and their scientific notations.
