Answer :
To determine which sign makes the statement true between [tex]\(8.3 \times 10^{13}\)[/tex] and [tex]\(8.3 \times 10^{-13}\)[/tex], let's compare the two expressions:
1. Understand the Expressions:
- [tex]\(8.3 \times 10^{13}\)[/tex]: This number is [tex]\(8.3\)[/tex] multiplied by [tex]\(10^{13}\)[/tex], which means it is a large number, specifically:
[tex]\[
8.3 \times 10^{13} = 83,000,000,000,000
\][/tex]
- [tex]\(8.3 \times 10^{-13}\)[/tex]: This number is [tex]\(8.3\)[/tex] divided by [tex]\(10^{13}\)[/tex], which means it is a very small number, specifically:
[tex]\[
8.3 \times 10^{-13} \approx 0.00000000000083
\][/tex]
2. Compare the Two Numbers:
- [tex]\(83,000,000,000,000\)[/tex] (a large number) is clearly greater than [tex]\(0.00000000000083\)[/tex] (a very small number).
3. Determine the Correct Sign:
- Since [tex]\(83,000,000,000,000\)[/tex] is greater than [tex]\(0.00000000000083\)[/tex], the correct sign to use is ">".
Therefore, the statement [tex]\(8.3 \times 10^{13} > 8.3 \times 10^{-13}\)[/tex] is true with the ">" sign.
1. Understand the Expressions:
- [tex]\(8.3 \times 10^{13}\)[/tex]: This number is [tex]\(8.3\)[/tex] multiplied by [tex]\(10^{13}\)[/tex], which means it is a large number, specifically:
[tex]\[
8.3 \times 10^{13} = 83,000,000,000,000
\][/tex]
- [tex]\(8.3 \times 10^{-13}\)[/tex]: This number is [tex]\(8.3\)[/tex] divided by [tex]\(10^{13}\)[/tex], which means it is a very small number, specifically:
[tex]\[
8.3 \times 10^{-13} \approx 0.00000000000083
\][/tex]
2. Compare the Two Numbers:
- [tex]\(83,000,000,000,000\)[/tex] (a large number) is clearly greater than [tex]\(0.00000000000083\)[/tex] (a very small number).
3. Determine the Correct Sign:
- Since [tex]\(83,000,000,000,000\)[/tex] is greater than [tex]\(0.00000000000083\)[/tex], the correct sign to use is ">".
Therefore, the statement [tex]\(8.3 \times 10^{13} > 8.3 \times 10^{-13}\)[/tex] is true with the ">" sign.
