use scientific notation to compare these numbers 12,740,876,635; 1,345,763,334; and 12,920,370,000, which has the greatest value?

A. 1.292037 x 10^10
B. 1.2740876635 x 10^10
C. 1.345763334 x 10^9

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To compare the numbers using scientific notation:

  1. 12,740,876,635 can be represented as: \[ 1.2740876635 \times 10^{10} \]

  2. 1,345,763,334 can be represented as: \[ 1.345763334 \times 10^9 \] To make the comparison easier, convert this to the same power of ten: \[ 1.345763334 \times 10^9 = 0.1345763334 \times 10^{10} \]

  3. 12,920,370,000 can be represented as: \[ 1.292037 \times 10^{10} \]

Now comparing the scientific notations:

  • For 12,740,876,635: \( 1.2740876635 \times 10^{10} \)
  • For 1,345,763,334: \( 0.1345763334 \times 10^{10} \)
  • For 12,920,370,000: \( 1.292037 \times 10^{10} \)

Now we can see that:

  • \( 1.2740876635 \times 10^{10} \) (from 12,740,876,635)
  • \( 0.1345763334 \times 10^{10} \) (from 1,345,763,334, which is much smaller)
  • \( 1.292037 \times 10^{10} \) (from 12,920,370,000)

To find the greatest, we can simply compare the coefficients of those quantities with the same power of ten:

  • \(1.2740876635\) (from 12,740,876,635)
  • \(0.1345763334\) (from 1,345,763,334)
  • \(1.292037\) (from 12,920,370,000)

Clearly, \(1.292037\) is the largest.

Thus, the number with the greatest value is:

12,920,370,000 (which is represented by A. 1.292037 x 10^{10})