Compare Very Large and Very Small Numbers Quick Check

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Question
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?(1 point)
Responses

1.292037×1010
1.292037 times 10 superscript 10 baseline

12,920,370,000
12,920,370,000

1.345763334×109
1.345763334 times 10 superscript 9 baseline

1.2740876635×1010
1.2740876635 times 10 superscript 10 baseline
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1 answer

To compare the three numbers using scientific notation, let's convert each into that format:

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

  2. 1,345,763,334 can be expressed as: \[ 1.345763334 \times 10^{9} \]

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

Now, comparing the numbers:

  • 1.2740876635 × 10^10 (which is 12,740,876,635)
  • 1.292037 × 10^10 (which is 12,920,370,000)
  • 1.345763334 × 10^9 (which is 1,345,763,334)

To find the one with the greatest value, we note that the first two numbers are in the \(10^{10}\) range, while the third is in the \(10^{9}\) range, so we can already see that the first two are larger than the third.

Next, compare the coefficients of the first two:

  • 1.292037 from 12,920,370,000 is greater than 1.2740876635 from 12,740,876,635.

Thus, the number with the greatest value is:

12,920,370,000 or 1.292037 × 10^10.

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