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?

Question

• 1.2740876635 × 1010
• 12,920,370,000
O 1.292037 × 1010
• 1.345763334 × 10°

Answer 1

To compare the numbers using scientific notation, we first convert each of the provided numbers into scientific notation.

1. 12,740,876,635:

   • This can be expressed as \(1.2740876635 \times 10^{10}\).

2. 1,345,763,334:

   • This can be expressed as \(1.345763334 \times 10^{9}\).

3. 12,920,370,000:

   • This can be expressed as \(1.292037 \times 10^{10}\).

Now, we'll compare the numbers represented in scientific notation:

• \(1.2740876635 \times 10^{10}\) corresponds to 12,740,876,635.
• \(1.345763334 \times 10^{9}\) corresponds to 1,345,763,334.
• \(1.292037 \times 10^{10}\) corresponds to 12,920,370,000.

To compare these, we note that \(10^{10}\) is greater than \(10^{9}\). Hence, any number with a base of \(10^{10}\) is greater than a number with a base of \(10^{9}\).

Now we compare the coefficients of the numbers with the same exponent:

• For \(1.2740876635 \times 10^{10}\) and \(1.292037 \times 10^{10}\):
  • \(1.2740876635 < 1.292037\)

Thus, \(1.292037 \times 10^{10}\) (which is 12,920,370,000) is greater than \(1.2740876635 \times 10^{10}\) (which is 12,740,876,635).

In conclusion, the number with the greatest value among the three is:

12,920,370,000 which is represented in scientific notation as \(1.292037 \times 10^{10}\).