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?

1.2740876635 x 10^(10)

1.292037 x 10^(10)

12,920,370,000

1.345763334 x 10^(9)

Answer 1

To compare the numbers using scientific notation, we first convert all the numbers into scientific notation:

1. \( 12,740,876,635 = 1.2740876635 \times 10^{10} \)

2. \( 1,345,763,334 = 1.345763334 \times 10^{9} \) (Note: Since this is a lesser exponent, we can rewrite this as \( 0.1345763334 \times 10^{10} \) for easier comparison)

3. \( 12,920,370,000 = 1.292037 \times 10^{10} \)

Now we can compare them:

- \( 1.2740876635 \times 10^{10} \)
- \( 0.1345763334 \times 10^{10} \) (This is the same as \( 1.345763334 \times 10^{9} \))
- \( 1.292037 \times 10^{10} \)

Since all the terms are expressed with \( 10^{10} \) for \( 1.2740876635 \) and \( 1.292037 \), and \( 10^{9} \) for \( 1.345763334 \), we can see that the largest exponent is \( 10^{10} \) and we can directly compare the coefficients.

Comparing the coefficients:

- \( 1.2740876635 \)
- \( 0.1345763334 \)
- \( 1.292037 \)

The greatest coefficient is \( 1.292037 \).

Therefore, the number with the greatest value is:

**12,920,370,000 (which is also written as \( 1.292037 \times 10^{10} \)).**