Question

Compare 12,740,876,635; 1,345,763,334; and 12,920,370,000 using scientific notation. Which number has the greatest value?

Answer 1

To compare the numbers 12,740,876,635; 1,345,763,334; and 12,920,370,000 using scientific notation, we will convert each number into scientific notation:

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

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

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

Now we can compare the numbers using their scientific notation:

- \(1.2740876635 \times 10^{10}\)
- \(1.345763334 \times 10^{9}\) (which we will convert to \(0.1345763334 \times 10^{10}\) for easier comparison)
- \(1.292037 \times 10^{10}\)

It's clear that the numbers with base \(10^{10}\) can be directly compared:

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

Among these values, it is clear that:

- **1.2740876635 \times 10^{10}** (12,740,876,635) is greater than 0.1345763334 (1,345,763,334).
- **1.292037 \times 10^{10}** (12,920,370,000) is greater than both of the previous values.

Thus, comparing all of them:
1. **12,740,876,635** is \(1.2740876635 \times 10^{10}\)
2. **12,920,370,000** is \(1.292037 \times 10^{10}\)
3. **1,345,763,334** is \(0.1345763334 \times 10^{10}\)

Therefore, the number with the greatest value is **12,920,370,000**.