Question

Use scientific notation to compare these numbers: 12,740,876,635; 1,345,763,334; and 12,920,370,000. Which number has the greatest value? 1) 12,740,876,635 2) 1,345,763,334 3) 12,920,370,000

Answer 1

To compare the given numbers using scientific notation, we first convert each number into scientific notation.

1. \( 12,740,876,635 \)
- This can be written as \( 1.2740876635 \times 10^{10} \).

2. \( 1,345,763,334 \)
- This can be written as \( 1.345763334 \times 10^{9} \).

3. \( 12,920,370,000 \)
- This can be written as \( 1.292037 \times 10^{10} \).

Now, we can compare the numbers in scientific notation:

- \( 1.2740876635 \times 10^{10} \) (first number)
- \( 1.345763334 \times 10^{9} \) (second number, which is effectively much smaller since it has a lower exponent)
- \( 1.292037 \times 10^{10} \) (third number)

Since both the first and third numbers have an exponent of \( 10^{10} \), we can directly compare their coefficients:

- First number: \( 1.2740876635 \)
- Third number: \( 1.292037 \)

Now, comparing \( 1.2740876635 \) and \( 1.292037 \):

- Since \( 1.292037 > 1.2740876635 \), this means that \( 12,920,370,000 > 12,740,876,635 \).

Next, we know that \( 1.345763334 \times 10^{9} \) is significantly smaller than either of the other two because it has a lower exponent.

Thus, the order of the numbers from greatest to least is:

1. \( 12,920,370,000 \)
2. \( 12,740,876,635 \)
3. \( 1,345,763,334 \)

The greatest value is **3) 12,920,370,000**.