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. 1.292037 x 10 to the tenth power
2. 12,920,370,000
3. 1.345763334 x 10 to the ninth power
4. 1.2740876635 x 10 to the tenth power

Answer 1

To compare the given numbers using scientific notation, we first convert all the numbers 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 have the three numbers in scientific notation:

• \(1.2740876635 \times 10^{10}\)
• \(1.345763334 \times 10^{9}\)
• \(1.292037 \times 10^{10}\)

To compare these, we will focus primarily on the exponents first:

• The first and third numbers have an exponent of \(10^{10}\).
• The second number has an exponent of \(10^{9}\), which is smaller.

Since \(10^{10}\) is much larger than \(10^{9}\), we can already conclude that \(1,274,087,663.5 \times 10^{10}\) and \(12,920,370,000\) are both greater than \(1,345,763,334\).

Next, we compare the two numbers with the same exponent \(10^{10}\):

• Compare \(1.2740876635\) (from \(12,740,876,635\)) and \(1.292037\) (from \(12,920,370,000\)).
• Since \(1.292037\) is greater than \(1.2740876635\), it follows that \(12,920,370,000\) is greater than \(12,740,876,635\).

In conclusion, the number with the greatest value is:

12,920,370,000 (Option 2).