Question

Write the number in scientific notation. You must show ALL work to earn full credit.

5,080,000,000,000

Answer 1

To convert the number 5,080,000,000,000 into scientific notation, follow these steps:

1. **Identify the significant figures**: For this number, the significant figures are the digits that contribute to its precision. In this case, the significant figures are 5.08 (the digits '5', '0', and '8').

2. **Determine the decimal point placement**: We need to position the decimal point after the first significant digit. This means placing the decimal after the '5':

\[
5.08
\]

3. **Count the number of places the decimal point has moved**: Initially, the decimal point is at the end of the number (to the right of '00000'):

- Original number: 5,080,000,000,000
- New position: 5.08

The decimal has moved 12 places to the left.

4. **Express the movement in the exponent**: The number of places the decimal has moved to the left gives us the exponent in the scientific notation. Since we moved the decimal 12 places, the exponent will be +12.

5. **Combine the components into scientific notation format**: The scientific notation format is written as:

\[
a \times 10^n
\]

where \(a\) is the number we calculated (5.08) and \(n\) is the exponent (12).

Putting it all together:

\[
5,080,000,000,000 = 5.08 \times 10^{12}
\]

Therefore, the scientific notation of 5,080,000,000,000 is:

\[
\boxed{5.08 \times 10^{12}}
\]