Question

an online data storage facility has 1.326×10 to the power of 13 bites of storage available. It has 2.6×10 to the power of four customers how many bites of storage can each customer use? Write your answer in scientific notation expressed to the exact decimal place.

Answer 1

To find out how many bites of storage each customer can use, we need to divide the total storage available by the number of customers.

Given:
- Total storage = \( 1.326 \times 10^{13} \) bites
- Number of customers = \( 2.6 \times 10^{4} \)

Now, we perform the division:

\[
\frac{1.326 \times 10^{13}}{2.6 \times 10^{4}}
\]

We can break this down into two parts: the coefficients and the powers of ten.

1. **Divide the coefficients:**

\[
\frac{1.326}{2.6} = 0.5107692307692308
\]

2. **Divide the powers of ten:**

\[
\frac{10^{13}}{10^{4}} = 10^{13 - 4} = 10^{9}
\]

Now combine these two results:

\[
0.5107692307692308 \times 10^{9}
\]

To express this in proper scientific notation, we need the coefficient to be between 1 and 10. Thus, we convert \( 0.5107692307692308 \) to \( 5.107692307692308 \) by moving the decimal point one place to the right and decreasing the power of ten by one.

So the result becomes:

\[
5.107692307692308 \times 10^{8}
\]

In scientific notation, it is typically rounded to a certain number of decimal places for clarity. Given the original numbers had three significant figures, we can round to three significant figures:

Thus, the final answer, rounded to three significant figures and in scientific notation, is:

\[
\boxed{5.11 \times 10^{8}}
\]

This means each customer can use approximately \( 5.11 \times 10^{8} \) bites of storage.