An online data storage facility has 1.326×1013

Question

1.326
×
10
13
bytes of storage available. It has 2.6×104
2.6
×
10
4
customers. How many bytes of storage can each customer use? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)

Answer 1

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

Given:

• Total storage = \( 1.326 \times 10^{13} \) bytes
• Number of customers = \( 2.6 \times 10^{4} \)

We will perform the division:

\[ \text{Storage per customer} = \frac{1.326 \times 10^{13}}{2.6 \times 10^{4}} \]

To divide the numbers in scientific notation, we divide the coefficients and subtract the exponents:

1. Divide the coefficients: \[ \frac{1.326}{2.6} \approx 0.51076923077 \]

2. Subtract the exponents: \[ 10^{13} \div 10^{4} = 10^{13 - 4} = 10^{9} \]

Now, combining the results:

\[ \text{Storage per customer} = 0.51076923077 \times 10^{9} \]

Next, we need to express this in proper scientific notation. To convert a number into scientific notation, we want the coefficient to be between 1 and 10.

So, we can change \( 0.51076923077 \) to \( 5.1076923077 \times 10^{-1} \):

Now, we add the exponents:

\[ \text{Storage per customer} = (5.1076923077 \times 10^{-1}) \times 10^{9} = 5.1076923077 \times 10^{8} \]

Finally, rounding to the appropriate decimal places: \[ \text{Storage per customer} \approx 5.11 \times 10^{8} \]

Thus, each customer can use approximately \( \boxed{5.11 \times 10^{8}} \) bytes of storage.