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Difficulty: MediumExponents, Roots, and Scientific Notation

A certain cloud database stores a total of 3.6×10153.6 \times 10^{15} bytes of data. If this data is distributed equally among 8.0×1048.0 \times 10^4 servers, how many megabytes of data are stored on each server? (Note: 1 megabyte=106 bytes1\text{ megabyte} = 10^6\text{ bytes})

  1. A
    4.5×1034.5 \times 10^3
  2. 4.5×1044.5 \times 10^4Answer
  3. C
    4.5×1054.5 \times 10^5
  4. D
    4.5×10104.5 \times 10^{10}
  5. E
    2.88×10202.88 \times 10^{20}

Answer

4.5×1044.5 \times 10^4 megabytes
The correct answer is the value that correctly represents the data per server in megabytes. Dividing the total data of 3.6×10153.6 \times 10^{15} bytes by the 8.0×1048.0 \times 10^4 servers gives 4.5×10104.5 \times 10^{10} bytes per server. Converting this to megabytes by dividing by 10610^6 gives 4.5×1044.5 \times 10^4 megabytes.

Step-by-Step Solution

1
Calculate the bytes of data stored on each server by dividing the total data by the number of servers.
0.45×1011 bytes=4.5×1010 bytes0.45 \times 10^{11}\text{ bytes} = 4.5 \times 10^{10}\text{ bytes}
Dividing the total bytes (3.6×10153.6 \times 10^{15}) by the total number of servers (8.0×1048.0 \times 10^4) gives the share of data per server. Mathematically, 3.68.0=0.45\frac{3.6}{8.0} = 0.45, and 1015104=1015−4=1011\frac{10^{15}}{10^4} = 10^{15-4} = 10^{11}.
2
Convert the result from bytes to megabytes using the conversion factor 1 megabyte=106 bytes1\text{ megabyte} = 10^6\text{ bytes}.
4.5×104 megabytes4.5 \times 10^4\text{ megabytes}
To convert bytes to megabytes, divide the number of bytes by 10610^6. Since 4.5×1010106=4.5×1010−6=4.5×104\frac{4.5 \times 10^{10}}{10^6} = 4.5 \times 10^{10-6} = 4.5 \times 10^4.

Key Concept

Division of numbers in scientific notation and unit conversion.
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Topics

Exponents, Roots, and Scientific Notation

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