Mary’s music files take up 8 gig of space on her hard drive. About how many bytes is that?
[A] 8,000,000,000
[B] 1,000,000,000
[C] 8,000,000
[D] 1,000,000
[E] 8,000,000,000,000
The correct answer and explanation is:
The correct answer is [A] 8,000,000,000.
To explain this, it’s important to understand the relationship between gigabytes (GB) and bytes. The standard conversion from gigabytes to bytes is based on powers of 10 for the decimal system (not the binary system, which is sometimes used in computing).
1 gigabyte (GB) is equal to 1,000,000,000 bytes (or 10^9 bytes). So, if Mary’s music files take up 8 GB of space, we can multiply 8 by the number of bytes in 1 GB: 8 GB×1,000,000,000 bytes/GB=8,000,000,000 bytes.8 \, \text{GB} \times 1,000,000,000 \, \text{bytes/GB} = 8,000,000,000 \, \text{bytes}.
This means that the 8 gigabytes of space are equivalent to 8,000,000,000 bytes, which is answer choice [A].
The other options are incorrect:
- [B] 1,000,000,000 bytes corresponds to 1 GB, not 8 GB.
- [C] 8,000,000 bytes would be 8 megabytes (MB), not gigabytes.
- [D] 1,000,000 bytes is 1 megabyte (MB), much smaller than the 8 GB.
- [E] 8,000,000,000,000 bytes is 8 terabytes (TB), which is far larger than the 8 GB.
Understanding these conversions is essential when dealing with file sizes in computing, and the correct conversion for gigabytes to bytes is based on multiplying by 1 billion (10^9).