How many bytes are in 47 gigabytes?
Express the answer in correct scientific notation.
[tex]47 GB=[?] \times 10^{[?]} B[/tex]
Enter the coefficient in the green box and the exponent in the yellow box.
Answer (1)
Convert gigabytes to bytes: 47 GB = 47 × 1 0 9 bytes .
Express 47 in scientific notation: 47 = 4.7 × 1 0 1 .
Combine the powers of 10: 4.7 × 1 0 1 × 1 0 9 = 4.7 × 1 0 10 .
State the final answer in scientific notation: 4.7 × 1 0 10 .
Explanation
Problem Analysis We need to convert 47 gigabytes (GB) into bytes (B) and express the answer in scientific notation. We know that 1 GB is equal to 1 0 9 bytes.
Conversion to Bytes To convert 47 GB to bytes, we multiply 47 by 1 0 9 :
47 GB = 47 × 1 0 9 bytes
Expressing in Scientific Notation Now, we need to express 47 × 1 0 9 in scientific notation. Scientific notation requires the coefficient to be between 1 and 10. So, we rewrite 47 as 4.7 × 1 0 1 . Therefore, 47 × 1 0 9 = 4.7 × 1 0 1 × 1 0 9 = 4.7 × 1 0 1 + 9 = 4.7 × 1 0 10
Final Result So, 47 GB is equal to 4.7 × 1 0 10 bytes.
Examples
Understanding data sizes is crucial in the digital age. For instance, when purchasing a new hard drive or cloud storage, knowing how many bytes are in a gigabyte helps you estimate how many files, such as photos, videos, or documents, you can store. If a movie file is 4.7 GB, you know it will take 4.7 × 1 0 9 bytes of storage space. This conversion is also important in networking, where bandwidth and data transfer rates are often measured in gigabytes per second, while actual data packets are measured in bytes.
