Question

1. an external computer flash drive can hold i gigabyte of data. how many bytes is this? 5. which is longer :a megawatt or a kilowatt? how many larger is it?

Explanation:

Question 4

Step1: Recall the conversion factor

We know that \( 1 \text{ gigabyte (GB)} = 2^{30} \text{ bytes} \) (in binary) or \( 1 \text{ GB} = 10^{9} \text{ bytes} \) (in decimal). Commonly, in computer storage, the binary conversion is often used, but sometimes decimal is also used. Let's use the binary conversion first. \( 2^{10}=1024 \approx 10^{3} \), \( 1 \text{ kilobyte (KB)} = 2^{10} \text{ bytes} \), \( 1 \text{ megabyte (MB)} = 2^{20} \text{ bytes} \), \( 1 \text{ gigabyte (GB)} = 2^{30} \text{ bytes} \).

Calculating \( 2^{30} \):
\( 2^{10}=1024 \), \( 2^{20}=(2^{10})^2 = 1024^2=1048576 \), \( 2^{30}=(2^{10})^3=1024\times1024\times1024 = 1073741824 \)

If we use decimal conversion: \( 1 \text{ GB}=10^{9}=1000000000 \) bytes. But in computer storage, the binary conversion (base - 2) is more accurate for the way data is stored (since computers use binary).

Step2: Conclusion

So, 1 gigabyte is \( 2^{30}=1073741824 \) bytes (binary) or \( 10^{9} = 1000000000 \) bytes (decimal). The most common usage in computer science for storage is the binary conversion, so 1 GB = 1073741824 bytes.

Step1: Recall the metric prefixes

We know that the metric prefix "kilo - " (k) represents \( 10^{3} \) and "mega - " (M) represents \( 10^{6} \). So, \( 1 \text{ kilowatt (kW)}=10^{3}\text{ watts (W)} \) and \( 1 \text{ megawatt (MW)} = 10^{6}\text{ watts (W)} \)

Step2: Compare the two units

To find how many times larger a megawatt is than a kilowatt, we divide the value of 1 megawatt by the value of 1 kilowatt.

\( \frac{1\text{ MW}}{1\text{ kW}}=\frac{10^{6}\text{ W}}{10^{3}\text{ W}}=10^{6 - 3}=10^{3} = 1000 \)

Answer:

1 gigabyte is \( \boldsymbol{1073741824} \) bytes (binary) or \( \boldsymbol{1000000000} \) bytes (decimal). The binary - based answer (used in computer storage) is 1073741824 bytes.

Question 5

First, we need to correct the term: megawatt (MW) and kilowatt (kW) are units of power, not length. So the question should be "Which is larger: a megawatt or a kilowatt? How many times larger is it?".