Question

Memory in computers is measured in kilobytes, gigabytes and terabytes. 1 kilobyte KB is $ {{10}^{3}} $ bytes. How many bytes are in 1 gigabyte and 1 terabyte? \[\]

Answer 1

Hint: We recall the definition of metric prefixes and especially metric prefixes that indicates multiple of the unit by order of 10. We use the fact that the metric prefixes that increase the unit by $ {{10}^{3}} $ times are called kilo, mega, giga, tera, peta, exam etc. We multiply $ {{10}^{3}} $ to 1 kilobyte to find how many bytes a megabyte has, then multiply again by $ {{10}^{3}} $ to megabyte to find how many bytes a gigabyte has, then multiply again by $ {{10}^{3}} $ to gigabyte get how many bytes a terabyte has.

Complete step-by-step answer:
We know that a metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or sub-multiple of the unit in the order of 10. The examples of metric prefixes are centi, milli, kilo etc.
We take the unit of measure for weight “gram” and add the metric prefix kilo to obtain kilogram. 1 kilogram is 1000 or $ {{10}^{3}} $ times the gram. So kilo is a metric prefix that indicates multiple of the unit gram with third order of 10.\[\]
The metric prefixes that increase the unit by $ {{10}^{3}} $ times are called kilo, mega, giga, tera, peta, exam etc. So mega increases kilo by $ {{10}^{3}} $ times and giga increases mega by $ {{10}^{3}} $ times and so on. \[\]
We are given in the question that memory in computers is measured in kilobytes, gigabytes and terabytes. So the unit is byte and we are also given $ 1\text{KB}={{10}^{3}} $ bytes. So we have 1 megabyte (MB) is $ {{10}^{3}} $ times the kilobyte. We use the exponential formula $ {{a}^{m}}\cdot {{a}^{n}}={{a}^{m+n}} $ for $ a=10,m=n=3 $ and have
\[1\text{MB}={{10}^{3}}\times 1\text{KB}={{10}^{3}}\times {{10}^{3}}\text{bytes=1}{{\text{0}}^{3+3}}\text{bytes}=\text{1}{{\text{0}}^{6}}\text{bytes}\]
We also have1 gigabyte (GB) is $ {{10}^{3}} $ times the megabyte. We use the exponential formula $ {{a}^{m}}\cdot {{a}^{n}}={{a}^{m+n}} $ for $ a=10,m=3,n=6 $ and have
 \[1\text{GB}={{10}^{3}}\times 1\text{MB}={{10}^{3}}\times {{10}^{6}}\text{bytes}={{10}^{3+6}}\text{bytes}={{10}^{9}}\text{bytes}\]
We further have1 terabyte (TB) is $ {{10}^{3}} $ times the megabyte. So we have,
\[1\text{TB}={{10}^{3}}\times 1\text{GB}={{10}^{3}}\times {{10}^{9}}\text{bytes}={{10}^{3+9}}\text{bytes}={{10}^{12}}\text{bytes}\]
So 1 gigabyte will have $ {{10}^{6}} $ bytes and 1 terabyte will have $ {{10}^{12}} $ bytes.\[\]

Note: The metric prefixes that decrease the unit by $ {{10}^{3}} $ times are called milli, micro, nano, pico, femto etc and they indicate sub-multiple of the unit by the order of 10. We note that computer memory always has to be in the order of 2 and 1 kilobyte is actually is $ {{2}^{10}}=1024 $ bytes not $ {{10}^{3}}=1000 $ bytes. 1 byte is further divided into 8 bits.