Question

A computer can do 1.7 gigacalculations per second. How many calculations can it do in a microsecond?

Answer 1

Hi! You want to convert the units. Do you know about using a conversion factor?

\(1\ second = 1,000,000\ microseconds\quad\\\implies\quad \dfrac{1\ second}{1,000,000\ microseconds}=1\)
(By dividing both sides by 1,000,000 microseconds)

Since it is equal to \(1\), you can multiply it with anything without actually changing the value. But you can use it to cancel your units of seconds! You know?

Answer 2

First of all @holden7008 : A Warm Welcome to 'Open Study'. Please Read CoC (compulsory to read by all "Open Study" users) : http://openstudy.com/code-of-conduct

Answer 3

1700

Answer 4

I think that looks right! :)

Answer 5

1.7 gigacalculations is \(1.7\times 10^9\ \dfrac{calculations}{second}\), and we can use the conversion factor of \(1=\dfrac{1\ second}{10^6 microsecond}\)

So \(\color{blue}{1.7\times 10^9\ \dfrac{calculations}{second}\times 1}\\\quad =1.7\times 10^9\ \dfrac{calculations}{second}\times\dfrac{1\ second}{10^6 microsecond}\\\quad=1.7\times 10^9\ \dfrac{calculations}{\cancel{second}}\times\dfrac{1\ \cancel{second}}{10^6 microsecond}\\\quad=1.7\times\dfrac{10^9}{10^6}\dfrac{calculations}{microsecond}\\\quad\color{blue}{=1.7\times10^3\dfrac{calculations}{microsecond}}\)

In case you wanted to see, \[\dfrac{10^9}{10^6}=\dfrac{\cancel{10}\times\cancel{10}\times\cancel{10}\times\cancel{10}\times\cancel{10}\times\cancel{10}\times10\times10\times10}{\cancel{10}\times\cancel{10}\times\cancel{10}\times\cancel{10}\times\cancel{10}\times\cancel{10}}=10^3\]