Question

A supercomputer can do \(136.8\) teracalculations per second. How many calculations can it do in a microsecond?

Short answer

The supercomputer does 136,800,000 calculations in a microsecond.

Step-by-step solution

Convert units

A microsecond is one millionth of a second or \(10^{-6}\) seconds. First, we need to convert teracalculations to regular calculations. We know that 1 teracalculation equals \(10^{12}\) calculations.

Calculate calculations per microsecond

Since the supercomputer can perform \(136.8 \times 10^{12}\) calculations per second, we need to calculate how many calculations it does in one microsecond. This is done by multiplying the number of calculations per second by \(10^{-6}\):\[136.8 \times 10^{12} \times 10^{-6} = 136.8 \times 10^{6}\]

Simplify the Final Answer

Now, simplify the expression. Note that \(136.8 \times 10^{6}\) is equal to \(136,800,000\). Thus, the supercomputer can perform \(136,800,000\) calculations in a microsecond.

Key concepts

Calculations per Second

When we talk about performance, especially for supercomputers, one common metric is "calculations per second." This measures how many operations a computer can complete in one second. It's like a speedometer that tells us the speed of a car but instead of miles per hour, it's calculations per second.

Why is this important? Knowing how many operations a computer can do in a second helps us understand its processing power. If a computer can do more calculations per second, it can solve bigger problems faster.

• Performance standards for computers often use concepts like flops (floating-point operations per second) or, as in our exercise, teracalculations per second.
• Understanding calculations per second helps in fields like data analysis, scientific research, and more.

Teracalculations

The term "teracalculations" comes from combining "tera," which means trillion, and "calculations." So, one teracalculation is equivalent to one trillion (or \(10^{12}\)) calculations. In the realm of supercomputing, we often deal with such large numbers because we are talking about processing vast amounts of data.

Imagine a puzzle with a trillion pieces. A computer capable of teracalculations can fit all those pieces together in just one second. That's why supercomputers, which can handle this level of processing, are used for tasks that need immense computational power.

• Supercomputers are used in complex simulations, weather forecasting, quantum mechanics, etc.
• Being able to do teracalculations means handling large datasets and performing intense calculations quickly.

Microsecond

A microsecond is a very short unit of time. In terms of units, a microsecond is one-millionth of a second. It's written as \(10^{-6} \) seconds. When comparing time units, microseconds are smaller than milliseconds, which are already pretty small themselves.

In our context, the supercomputer's speed of 136.8 teracalculations per second means finding out how many calculations fit into a brief moment, like a microsecond. Converting between these time units is crucial when dealing with operations happening incredibly fast.

• Microseconds help in measuring extremely fast processes in computing and electronics.
• In a day-to-day computer task, processes happen in microseconds without us noticing it.

Scientific Notation

Scientific notation is a way of writing very large or very small numbers in an understandable format. Instead of writing out all the zeroes, scientific notation uses powers of ten. For instance, \(10^{6}\) means moving 6 decimal places. It's especially handy in fields like science and engineering.

In the exercise solution, we converted large numbers into scientific notation to simplify calculations. For example, \(136.8 \times 10^{12}\) simplifies that enormous number, making it manageable for calculations. By converting numbers into scientific notation, we can perform multiplication and division without dealing with cumbersome zeros.

• Scientific notation is essential when working with calculations involving very large or very small numbers.
• This system helps scientists and engineers avoid errors in their work.