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Chapter 4: Problem 92

A computer can perform \(466,000,000\) calculations per second. How many calculations can it perform per minute? Per hour?

Short Answer

Expert verified
27,960,000,000 calculations per minute. 1,677,600,000,000 calculations per hour.

Step by step solution

01

- Calculations per minute

First, find out how many seconds are in a minute. There are 60 seconds in a minute. Multiply the number of calculations per second by the number of seconds in a minute: \(466,000,000 \times 60\).
02

- Perform the multiplication for minutes

Multiply 466,000,000 by 60 to find the total number of calculations per minute: \[ 466,000,000 \times 60 = 27,960,000,000 \]
03

- Calculations per hour

Next, find out how many minutes are in an hour. There are 60 minutes in an hour. Multiply the number of calculations per minute by the number of minutes in an hour: \(27,960,000,000 \times 60\).
04

- Perform the multiplication for hours

Multiply 27,960,000,000 by 60 to find the total number of calculations per hour: \[ 27,960,000,000 \times 60 = 1,677,600,000,000 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

calculations per second
Understanding calculations per second is essential for analyzing computer performance. In this exercise, we know that the computer can perform 466,000,000 calculations per second. This means, every single second, the computer completes 466 million calculations. To comprehend this better, think of it as a continual and incredibly rapid sequence of mathematical operations happening every moment.
calculations per minute
To convert calculations per second to calculations per minute, we need to understand that there are 60 seconds in one minute. This transformation involves multiplication:

Take the original number of calculations per second and multiply it by 60:
\[ 466,000,000 \times 60 = 27,960,000,000 \]

As a result, the computer can perform 27,960,000,000 calculations in a single minute. This large number shows how exponentially the calculations increase when moving from a single second to a whole minute.
calculations per hour
After converting to calculations per minute, converting to calculations per hour is the next step. There are 60 minutes in an hour. So, we multiply the number of calculations per minute by 60:

\[ 27,960,000,000 \times 60 = 1,677,600,000,000 \]

This calculation tells us that the computer can perform 1,677,600,000,000 calculations in one hour. Notice how the number continues to grow massively when we scale from minutes to hours. This growth highlights the powerful capabilities of modern computing systems over time.

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Most popular questions from this chapter

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ can be used to perform some multiplication problems. Here are two examples. $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1 \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 201 \times 199 $$

The special product $$ (x+y)(x-y)=x^{2}-y^{2} $$ can be used to perform some multiplication problems. Here are two examples. $$ \begin{aligned} 51 \times 49 &=(50+1)(50-1) \\ &=50^{2}-1^{2} \\ &=2500-1 \\ &=2499 \end{aligned} \quad | \begin{aligned} 102 \times 98 &=(100+2)(100-2) \\ &=100^{2}-2^{2} \\ &=10,000-4 \\ &=9996 \end{aligned} $$ Once these patterns are recognized, multiplications of this type can be done mentally. Use this method to calculate each product mentally. $$ 103 \times 97 $$

Simplify by writing each expression wth positive exponents. Assume that all variables represent nonzero real numbers. $$ \frac{\left(4 a^{2} b^{3}\right)^{-2}\left(2 a b^{-1}\right)^{3}}{\left(a^{3} b\right)^{-4}} $$

In September of 2009 , the population of the United States was about 307.5 million. To the nearest dollar, calculate how much each person in the United States would have had to contribute in order to make one lucky person a trillionaire (that is, to give that person 1,000,000,000,000 dollars) . (Source: U.S. Census Bureau.)

Find each product. In Exercises \(81-84,89,\) and \(90,\) apply the meaning of exponents. $$ 7(4 m-3)(2 m+1) $$
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