David Weber, Talei Kunkel, Rose Harrison and, Fatima Remtulla Solutions for Chapter: Number Discoveries and Developments, Exercise 38: Practice 6

If $c=8.32\times {10}^4 \text{and} e=5.32\times {10}^5$

Evaluate the following. Represent your answers in scientific notation.

$e^2-c^2$

If $d=7.6\times {10}^{-3}$

Evaluate the following. Represent your answers in scientific notation.

$\frac{1}{d}$

If $a=1.3\times {10}^6, b=4.9\times {10}^{-2}, d=7.6\times {10}^{-3}$

Evaluate the following. Represent your answers in scientific notation.

$2abd$

If $c=8.32\times {10}^4$ and $e=5.32\times {10}^5$

Evaluate the following. Represent your answers in scientific notation.

${\left(ce\right)}^2$

In the Tower of Hanoi puzzle, it would take the priests $2^{64}-1$ moves to transfer the $64$ disks to a different post, maintaining their order. Using a calculator, write down the number of moves using scientific notation.

Calculate the number of seconds in one year. Represent your answer in scientific notation.

In the Tower of Hanoi puzzle, it would take the priests $2^{64}-1$ moves to transfer the $64$ disks to a different post, maintaining their order. Legend has it that the world will end when the monks move the final disk to the new post. Suppose each move takes $1$ second. Find the number of years it will take the monks to complete the puzzle if there are $64$ disks. Show your working using scientific notation.

Satellite technology was developed in the year $1960$ as a means of communication, but also as a way to spy on other people. Satellites are now used for so much more, including weather data, broadcasting television signals, and even helping you navigate to a new destination. A satellite travels around the Earth in a circular orbit $500 KM$ above the Earth's surface. The radius of the Earth is $6375$ kilometres. Calculate the maximum distance travelled by the satellite in one orbit of the earth in kilometres. Use the value of $\mathrm{\pi }=3.14$, or the pi button on your calculator. Write your answer in standard form with the coefficient rounded to two decimal places.