Lesson 6: Rational Exponents

Module 2: Roots and Powers

 

Connect

Lesson Assessment

 

Complete the lesson quiz posted under under the Assess tab or by using the Quizzes link under the Activities block. Also, ensure your work in your binder (course folder) is complete. 

Project Connection **NOT ASSIGNED**

 

In the last Project Connection you learned about binary numbers and how to convert between decimal (base 10) numbers and binary numbers. You also learned that computers use binary numbers to store data, communicate information, and run programs. In this lesson you will see how binary numbers can be used to encode characters on a computer keyboard, not just numbers.

When computers were in the beginning stages of development, there was no standard way of using binary numbers to represent letters. One computer might be programmed to recognize 10010101 as the letter K and another might recognize 01001011 as the same letter. Eventually, computer manufacturers agreed to use a standard code so all computers would assign the same letter for a given binary number. This code is called the American Standard Code for Information Interchange or ASCII.

The ASCII code assigns eight-digit binary numbers to letters and punctuation marks. Each eight-digit or eight-bit number can be stored as a byte. The table shows how some of those numbers are assigned.

You can use the ASCII table and your knowledge of decimal to binary conversions to encode secret messages. The following section outlines the steps for encoding the message “Hello Eva.”

Step 1: Create a chart like the following:

Letter	Decimal Number	Binary

 Step 2: Write the letters of the secret message in the first column. Note that the chart provides different codes for upper case and lower case letters.

Letter	Decimal Number	Binary
H
e
l
l
o
E
v
a

 Step 3: Use the ASCII table to locate the decimal or binary numbers.

Letter	Decimal Number	Binary
H	72	1001000
e	101	1100101
l	108	1101100
l	108	1101100
o	111	1101111
E	69	1000101
v	118	1110110
a	97	1100001

 Step 4: Express your code in the format of your choice:

72.101.108.108.111.69.118.97

OR

1001000-1100101-1101100-1101100-1101111-1000101-1110110-1100001

At this time, go to the Unit 2 Project and complete the Module 2: Lesson 6 portion of the project.

 

Going Beyond

 

If you have ever worked with Internet that was delivered using a satellite, you may have experienced a slight hesitation in the transmission of information. Why is that?

One of the disadvantages of the geosynchronous orbit (an orbit that keeps the satellite at the same place with regards to Earth) is the signal delay.

When a satellite is 22 240 mi away from the surface of Earth and the speed of light is around 186 000 mi per second, there is a delay of around one-quarter of a second from the time a signal is sent up to the satellite to the time the signal is received by an antenna back here on Earth.

Here is the formula that has been developed by scientists:

t = satellite’s time duration of orbit

d = distance from the centre of Earth

k = a constant

Using this formula, you could find out what the time lag would be with satellites in other orbits. What if, for example, there is a satellite that orbits in 12 hours? Or what about a satellite that orbits in 18 hours? Would the light lag be half as much or something different?

If you know the lag for a 24-hour orbit, you can find the value for k. Then you can use it and the formula to find the lag for other orbits.

Duration of Orbit	Light Lag
24 hours	0.24 seconds
18 hours
12 hours

Mathematics 10C Learn EveryWare © 2010 Alberta Education