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Mathematics

Grade 8

Rational numbers, circles and triangles

Module 15

Differentiating between rational and irrational numbers

Activity 1

Differentiating between rational and irrational numbers

[lo 1.2.7]

1. Can you remember what each of the following represents?

N = { ........................................................................... }

N 0 = { ........................................................................... }

Z = { ........................................................................... }

R = { ........................................................................... }

2. Provide the definition for:

a rational number:

an irrational number:

3. How would you represent each of the following?

3.1 Rational number......................... 3.2 Irrational number .........................

4. Complete the following table by marking relevant numbers with an X:

5. Select the required numbers from the list:

2 3 size 12{ { { size 8{ - 2} } over { size 8{3} } } } {} ; 1 + 4 size 12{ sqrt {4} } {} ; 9 + 4 size 12{ sqrt {9+4} } {} ; -4 ; 12 1 5 size 12{"12" { { size 8{1} } over { size 8{5} } } } {} ; 1 + 2 2 size 12{ { {1+ sqrt {2} } over { sqrt {2} } } } {}

5.1 Integers:

5.2 Rational numbers:

5.3 Irrational numbers:

6. Explain what you know about an equivalent fraction.

7. Provide two equivalent fractions for the following: 2 7 size 12{ { { size 8{2} } over { size 8{7} } } } {} = ............... = ...............

8. Provide the terms used to identify each of the following (e.g. proper fraction):

8.1 2 7 size 12{ { { size 8{2} } over { size 8{7} } } } {}

8.2 7 2 size 12{ { { size 8{7} } over { size 8{2} } } } {}

8.3 6 2 7 size 12{6 { { size 8{2} } over { size 8{7} } } } {}

8.4 0,67

8.5 0, 6 ˙ 7 ˙ size 12{0, { dot {6}} { dot {7}}} {}

8.6 23 %

Any of the above can be reduced to any of the others.

Activity 2:

Reduction of fractions to decimal numbers / recurring decimal numbers and vice versa

[lo 1.2.2, 1.2.6, 1.3, 1.6.1, 1.9.1]

  1. Use your pocket calculator to reduce the following fraction to a decimal number:

2. Explain how you would reduce this to a decimal number without the use of your pocket calculator. There are two methods:

Method 1: .................................................. (reduce denominator to 10 / 100 / 1 000)

Method 2: .................................................. (do division)

(Let your educator assist you.)

  • Do you see that the answer is the same – if the denominator cannot be reduced to multiples of 10 you have to apply the second method.

3. Now reduce each of the following to decimal numbers (round off, if necessary, to two digits):

3.1 5 8 size 12{ { { size 8{5} } over { size 8{8} } } } {} ..................................................

3.2 13 4 size 12{ { { size 8{"13"} } over { size 8{4} } } } {} ..................................................

3.3 5 3 4 size 12{5 { { size 8{3} } over { size 8{4} } } } {} ..................................................

3.4 3 7 8 size 12{3 { { size 8{7} } over { size 8{8} } } } {} ..................................................

3.5 6 7 size 12{ { { size 8{6} } over { size 8{7} } } } {} ..................................................

3.6 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {} ..................................................

4. Write the following decimal numbers as fractions or mixed numbers:(N.B.: All fractions have to be presented in their simplest form.)

4.1 6,008 ..................................................

4.2 4,65 ..................................................

4.3 0,375 ..................................................

4.4 7,075 ..................................................

4.5 13,65 ..................................................

4.6 0,125 ..................................................

5. How do we reduce fractions to recurring decimal numbers?

E.g. 5 11 size 12{ { { size 8{5} } over { size 8{"11"} } } } {}

Step 1: place a comma after the 5, i.e. 5, 0000

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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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