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JSS2: MATHEMATICS - 1ST TERM

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  1. Properties of Whole Numbers I | Week 1
    4 Topics
    |
    1 Quiz
  2. Properties of Whole Numbers II | Week 2
    4 Topics
    |
    1 Quiz
  3. Properties of Whole Numbers III | Week 3
    5 Topics
    |
    1 Quiz
  4. Indices | Week 4
    2 Topics
    |
    1 Quiz
  5. Laws of Indices | Week 5
    5 Topics
    |
    1 Quiz
  6. Whole Numbers & Decimal Numbers | Week 6
    4 Topics
    |
    1 Quiz
  7. Standard Form | Week 7
    3 Topics
    |
    1 Quiz
  8. Significant Figures (S.F) | Week 8
    4 Topics
    |
    1 Quiz
  9. Fractions, Ratios, Proportions & Percentages I | Week 9
    6 Topics
    |
    1 Quiz
  10. Fractions, Ratios, Proportions & Percentages II | Week 10
    4 Topics
    |
    1 Quiz
  11. Fractions, Ratios, Proportions & Percentages III | Week 11
    3 Topics
    |
    1 Quiz
  12. Approximation & Estimation | Week 12
    1 Topic
    |
    1 Quiz



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Lesson 4, Topic 2
In Progress

Fractional Base Number & Decimal Base Number

Lesson Progress
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Whenever there is an index with a fractional base, or decimal base number, multiply the base number the same number of times as the index
e.g

\(\left ( \frac{2}{5} \right) ^5 \\ = \left ( \frac{2}{5} \: \times \: \frac{2}{5}\: \times \: \frac{2}{5}\: \times \: \frac{2}{5}\: \times \: \frac{2}{5} \right) \)

(0.2) =  0.2 x 0.2 x 0.2 x 0.2

Example 1

Change the following to ordinary form expanded

a. \(\left ( \frac{1}{4} \right) ^6 \)

b. \(\left ( \frac{1}{2} \right) ^3 \)

c. \(\left ( \frac{3}{5} \right) ^2 \)

d. (1.5)3

e. (2.7)4

Solution

a. \(\left ( \frac{1}{4} \right) ^6 \\ = \frac{1}{4} \: \times \: \frac{1}{4}\: \times \: \frac{1}{4}\: \times \: \frac{1}{4}\\ \: \times \: \frac{1}{4}\: \times \: \frac{1}{4}\)

b. \(\left ( \frac{1}{2} \right) ^3 \\ = \left ( \frac{1}{2} \: \times \: \frac{1}{2}\: \times \: \frac{1}{2} \right) \)

c. \(\left ( \frac{3}{5} \right) ^2 \\ = \left ( \frac{3}{5} \: \times \: \frac{3}{5} \right) \)

d. (1.5)3 = \( \scriptsize 1.5 \: \times \: 1.5\: \times \: 1.5\)

e. (2.7)4 =  \( \scriptsize 2.7 \: \times \: 2.7\: \times \: 2.7 \: \times \: 2.7\)

Example 2

Evaluate the following

a. \( \left (\frac{1}{4} \right) ^2 \)

b. \(\left ( \frac{1}{2} \right) ^4 \)

c. \( \left (\frac{3}{5} \right) ^4 \)

d. \(\scriptsize (1.5)^2\)

e. \(\scriptsize (0.2)^3 \)

Solution

a. \( \left (\frac{1}{4} \right) ^2 \\ = \frac{1}{4} \: \times \: \frac{1}{4}\\ = \frac{1 \: \times \: 1}{4 \: \times \: 4} \\ = \frac{1}{16} \)

b. \(\left ( \frac{1}{2} \right) ^4 \\ = \frac{1}{2} \: \times \: \frac{1}{2} \: \times \: \frac{1}{2}\: \times \: \frac{1}{2} \\= \frac{1 \: \times \: 1\: \times \: 1\: \times \: 1}{2 \: \times \: 2\: \times \: 2\: \times \: 2}\\ = \frac{1}{16} \)

c. \( \left (\frac{3}{5} \right) ^4 \\= \frac{3}{5} \: \times \: \frac{3}{5} \: \times \: \frac{3}{5}\: \times \: \frac{3}{5}\\= \frac{3 \: \times \: 3 \: \times \: 3\: \times \: 3}{5 \: \times \: 5\: \times \: 5\: \times \: 5} \\ = \frac{81}{625} \)

d. \(\scriptsize (1.5)^2\\ \scriptsize = 1.5 \: \times \: 1.5 \\ \frac{15}{10} \: \times \: \frac{15}{10}\\ = \frac{225}{100}\\ \scriptsize = 2.25\)

e. \(\scriptsize (0.2)^3 \\ \scriptsize = 0.2 \: \times \: 0.2 \: \times \: 0.2 \\ = \frac{2}{10} \: \times \: \frac{2}{10} \: \times \: \frac{2}{10}\\ = \frac{8}{1000}\\ \scriptsize = 0.008\)

Evaluation

1. Write the following in index forms.

a. 4 x 4 x 4 x 4
b. 2 x 2 x 2 x 2
c. 9 x 9 x 9 x 9
d. 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11
e. 13 x 13 x 13 x 13 x 13

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2. Express the following in index form

a. 64
b. 343
c. 243
d. 27 x 8
e. 49 x 343

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3. Find the value of the following 

a. 4 x 4 x 4
b. 2 x 2 x 2 x 2 x 2
c. 6 x 6 x 6 x 6 x 6
d. 10 x 10 x 10 x 10 x 10 x 10

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4. Change the following to ordinary expanded form.

a. \( \left(\frac{2}{5} \right)^5 \)

b. \( \left(\frac{1}{6} \right)^3 \)

c. \( \left(\frac{2}{7} \right)^7 \)

d. \( \left(\scriptsize 0.25 \right)^4 \)

e. \( \left(\scriptsize 1.2 \right)^2 \)

f. \( \left(\scriptsize 1.3 \right)^3 \)

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5. Evaluate the following:

a. \( \left(\frac{2}{5} \right)^2 \)

b. \( \left(\frac{1}{6} \right)^3 \)

c. \( \left(\frac{2}{7} \right)^3 \)

d. \( \left(\scriptsize 0.25 \right)^4 \)

e. \( \left(\scriptsize 1.2 \right)^5 \)

f. \( \left(\scriptsize 1.3 \right)^3 \)

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Evaluation Question 1

Index form

a. \( \scriptsize 4^4 \)

b.\( \scriptsize 2^4 \)

c. \( \scriptsize 9^4 \)

d. \( \scriptsize 11^9 \)

e. \( \scriptsize 13^5 \)

Evaluation Question 2

Index form

a. \( \scriptsize 8^2 \)

b. \( \scriptsize 7^3 \)

c. \( \scriptsize 3^5 \)

d. \( \scriptsize 3^3 \: \times \: 2^3 \)

e. \( \scriptsize 7^2 \: \times \: 7^3 \)

Evaluation Question 3

a. \(\scriptsize 4^3 \)

b. \( \scriptsize 2^5 \)

c. \( \scriptsize 6^5 \)

d. \( \scriptsize 10^6  \)

Evaluation Question 4

To ordinary expanded form.

a. \(\frac{2}{5} \: \times \:  \frac{2}{5}\: \times \:  \frac{2}{5}\: \times \:  \frac{2}{5}\: \times \:  \frac{2}{5} \)

b. \(\frac{1}{6} \: \times \:  \frac{1}{6}\: \times \:  \frac{1}{6} \)

c. \(\frac{2}{7} \: \times \:  \frac{2}{7}\: \times \:  \frac{2}{7} \: \times \:  \frac{2}{7}\\ \: \times \:  \frac{2}{7}\: \times \:  \frac{2}{7}\: \times \:  \frac{2}{7}\)

d. 0.25 x 0.25 x 0.25 x 0.25

e. 1.2 x 1.2

f.   1.3 x 1.3 x 1.3

Evaluation Question 5

a. \(\frac{4}{25} \)

b. \(\frac{1}{216} \)

c. \(\frac{8}{343} \)

d. \(\frac{1}{256} \)

e. \(\frac{248832}{100000} \\  \scriptsize = 2.488 \)

f. \(\frac{2197}{1000} \scriptsize = 2.197 \)

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