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Properties of Whole Numbers I | Week 14 Topics1 Quiz
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Properties of Whole Numbers II | Week 24 Topics1 Quiz
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Properties of Whole Numbers III | Week 35 Topics1 Quiz
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Indices | Week 42 Topics1 Quiz
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Laws of Indices | Week 55 Topics1 Quiz
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Whole Numbers & Decimal Numbers | Week 64 Topics1 Quiz
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Standard Form | Week 73 Topics1 Quiz
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Significant Figures (S.F) | Week 84 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages I | Week 96 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages II | Week 104 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages III | Week 113 Topics1 Quiz
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Approximation & Estimation | Week 121 Topic1 Quiz
Topic Content:
- Fractional Base Number & Decimal Base Number
- Evaluation Questions
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.
(0.2)4 = 0.2 × 0.2 × 0.2 × 0.2
Worked Example 4.2.1:
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 = \( \scriptsize 2.7 \: \times \: 2.7\: \times \: 2.7 \: \times \: 2.7\)
Worked Example 4.2.2:
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 Questions:
1. Write the following in index forms.
a. 4 × 4 × 4 × 4
b. 2 × 2 × 2 × 2
c. 9 × 9 × 9 × 9
d. 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11 × 11
e. 13 × 13 × 13 × 13 × 13
2. Express the following in index form
a. 64
b. 343
c. 243
d. 27 × 8
e. 49 × 343
3. Find the value of the following
a. 4 × 4 × 4
b. 2 × 2 × 2 × 2 × 2
c. 6 × 6 × 6 × 6 × 6
d. 10 × 10 × 10 × 10 × 10 × 10
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. \( \left(\scriptsize 1.3 \right)^3 \)
View Answers
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. \( \left(\scriptsize 1.3 \right)^3 \)
View Answers