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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:
- Meaning of Index Number
- Worked Examples
What is an Index Number?
An index is the number of times a given number has been multiplied by itself.
For example:
5 × 5 × 5 × 5 × 5 × 5 = 56, ‘5’ has been multiplied by itself 6 times.
5 is the base number and 6 is the index or power
The plural of index is indices.
Worked Example 4.1.1:
Write the following in index form
a. 5 × 5 × 5
b. 2 × 2 × 2 × 2 × 2
c. 3 × 3 × 3 × 3
d. 128
e. 81
Solution
a. 5 × 5 × 5 = 53
b. 2 × 2 × 2 × 2 × 2 = 25
c. 3 × 3 × 3 × 3 = 34
d. Express 128 as a product of its prime factors.
128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 27
e. Express 81 as a product of prime factors
81 = 3 × 3 × 3 × 3 = 34
Worked Example 4.1.2:
Evaluate the following;
a. 25
b. 34
c. 55
d. 73
Solution
a. 25 = 2 × 2 × 2 × 2 × 2
= 4 × 4 × 2
= 16 × 2
= 32
b. 34 = 3 × 3 × 3 × 3
= 9 × 9
= 81
c. 55 = 5 × 5 × 5 × 5 × 5
= 25 × 25 × 5
= 625 × 5
= 3125
d. 73 = 7 × 7 × 7
= 49 × 7
= 343
