Question 14 of 21intermediate🔧 ApplyShort Answer2 marks

Give a simple rule to multiply a given number by 5 in the base-5 system that we created.

Correct Answer

Rule: In a base-5 system, multiplying a number by 5 is equivalent to shifting all digits one position to the left and adding a 0 in the rightmost position.

This is analogous to multiplying by 10 in the base-10 (Hindu) system.

Example: If a number is written as 'abc' in base-5 (where a, b, c are digits), then multiplying by 5 gives 'abc0' in base-5.

Why it works: Each position's value increases by a factor of 5 when shifted left.

Exercise: Figure it Out (Section 7) | Q: 3 | (Page Page 23)
For More Understanding

Explanation

The chapter explains that in a base-n system, multiplying by n shifts all digits one position left. This is because each position represents a power of n, and shifting left increases each power by 1, effectively multiplying the entire number by n. In base-5, multiplying by 5 shifts digits left, just as multiplying by 10 shifts digits left in base-10.

Solution Steps

  1. Shift all digits one position to the left.

  2. Add a 0 in the rightmost position.

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