Question
Identify the features of the Hindu number system that make it efficient when compared to the Roman number system.
✓
Answer
The Hindu number system is much more efficient than the Roman number system because :
(i) Large numbers are written compactly (e.g., 1,000,000), unlike Roman numerals, which become long and clumsy.
(ii) It uses place value, where a digit’s position (units, tens, hundreds) affects its value. Roman numerals lack this.
(iii) It includes zero, both as a number and a placeholder. Roman numerals have no symbol for zero.
(iv) It uses just 10 digits (0–9) to write any number, while Roman numerals need many symbols.
(v) Arithmetic operations are easy using standard rules. Roman operations are complex and often require conversion.
(i) Large numbers are written compactly (e.g., 1,000,000), unlike Roman numerals, which become long and clumsy.
(ii) It uses place value, where a digit’s position (units, tens, hundreds) affects its value. Roman numerals lack this.
(iii) It includes zero, both as a number and a placeholder. Roman numerals have no symbol for zero.
(iv) It uses just 10 digits (0–9) to write any number, while Roman numerals need many symbols.
(v) Arithmetic operations are easy using standard rules. Roman operations are complex and often require conversion.
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Fill in the blanks in the following table
| Numbers | Closed under | |||
| Addition | Substraction | Multiplication | Division | |
| Rational numbers | Yes | Yes | No | |
| Integers | Yes | No | ||
| Whole numbers | Yes | |||
| Natural numbers | No | |||
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243
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(iii) If abcdef is a multiple of 6 , then badcef will be a multiple of 6 .
(iv) $8(7 b-3)-4(11 b+1)$ is a multiple of 12 .
→(i) The product of a multiple of 6 and a multiple of 3 is a multiple of 9 .
(ii) The sum of three consecutive even numbers will be divisible by 6 .
(iii) If abcdef is a multiple of 6 , then badcef will be a multiple of 6 .
(iv) $8(7 b-3)-4(11 b+1)$ is a multiple of 12 .
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(ii) If it is a rhombus and AC = 12 cm and BD = 16 cm, then find the perimeter of rhombus.
(i) Is it a rectangle? Why or why not?
(ii) If it is a rhombus and AC = 12 cm and BD = 16 cm, then find the perimeter of rhombus.
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(i) One of the persons fell ill before the work started. How long would the job take now ?
(ii) How many persons would be needed to fit the windows in one day?
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(ii) How many persons would be needed to fit the windows in one day?
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