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Which of the following conversions "is"/...

Which of the following conversions `"is"//"are"` incorrect?
(i) 10 decades = 1 century
(ii) 100 centuries = 1 millennium
(iii) 100 inches = 2.54 metres
(iv) 100 millimetres = 10 centimetres

A

(ii) only

B

(iv) only

C

(i) and (ii) only

D

(iii) and (iv) only

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the given conversions are incorrect, let's analyze each option step by step: ### Step 1: Analyze the first conversion **Conversion (i): 10 decades = 1 century** - **Definition of a decade**: 1 decade = 10 years - **Calculating 10 decades**: - 10 decades = 10 × 10 years = 100 years - **Definition of a century**: 1 century = 100 years **Conclusion**: 10 decades = 1 century is **correct**. ### Step 2: Analyze the second conversion **Conversion (ii): 100 centuries = 1 millennium** - **Definition of a century**: 1 century = 100 years - **Calculating 100 centuries**: - 100 centuries = 100 × 100 years = 10,000 years - **Definition of a millennium**: 1 millennium = 1,000 years **Conclusion**: 100 centuries = 1 millennium is **incorrect** (100 centuries = 10 millennia). ### Step 3: Analyze the third conversion **Conversion (iii): 100 inches = 2.54 metres** - **Definition of an inch**: 1 inch = 0.0254 metres - **Calculating 100 inches**: - 100 inches = 100 × 0.0254 metres = 2.54 metres **Conclusion**: 100 inches = 2.54 metres is **correct**. ### Step 4: Analyze the fourth conversion **Conversion (iv): 100 millimetres = 10 centimetres** - **Definition of a centimetre**: 1 cm = 10 mm - **Calculating 100 millimetres**: - 100 mm = 100 ÷ 10 cm = 10 cm **Conclusion**: 100 millimetres = 10 centimetres is **correct**. ### Final Summary - **Correct conversions**: (i), (iii), (iv) - **Incorrect conversion**: (ii) Thus, the incorrect conversion is **(ii) 100 centuries = 1 millennium**. ---
To determine which of the given conversions are incorrect, let's analyze each option step by step: ### Step 1: Analyze the first conversion **Conversion (i): 10 decades = 1 century** - **Definition of a decade**: 1 decade = 10 years - **Calculating 10 decades**: - 10 decades = 10 × 10 years = 100 years ...
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