Convert to kilometres. It is . Verify this.

Understand the Question To convert a smaller unit of length into a larger unit, we divide: We can first convert centimetres to metres by dividing by , and then convert metres to kilometres by dividing by . Step 1 · Convert Centimetres to Metres Since : Step 2 · Convert Metres to Kilometres Since : Hence, is verified. Answer > (Verified) Common Mistakes Operation Error: Multiplying by and instead of dividing when converting from a smaller unit () to a larger unit (). Counting Zeros: Forgetting that ( zeros total), leading to incorrect decimal point placement.

Proportional Reasoning - 2 | IT

Question 3

Convert $60,00,000 \text{ cm}$ to kilometres.

It is $60 \text{ km}$ . Verify this.

Solution

Understand the Question

To convert a smaller unit of length into a larger unit, we divide:
- $1 \text{ m} = 100 \text{ cm} \implies 1 \text{ cm} = \dfrac{1}{100} \text{ m}$
- $1 \text{ km} = 1000 \text{ m} \implies 1 \text{ m} = \dfrac{1}{1000} \text{ km}$
We can first convert centimetres to metres by dividing by $100$ , and then convert metres to kilometres by dividing by $1000$ .

Step 1 · Convert Centimetres to Metres

Since $1 \text{ m} = 100 \text{ cm}$ : Diagram 1

\begin{aligned} 60,00,000 \text{ cm} &= \dfrac{60,00,000}{100} \text{ m} \\[0.6em] &= 60,000 \text{ m} \end{aligned}

Step 2 · Convert Metres to Kilometres

Since $1 \text{ km} = 1000 \text{ m}$ :

\begin{aligned} 60,000 \text{ m} &= \dfrac{60,000}{1000} \text{ km} \\[0.6em] &= 60 \text{ km} \end{aligned}

Hence, $60,00,000 \text{ cm} = 60 \text{ km}$ is verified.

Answer

$60 \text{ km}$ (Verified)

Common Mistakes

Operation Error: Multiplying by $100$ and $1000$ instead of dividing when converting from a smaller unit ( $\text{cm}$ ) to a larger unit ( $\text{km}$ ).
Counting Zeros: Forgetting that $1 \text{ km} = 100,000 \text{ cm}$ ( $5$ zeros total), leading to incorrect decimal point placement.

Question 3

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