Convert Fraction: 1/5 km to m Using Metric System

Q: Why do I multiply by 1000 instead of dividing?

Because you're converting from a larger unit (km) to a smaller unit (m). Since meters are smaller, you need more of them to equal the same distance. Think: 1 km = 1000 m, so $ \frac{1}{5} $ km needs 1000 ÷ 5 = 200 meters!

Q: How do I remember the conversion factor?

Remember the prefix kilo- means 1000! So 1 kilometer = 1000 meters, 1 kilogram = 1000 grams. The word itself tells you the conversion factor.

Q: Can I convert the fraction to decimal first?

Yes! $ \frac{1}{5} = 0.2 $, then 0.2 × 1000 = 200 meters. Both methods work, but working with fractions directly often gives cleaner calculations.

Q: What if I get confused about multiplying or dividing?

Use this trick: bigger unit to smaller unit = multiply. Since km is bigger than m, you multiply. Smaller to bigger = divide. So m to km would mean dividing by 1000.

Q: How can I check if 200 meters makes sense?

Think about it: $ \frac{1}{5} $ km is one-fifth of a kilometer. Since 1 km = 1000 m, then one-fifth should be 1000 ÷ 5 = 200 m. Perfect!

Unit Conversion with Fraction Multiplication

$\frac{1}{5}km=?m$

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Understand the problem

$\frac{1}{5}km=?m$

Step-by-step solution

To convert $\frac{1}{5}$ kilometers to meters, we follow these steps:

Step 1: Recognize that the conversion factor is $1$ kilometer = $1000$ meters.
Step 2: Multiply $\frac{1}{5}$ kilometers by $1000$ to find the equivalent in meters.

Let's carry out the calculation:

$\frac{1}{5} \text{ km} = \frac{1}{5} \times 1000 \text{ m}$ $= \frac{1000}{5} \text{ m}$ $= 200 \text{ meters}$

Therefore, the equivalent of $\frac{1}{5}$ kilometers in meters is $\boxed{200}$ .

Final Answer

$200$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: 1 kilometer equals 1000 meters exactly
Technique: Multiply $\frac{1}{5} \times 1000 = \frac{1000}{5} = 200$
Check: Verify 200 m ÷ 1000 = 0.2 km = $\frac{1}{5}$ km ✓

Common Mistakes

Avoid these frequent errors

Using wrong conversion factor or forgetting to multiply
Don't just convert $\frac{1}{5}$ to decimal 0.2 and think that's the answer in meters = 0.2 m! This ignores the unit conversion completely. Always multiply by 1000 when converting kilometers to meters: $\frac{1}{5} \times 1000 = 200$ meters.

Practice Quiz

Test your knowledge with interactive questions

$$ 291cm^2=?m^2 $$

FAQ

Everything you need to know about this question

Why do I multiply by 1000 instead of dividing?

Because you're converting from a larger unit (km) to a smaller unit (m). Since meters are smaller, you need more of them to equal the same distance. Think: 1 km = 1000 m, so $\frac{1}{5}$ km needs 1000 ÷ 5 = 200 meters!

How do I remember the conversion factor?

Remember the prefix kilo- means 1000! So 1 kilometer = 1000 meters, 1 kilogram = 1000 grams. The word itself tells you the conversion factor.

Can I convert the fraction to decimal first?

Yes! $\frac{1}{5} = 0.2$ , then 0.2 × 1000 = 200 meters. Both methods work, but working with fractions directly often gives cleaner calculations.

What if I get confused about multiplying or dividing?

Use this trick: bigger unit to smaller unit = multiply. Since km is bigger than m, you multiply. Smaller to bigger = divide. So m to km would mean dividing by 1000.

How can I check if 200 meters makes sense?

Think about it: $\frac{1}{5}$ km is one-fifth of a kilometer. Since 1 km = 1000 m, then one-fifth should be 1000 ÷ 5 = 200 m. Perfect!

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