Solve for x²: Converting 100kg Expression to Tonnes

Q: Why do we divide by 1000 to convert kg to tonnes?

Because 1 tonne = 1000 kg, so 1 kg = 1/1000 tonnes. When you have more kg, you divide by 1000 to find how many tonnes that represents.

Q: What happens to the x² when we convert units?

The algebraic part stays the same - only the numerical coefficient changes during unit conversion. So $ x^2 \times 100 $ becomes $ \frac{x^2}{10} $.

Q: How can I remember which way to convert?

Think: tonnes are bigger than kg, so you need fewer tonnes than kg. When going to a bigger unit, divide. When going to a smaller unit, multiply.

Q: Can I check my answer with actual numbers?

Yes! Try x=3: $ 3^2 \times 100 = 900 $ kg. Converting: 900 ÷ 1000 = 0.9 tonnes. Using our formula: $ \frac{3^2}{10} = \frac{9}{10} = 0.9 $ tonnes ✓

Q: Why isn't the answer just 100x²?

That would mean no unit conversion happened! We started with kg and need tonnes. The number must change because tonnes are 1000 times bigger than kg.

Unit Conversion with Algebraic Expressions

$x^2\times100kg=?T$

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Understand the problem

$x^2\times100kg=?T$

Step-by-step solution

To convert the given expression from kilograms to tons, we need to follow these steps:

Step 1: Express the weight in kilograms. The given expression is $x^2 \times 100 \text{ kg}$ .
Step 2: Convert kilograms to tons by dividing by 1000, because $1 \text{ ton} = 1000 \text{ kg}$ .

Now, implementing these steps, we first have the expression in kilograms:
$x^2 \times 100 \text{ kg}$

To convert this to tons, divide by 1000:
$\frac{x^2 \times 100}{1000}$

Simplify the expression:
$= \frac{x^2}{10}$

This result shows that the expression $x^2 \times 100 \text{ kg}$ is equivalent to $\frac{x^2}{10} \text{ tons}$ .

Therefore, the correct answer is:

$\frac{x^2}{10}$

Final Answer

$\frac{x^2}{10}$

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: One tonne equals 1000 kilograms for all conversions
Technique: Divide kg by 1000: $\frac{x^2 \times 100}{1000} = \frac{x^2}{10}$
Check: If x=2, then 400kg = 0.4T and $\frac{4}{10} = 0.4$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying by 1000 instead of dividing
Don't multiply by 1000 when converting kg to tonnes = answer 1000 times too big! This happens because students think bigger unit needs bigger number. Always divide by 1000 when going from smaller unit (kg) to larger unit (tonnes).

Practice Quiz

Test your knowledge with interactive questions

$$ 7kg=?gr $$

FAQ

Everything you need to know about this question

Why do we divide by 1000 to convert kg to tonnes?

Because 1 tonne = 1000 kg, so 1 kg = 1/1000 tonnes. When you have more kg, you divide by 1000 to find how many tonnes that represents.

What happens to the x² when we convert units?

The algebraic part stays the same - only the numerical coefficient changes during unit conversion. So $x^2 \times 100$ becomes $\frac{x^2}{10}$ .

How can I remember which way to convert?

Think: tonnes are bigger than kg, so you need fewer tonnes than kg. When going to a bigger unit, divide. When going to a smaller unit, multiply.

Can I check my answer with actual numbers?

Yes! Try x=3: $3^2 \times 100 = 900$ kg. Converting: 900 ÷ 1000 = 0.9 tonnes. Using our formula: $\frac{3^2}{10} = \frac{9}{10} = 0.9$ tonnes ✓

Why isn't the answer just 100x²?

That would mean no unit conversion happened! We started with kg and need tonnes. The number must change because tonnes are 1000 times bigger than kg.

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