Solve the Decimal Division: 99.9 ÷ 33.3

Q: Why do we multiply both parts by 10 instead of just removing the decimals?

We multiply by 10 to preserve the ratio! Just removing decimals would change $ \frac{99.9}{33.3} $ to $ \frac{999}{333} $ incorrectly. Multiplying keeps the fraction equivalent.

Q: How do I know what number to multiply by?

Count the decimal places in both numbers. Since 99.9 and 33.3 each have 1 decimal place, multiply by $ 10^1 = 10 $. For 2 decimal places, use 100.

Q: Can I use long division instead of simplifying fractions?

Absolutely! You could divide 999 ÷ 333 directly. But simplifying first makes the division much easier and helps you spot patterns like $ \frac{999}{333} = \frac{3 \times 333}{333} = 3 $.

Q: What if the decimals have different numbers of decimal places?

Use enough zeros to match the longest decimal. For example, with 12.5 ÷ 3.25, multiply both by 100 to get $ \frac{1250}{325} $.

Q: How do I check my answer when dividing decimals?

Use multiplication to check: 3 × 33.3 should equal 99.9. You can also estimate: 100 ÷ 33 is about 3, so our answer makes sense!

Decimal Division with Simplification Strategies

Solve the following:

$\frac{99.9}{33.3}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following:

$\frac{99.9}{33.3}=$

Step-by-step solution

To solve the problem $\frac{99.9}{33.3}$ , we will simplify it by transforming each decimal into a whole number to make calculation straightforward.

Step 1: Multiply both the numerator and the denominator by $10$ to eliminate decimals. This gives us:
$\frac{99.9 \times 10}{33.3 \times 10} = \frac{999}{333}$ .
Step 2: Notice that both $999$ and $333$ can be divided by $3$ (a common factor). Divide each by $3$ :
$\frac{999 \div 3}{333 \div 3} = \frac{333}{111}$ .
Step 3: Notice again that $333$ and $111$ can be simplified further by dividing each by $111$ (another common factor).
$\frac{333 \div 111}{111 \div 111} = \frac{3}{1} = 3$ .

Therefore, the solution to the problem is $3$ .

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by same power of 10
Technique: Convert $\frac{99.9}{33.3}$ to $\frac{999}{333}$ by multiplying by 10
Check: Verify 3 × 33.3 = 99.9 using multiplication ✓

Common Mistakes

Avoid these frequent errors

Moving decimal points separately in numerator and denominator
Don't move the decimal point 1 place in 99.9 and 1 place in 33.3 separately = changes the value! This creates a completely different problem with wrong answer. Always multiply both parts by the exact same number.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{1}{2}:\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why do we multiply both parts by 10 instead of just removing the decimals?

We multiply by 10 to preserve the ratio! Just removing decimals would change $\frac{99.9}{33.3}$ to $\frac{999}{333}$ incorrectly. Multiplying keeps the fraction equivalent.

How do I know what number to multiply by?

Count the decimal places in both numbers. Since 99.9 and 33.3 each have 1 decimal place, multiply by $10^1 = 10$ . For 2 decimal places, use 100.

Can I use long division instead of simplifying fractions?

Absolutely! You could divide 999 ÷ 333 directly. But simplifying first makes the division much easier and helps you spot patterns like $\frac{999}{333} = \frac{3 \times 333}{333} = 3$ .

What if the decimals have different numbers of decimal places?

Use enough zeros to match the longest decimal. For example, with 12.5 ÷ 3.25, multiply both by 100 to get $\frac{1250}{325}$ .

How do I check my answer when dividing decimals?

Use multiplication to check: 3 × 33.3 should equal 99.9. You can also estimate: 100 ÷ 33 is about 3, so our answer makes sense!

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