Solve the Division Equation: Finding the Number That Equals 0.0111 × 100

Q: Why do I multiply both sides by 100?

Because dividing by 100 is the opposite of multiplying by 100! To isolate the unknown number, we use the inverse operation on both sides of the equation.

Q: How do I multiply 0.0111 by 100?

Move the decimal point 2 places to the right: 0.0111 becomes 1.11. Remember, multiplying by 100 = multiplying by 10².

Q: How can I check if 1.11 is correct?

Substitute back: $ \frac{1.11}{100} = 0.0111 $. Since this matches our original equation, 1.11 is correct!

Q: Is there a faster way to solve this?

Yes! When you see $ ? ÷ 100 = 0.0111 $, just multiply the decimal by 100 directly. It's the same as the algebra method but quicker.

Division Equations with Decimal Multipliers

$?:100=0.0111$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 Multiply by the factor to find the unknown

00:09 Move the decimal point according to the number of zeros, and find the unknown

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$?:100=0.0111$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Start with the equation $\frac{x}{100} = 0.0111$ .
Step 2: Multiply both sides of the equation by 100 to isolate $x$ .

Now, let's work through each step:
Step 1: We have $\frac{x}{100} = 0.0111$ .
Step 2: To solve for $x$ , multiply both sides by 100:
$(x = 0.0111 \times 100)$

This simplifies to:
$x = 1.11$

Therefore, the number that fits the equation is $x = 1.11$ .

Looking at the choices provided, the correct answer is $1.11$ .

Final Answer

$1.11$

Key Points to Remember

Essential concepts to master this topic

Rule: To solve x ÷ 100 = decimal, multiply both sides by 100
Technique: Moving decimal point: 0.0111 × 100 = 1.11
Check: Substitute back: 1.11 ÷ 100 = 0.0111 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point incorrectly when multiplying by 100
Don't just add two zeros to 0.0111 = 0.0111100! This ignores how decimal multiplication actually works. Always move the decimal point exactly 2 places right when multiplying by 100.

Practice Quiz

Test your knowledge with interactive questions

$$ 20.1:10= $$

FAQ

Everything you need to know about this question

Why do I multiply both sides by 100?

Because dividing by 100 is the opposite of multiplying by 100! To isolate the unknown number, we use the inverse operation on both sides of the equation.

How do I multiply 0.0111 by 100?

Move the decimal point 2 places to the right: 0.0111 becomes 1.11. Remember, multiplying by 100 = multiplying by 10².

What if I got 11.1 or 111.1 as my answer?

You moved the decimal point too far! For 0.0111 × 100, move only 2 places right: 0.01|1|1 becomes 1.11, not 11.1 or 111.1.

How can I check if 1.11 is correct?

Substitute back: $\frac{1.11}{100} = 0.0111$ . Since this matches our original equation, 1.11 is correct!

Is there a faster way to solve this?

Yes! When you see $? ÷ 100 = 0.0111$ , just multiply the decimal by 100 directly. It's the same as the algebra method but quicker.

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