Solve Decimal Division: 10.1 ÷ 101 Step-by-Step

Q: Why do I need to convert 10.1 to a fraction?

Converting to fractions makes division much easier! Instead of messy decimal division, you can simplify $ \frac{101}{1010} $ by canceling common factors.

Q: How do I know what to multiply by to eliminate the decimal?

Count the decimal places! Since 10.1 has 1 decimal place, multiply both numbers by 10. For 2 decimal places, multiply by 100, and so on.

Q: Can I just use a calculator instead?

While calculators work, understanding the fraction method helps you see patterns and builds number sense. Plus, you'll get exact answers instead of rounded decimals!

Q: What if the numbers don't divide evenly after converting?

That's okay! Look for common factors in the numerator and denominator. In this problem, both 101 and 1010 are divisible by 101.

Q: How can I check if 0.1 is really correct?

Multiply your answer by the divisor: $ 0.1 \times 101 = 10.1 $. If you get the original dividend, your answer is right!

Decimal Division with Fraction Simplification

$10.1:101=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply each factor by 100 to eliminate the decimal point

00:29 Convert division to fraction

00:39 Break down 1010 into factors 101 and 10

00:44 Reduce what's possible

00:50 According to the number of zeros in the denominator, shift the decimal point

00:54 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$10.1:101=$

Step-by-step solution

To solve this problem, we need to divide $10.1$ by $101$ . The division can be represented as follows:

First, consider the expression $10.1 \div 101$ . To simplify this division, express it as a fraction: $\frac{10.1}{101}$ .

To deal with the decimal, convert $10.1$ to an equivalent fraction by multiplying both the numerator and the denominator by 10 to eliminate the decimal point:

\frac{10.1}{101} = \frac{101}{1010}

At this point, you can simplify the fraction. Divide both the numerator and the denominator by 101. Thus:

\frac{101}{1010} = \frac{1}{10}

Evaluating $\frac{1}{10}$ gives us the decimal form of $0.1$ .

Therefore, the solution to the problem $10.1 \div 101$ is $0.1$ .

Final Answer

$0.1$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert decimal division to fraction form for easier calculation
Technique: Multiply numerator and denominator by 10: $\frac{10.1}{101} = \frac{101}{1010}$
Check: Verify $\frac{1}{10} = 0.1$ by multiplying 0.1 × 101 = 10.1 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to eliminate decimals before dividing
Don't try to divide 10.1 ÷ 101 directly without converting to fractions = messy long division! This makes the problem unnecessarily complex and error-prone. Always convert decimals to fractions by multiplying both numbers by the same power of 10.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why do I need to convert 10.1 to a fraction?

Converting to fractions makes division much easier! Instead of messy decimal division, you can simplify $\frac{101}{1010}$ by canceling common factors.

How do I know what to multiply by to eliminate the decimal?

Count the decimal places! Since 10.1 has 1 decimal place, multiply both numbers by 10. For 2 decimal places, multiply by 100, and so on.

Can I just use a calculator instead?

While calculators work, understanding the fraction method helps you see patterns and builds number sense. Plus, you'll get exact answers instead of rounded decimals!

What if the numbers don't divide evenly after converting?

That's okay! Look for common factors in the numerator and denominator. In this problem, both 101 and 1010 are divisible by 101.

How can I check if 0.1 is really correct?

Multiply your answer by the divisor: $0.1 \times 101 = 10.1$ . If you get the original dividend, your answer is right!

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