Convert 0.1 to Fraction: Step-by-Step Decimal Transformation

Q: How do I know what denominator to use?

Count the decimal places after the decimal point! One place = denominator of 10, two places = denominator of 100, three places = denominator of 1000.

Q: Why is 0.1 equal to 1/10 and not 10/10?

Think about what 0.1 means: it's one-tenth of a whole. $ \frac{10}{10} $ equals 1 whole, but 0.1 is much smaller than 1!

Q: Do I need to simplify the fraction?

For 0.1, $ \frac{1}{10} $ is already in simplest form since 1 and 10 share no common factors. Always check if you can reduce your fraction!

Q: What if the decimal has more digits like 0.15?

Same process! 0.15 has two decimal places, so it becomes $ \frac{15}{100} $. Then simplify: $ \frac{15}{100} = \frac{3}{20} $.

Q: Can I check my answer?

Always! Divide your numerator by denominator. If $ \frac{1}{10} $ is correct, then $ 1 \div 10 = 0.1 $ ✓

Decimal Conversion with Place Value Recognition

Convert 0.1 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple fraction

00:03 Move the decimal point right until the number is whole

00:06 In a decimal fraction, the denominator must be some multiple of 10 by 10

00:09 We moved the decimal point once to the right, so we'll add one 0 to the denominator

00:12 Write the digits in the numerator

00:15 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

Convert 0.1 into a fraction.

Step-by-step solution

To solve this problem, we'll convert the decimal 0.1 into a fraction:

Step 1: Recognize that in the decimal 0.1, the digit "1" is in the tenths place.
Step 2: Convert 0.1 directly into a fraction by placing 1 over 10. This is because 0.1 means 1 part out of 10, i.e., $\frac{1}{10}$ .

Now, let's consider the problem:

Step 1: Observe the decimal 0.1. The "1" is in the tenths place, which means it represents one-tenth.
Step 2: Hence, as a fraction, 0.1 is $\frac{1}{10}$ since there is one digit after the decimal point, implying a denominator of 10.

Therefore, the correct answer to converting 0.1 into a fraction is $\frac{1}{10}$ .

Final Answer

$\frac{1}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: The decimal place determines the denominator of fraction
Technique: 0.1 has 1 in tenths place so equals $\frac{1}{10}$
Check: Divide numerator by denominator: $1 \div 10 = 0.1$ ✓

Common Mistakes

Avoid these frequent errors

Confusing place values when writing denominators
Don't put 0.1 as $\frac{1}{100}$ = 0.01! This happens when you count decimal places wrong. Always remember: 1 decimal place means denominator of 10, 2 places means 100.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

How do I know what denominator to use?

Count the decimal places after the decimal point! One place = denominator of 10, two places = denominator of 100, three places = denominator of 1000.

Why is 0.1 equal to 1/10 and not 10/10?

Think about what 0.1 means: it's one-tenth of a whole. $\frac{10}{10}$ equals 1 whole, but 0.1 is much smaller than 1!

Do I need to simplify the fraction?

For 0.1, $\frac{1}{10}$ is already in simplest form since 1 and 10 share no common factors. Always check if you can reduce your fraction!

What if the decimal has more digits like 0.15?

Same process! 0.15 has two decimal places, so it becomes $\frac{15}{100}$ . Then simplify: $\frac{15}{100} = \frac{3}{20}$ .

Can I check my answer?

Always! Divide your numerator by denominator. If $\frac{1}{10}$ is correct, then $1 \div 10 = 0.1$ ✓

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