Convert Fraction 1/10 to Decimal: Step-by-Step Solution

Q: Why isn't 1/10 equal to 1.0?

Because $ \frac{1}{10} $ means one part out of ten, which is smaller than 1. Think of it like having 1 slice out of a pizza cut into 10 pieces - that's much less than a whole pizza!

Q: How do I remember where the decimal point goes?

Count the zeros in the denominator! For $ \frac{1}{10} $, there's 1 zero, so move the decimal point 1 place to the left: 1.0 becomes 0.1.

Q: What's the difference between 0.1 and 0.01?

0.1 is ten times bigger than 0.01! Think: 0.1 = $ \frac{1}{10} $ (one-tenth) while 0.01 = $ \frac{1}{100} $ (one-hundredth). Always check your decimal places carefully.

Q: Can I just cross out the zero in 1/10?

Never! That would give you 1/1 = 1, which is completely wrong. You must divide properly: 1 ÷ 10 = 0.1. There's no shortcut for fraction-to-decimal conversion.

Q: Why do some fractions have repeating decimals but 1/10 doesn't?

Great question! $ \frac{1}{10} $ gives a terminating decimal because 10 only has factors of 2 and 5. Fractions with denominators containing other prime factors (like 3 or 7) create repeating decimals.

Fraction to Decimal with Simple Division

Convert $\frac{1}{10}$ into a decimal.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Based on the number of zeros in the denominator, we'll know how many places to move the decimal point left

00:06 There is one zero in the denominator, so we'll move the decimal point one place left

00:09 Place the numerator in the appropriate position after the decimal point

00:12 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 $\frac{1}{10}$ into a decimal.

Step-by-step solution

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

Step 1: Identify the given fraction $\frac{1}{10}$ .
Step 2: Convert the fraction to a decimal by dividing the numerator by the denominator.
Step 3: Perform the division and compare with the given choices.

Let's work through the solution:

Step 1: We start with the fraction $\frac{1}{10}$ .

Step 2: Perform the division: $1 \div 10 = 0.1$ .

Step 3: Therefore, the decimal equivalent of $\frac{1}{10}$ is $0.1$ .

Among the given answer choices, 0.1 corresponds to choice 3, which is the correct answer.

Thus, the solution to the problem is $0.1$ .

Final Answer

0.1

Key Points to Remember

Essential concepts to master this topic

Method: Divide numerator by denominator to convert any fraction
Technique: Calculate 1 ÷ 10 = 0.1 using long division
Check: Multiply back: 0.1 × 10 = 1, confirming our decimal is correct ✓

Common Mistakes

Avoid these frequent errors

Adding zeros incorrectly when dividing
Don't write 1 ÷ 10 = 1.0 or 0.01! This happens when students misplace the decimal point during division. Always remember that 1 ÷ 10 means 'how many tens fit into 1', which is 0.1 (one-tenth).

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why isn't 1/10 equal to 1.0?

Because $\frac{1}{10}$ means one part out of ten, which is smaller than 1. Think of it like having 1 slice out of a pizza cut into 10 pieces - that's much less than a whole pizza!

How do I remember where the decimal point goes?

Count the zeros in the denominator! For $\frac{1}{10}$ , there's 1 zero, so move the decimal point 1 place to the left: 1.0 becomes 0.1.

What's the difference between 0.1 and 0.01?

0.1 is ten times bigger than 0.01! Think: 0.1 = $\frac{1}{10}$ (one-tenth) while 0.01 = $\frac{1}{100}$ (one-hundredth). Always check your decimal places carefully.

Can I just cross out the zero in 1/10?

Never! That would give you 1/1 = 1, which is completely wrong. You must divide properly: 1 ÷ 10 = 0.1. There's no shortcut for fraction-to-decimal conversion.

Why do some fractions have repeating decimals but 1/10 doesn't?

Great question! $\frac{1}{10}$ gives a terminating decimal because 10 only has factors of 2 and 5. Fractions with denominators containing other prime factors (like 3 or 7) create repeating decimals.

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