Convert Fraction to Decimal: Solving 4/10 Step by Step

Q: Why does dividing by 10 move the decimal point left?

Dividing by 10 makes numbers ten times smaller. Moving the decimal point one place left does exactly that! Think of it as 4 ÷ 10 = 0.4.

Q: What if the fraction was 4/100 instead?

With 100 in the denominator, you'd move the decimal two places left! So $ \frac{4}{100} = 0.04 $. Each zero in the denominator means one more place left.

Q: Do I need to write the zero before the decimal point?

Yes, always! Writing 0.4 instead of just .4 makes your answer clearer and follows proper mathematical notation.

Q: How do I know if I moved the decimal the right direction?

Remember: dividing makes numbers smaller, so move left. Multiplying makes them bigger, so move right. Since $ \frac{4}{10} $ means 4 ÷ 10, move left!

Q: What if my fraction doesn't have 10, 100, or 1000 in the denominator?

Then you'll need to use long division instead of the decimal point shortcut. The shortcut only works with denominators that are powers of 10.

Decimal Conversion with Powers of Ten

Write the following fraction as a decimal:

$\frac{4}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's convert a fraction into a decimal.

00:08 First, use the numerator as your whole number.

00:13 Now, look at the denominator to place the decimal point.

00:17 If the denominator is ten, move the decimal left by one place.

00:22 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following fraction as a decimal:

$\frac{4}{10}=$

Step-by-step solution

Let's write the simple fraction as a decimal fraction

$4.0$

Since the fraction divides by 10, we'll move the decimal point one place to the left and get:

$.4$

We'll complete the zero before the decimal point and get:

$0.4$

Final Answer

0.4

Key Points to Remember

Essential concepts to master this topic

Rule: Denominator of 10 means move decimal one place left
Technique: Convert $\frac{4}{10}$ by writing 4.0 then moving decimal left
Check: Verify 0.4 × 10 = 4, confirming $\frac{4}{10} = 0.4$ ✓

Common Mistakes

Avoid these frequent errors

Adding extra zeros after the decimal point
Don't write 0.40 or 0.400 thinking more zeros make it more accurate = unnecessarily complicated answer! The value is the same, but it's not in simplest form. Always write 0.4 as the final answer since trailing zeros after decimals are unnecessary.

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

Why does dividing by 10 move the decimal point left?

Dividing by 10 makes numbers ten times smaller. Moving the decimal point one place left does exactly that! Think of it as 4 ÷ 10 = 0.4.

What if the fraction was 4/100 instead?

With 100 in the denominator, you'd move the decimal two places left! So $\frac{4}{100} = 0.04$ . Each zero in the denominator means one more place left.

Do I need to write the zero before the decimal point?

Yes, always! Writing 0.4 instead of just .4 makes your answer clearer and follows proper mathematical notation.

How do I know if I moved the decimal the right direction?

Remember: dividing makes numbers smaller, so move left. Multiplying makes them bigger, so move right. Since $\frac{4}{10}$ means 4 ÷ 10, move left!

What if my fraction doesn't have 10, 100, or 1000 in the denominator?

Then you'll need to use long division instead of the decimal point shortcut. The shortcut only works with denominators that are powers of 10.

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