Convert Decimal 0.012 to Fraction Form: Step-by-Step Solution

Q: Why does 0.012 become 12/1000 and not 12/100?

Count carefully! The decimal 0.012 has three places after the decimal point: 0, 1, and 2. Three decimal places means the denominator is 1000 (10³).

Q: Do I need to simplify the fraction 12/1000?

Yes, you should! Both 12 and 1000 are divisible by 4, so $ \frac{12}{1000} = \frac{3}{250} $ in lowest terms.

Q: What if there are zeros at the end of the decimal?

Zeros at the end don't matter (0.120 = 0.12), but zeros between the decimal point and other digits do count! For example, 0.012 has that important zero.

Q: How do I remember the place value pattern?

Think powers of 10: 1 decimal place = 10¹, 2 places = 10², 3 places = 10³ = 1000. Each extra decimal place adds another zero to the denominator!

Q: Can I write the numerator with leading zeros?

You can write $ \frac{0012}{1000} $, but it's better to remove unnecessary leading zeros and write $ \frac{12}{1000} $ for clarity.

Decimal to Fraction with Place Value

Convert into fraction form:

0.012

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to fraction

00:06 Divide the digits after the decimal point into appropriate division quantities

00:13 Place our number in the numerator, with the appropriate denominator

00:25 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 into fraction form:

0.012

Step-by-step solution

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are three numbers after the zero, so the number is divided by 1000

Let's write the fraction in the following way:

$\frac{0012}{1000}$

We'll then remove the unnecessary zeros as follows:

$\frac{12}{1000}$

Final Answer

$\frac{12}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Count decimal places to determine denominator
Technique: 0.012 has 3 decimal places, so denominator is 1000
Check: Verify 12/1000 = 0.012 by dividing 12 ÷ 1000 ✓

Common Mistakes

Avoid these frequent errors

Miscounting decimal places
Don't count only the non-zero digits after decimal point = wrong denominator! This gives fractions like 12/100 instead of 12/1000. Always count all digits after the decimal point, including zeros.

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 0.012 become 12/1000 and not 12/100?

Count carefully! The decimal 0.012 has three places after the decimal point: 0, 1, and 2. Three decimal places means the denominator is 1000 (10³).

Do I need to simplify the fraction 12/1000?

Yes, you should! Both 12 and 1000 are divisible by 4, so $\frac{12}{1000} = \frac{3}{250}$ in lowest terms.

What if there are zeros at the end of the decimal?

Zeros at the end don't matter (0.120 = 0.12), but zeros between the decimal point and other digits do count! For example, 0.012 has that important zero.

How do I remember the place value pattern?

Think powers of 10: 1 decimal place = 10¹, 2 places = 10², 3 places = 10³ = 1000. Each extra decimal place adds another zero to the denominator!

Can I write the numerator with leading zeros?

You can write $\frac{0012}{1000}$ , but it's better to remove unnecessary leading zeros and write $\frac{12}{1000}$ for clarity.

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