Convert 0.013 to Fraction Form: Decimal-to-Fraction Exercise

Q: Why does 0.013 have three decimal places when I only see two numbers?

You need to count all positions after the decimal point! In 0.013, you have: 0 (tenths), 1 (hundredths), and 3 (thousandths) = three decimal places.

Q: How do I remember which denominator to use?

Use this pattern: 1 decimal place = 10, 2 places = 100, 3 places = 1000. The number of zeros in the denominator matches the number of decimal places!

Q: What if the decimal has trailing zeros like 0.130?

Trailing zeros after the decimal don't change the value! 0.130 = 0.13, so you'd still get $ \frac{13}{100} $, not $ \frac{130}{1000} $.

Q: How can I check if my fraction is correct?

Divide the numerator by the denominator: 13 ÷ 1000 = 0.013. If you get back your original decimal, your fraction is right!

Decimal-to-Fraction Conversion with Thousandths

Convert into fraction form:

$0.013=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to fraction

00:04 First, we'll match the digit positions to the appropriate division

00:11 We'll place the number in the numerator, and the last digit position in the denominator

00:17 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:

$0.013=$

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:

$\frac{0013}{1000}$

We'll then proceed to remove the unnecessary zeros as follows:

$\frac{13}{1000}$

Final Answer

$\frac{13}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Count decimal places to determine denominator power
Technique: Three decimal places means divide by 1000: 0.013 = 13/1000
Check: Divide 13 ÷ 1000 = 0.013 to verify conversion ✓

Common Mistakes

Avoid these frequent errors

Miscounting decimal places
Don't count only the non-zero digits = wrong denominator! Counting just "13" gives 13/100 instead of 13/1000. 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 0.013 have three decimal places when I only see two numbers?

You need to count all positions after the decimal point! In 0.013, you have: 0 (tenths), 1 (hundredths), and 3 (thousandths) = three decimal places.

How do I remember which denominator to use?

Use this pattern: 1 decimal place = 10, 2 places = 100, 3 places = 1000. The number of zeros in the denominator matches the number of decimal places!

Do I need to simplify 13/1000?

Check if 13 and 1000 share any common factors. Since 13 is prime and doesn't divide 1000, 13/1000 is already in simplest form!

What if the decimal has trailing zeros like 0.130?

Trailing zeros after the decimal don't change the value! 0.130 = 0.13, so you'd still get $\frac{13}{100}$ , not $\frac{130}{1000}$ .

How can I check if my fraction is correct?

Divide the numerator by the denominator: 13 ÷ 1000 = 0.013. If you get back your original decimal, your fraction is right!

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