Convert Decimal to Fraction: Finding the Fractional Form of 0.031

Decimal to Fraction with Thousandths Place

Convert into fraction form:

0.031

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's turn our decimal into a fraction.
00:08 First, we'll align each digit with its place value, just like in division.
00:13 Next, add a zero to the end of our fraction.
00:18 Put all numbers after the decimal in the numerator.
00:22 And, match the denominator with the highest decimal place value.
00:27 And that's how we find the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Convert into fraction form:

0.031

2

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:

00311000 \frac{0031}{1000}

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

311000 \frac{31}{1000}

3

Final Answer

311000 \frac{31}{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 denominator is 1000, so 0.031 = 31/1000
  • Check: Divide numerator by denominator: 31 ÷ 1000 = 0.031 ✓

Common Mistakes

Avoid these frequent errors
  • Counting decimal places incorrectly
    Don't count just the non-zero digits after the decimal = wrong denominator! This gives fractions like 31/100 instead of 31/1000. Always count ALL decimal places including zeros to find the correct power of 10.

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 0.031 have 1000 in the denominator when I only see 31?

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The denominator comes from counting decimal places, not the digits themselves! 0.031 has three places after the decimal point, so you need 103=1000 10^3 = 1000 as the denominator.

Do I need to simplify 31/1000?

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Check if the numerator and denominator share any common factors. Since 31 is prime and doesn't divide 1000, 311000 \frac{31}{1000} is already in simplest form!

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

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Trailing zeros after the decimal point do count as decimal places! For example, 0.310 would be 3101000=31100 \frac{310}{1000} = \frac{31}{100} after simplifying.

How do I remember which power of 10 to use?

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Use this pattern: 1 decimal place = 10, 2 places = 100, 3 places = 1000. Each additional decimal place adds another zero to the denominator!

Can I write 0.031 as 31/1000 without the leading zeros?

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Yes! Leading zeros in the numerator don't change the value. 00311000=311000 \frac{0031}{1000} = \frac{31}{1000} . Always remove unnecessary leading zeros from your final answer.

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