Convert 0.022 to Its Equivalent Fraction Form

Q: Why does 0.022 become 22/1000 and not 022/1000?

Leading zeros don't change a number's value! $ \frac{022}{1000} $ and $ \frac{22}{1000} $ are exactly the same because 022 = 22. We remove unnecessary zeros to simplify the fraction.

Q: How do I know what denominator to use?

Count the decimal places! 1 place = 10, 2 places = 100, 3 places = 1000, and so on. Since 0.022 has 3 decimal places, use 1000 as your denominator.

Q: Should I simplify 22/1000 further?

Yes! You can simplify by finding the greatest common factor. Both 22 and 1000 are divisible by 2, giving you $ \frac{11}{500} $ in lowest terms.

Q: What if I miscounted and used 100 instead of 1000?

You'd get $ \frac{22}{100} = 0.22 $, which is 10 times larger than 0.022! Always double-check by converting your fraction back to decimal.

Decimal to Fraction with Place Value

Convert into fraction form:

$0.022=$

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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

00:22 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:

$0.022=$

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:

$\frac{0022}{1000}$

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

$\frac{22}{1000}$

Final Answer

$\frac{22}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Three decimal places means denominator of 1000
Technique: Write 0.022 as $\frac{22}{1000}$ by removing leading zeros
Check: Divide 22 ÷ 1000 = 0.022 to verify correctness ✓

Common Mistakes

Avoid these frequent errors

Counting decimal places incorrectly
Don't count from the decimal point as 0.022 = 22/100! This ignores the leading zero and gives a wrong answer 10 times too large. Always count all digits after the decimal point: 0.022 has three places, so use 1000 as denominator.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{1}{100}=$

FAQ

Everything you need to know about this question

Why does 0.022 become 22/1000 and not 022/1000?

Leading zeros don't change a number's value! $\frac{022}{1000}$ and $\frac{22}{1000}$ are exactly the same because 022 = 22. We remove unnecessary zeros to simplify the fraction.

How do I know what denominator to use?

Count the decimal places! 1 place = 10, 2 places = 100, 3 places = 1000, and so on. Since 0.022 has 3 decimal places, use 1000 as your denominator.

Should I simplify 22/1000 further?

Yes! You can simplify by finding the greatest common factor. Both 22 and 1000 are divisible by 2, giving you $\frac{11}{500}$ in lowest terms.

What if I miscounted and used 100 instead of 1000?

You'd get $\frac{22}{100} = 0.22$ , which is 10 times larger than 0.022! Always double-check by converting your fraction back to decimal.

Does the position of zeros matter?

Absolutely! 0.022 (twenty-two thousandths) is very different from 0.22 (twenty-two hundredths). The zeros tell you exactly which place value you're working with.

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