Convert 0.021 to Fraction: Decimal Transformation Exercise

Q: How do I know what denominator to use?

Count the total number of digits after the decimal point. Each place value gives you a power of 10: 1 place = 10, 2 places = 100, 3 places = 1000, and so on.

Q: Why do we remove the leading zeros in the numerator?

Leading zeros don't change the value! $ \frac{021}{1000} $ is the same as $ \frac{21}{1000} $. We remove them to simplify the fraction's appearance.

Q: What if the decimal has trailing zeros like 0.210?

Trailing zeros after the decimal point do matter for place value! 0.210 has 3 decimal places, so it becomes $ \frac{210}{1000} = \frac{21}{100} $ after simplifying.

Decimal Conversion with Three-Digit Place Values

Convert into fraction form:

$0.021=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to fraction

00:03 First, we'll match the digit positions with the appropriate division

00:08 We'll place the number in the numerator, and the last digit position in the denominator

00:13 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:

$0.021=$

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:

$\frac{0021}{1000}$

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

$\frac{21}{1000}$

Final Answer

$\frac{21}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Count decimal places to find denominator power
Technique: 0.021 has 3 places, so use 1000: $\frac{21}{1000}$
Check: Divide 21 ÷ 1000 = 0.021 to verify conversion ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't count only non-zero digits = wrong denominator! If you use 100 instead of 1000 for 0.021, you get $\frac{21}{100} = 0.21$ which is wrong. Always count ALL decimal places from the decimal point.

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

How do I know what denominator to use?

Count the total number of digits after the decimal point. Each place value gives you a power of 10: 1 place = 10, 2 places = 100, 3 places = 1000, and so on.

Why do we remove the leading zeros in the numerator?

Leading zeros don't change the value! $\frac{021}{1000}$ is the same as $\frac{21}{1000}$ . We remove them to simplify the fraction's appearance.

Can I simplify this fraction further?

Check if the numerator and denominator share common factors. For $\frac{21}{1000}$ , since 21 = 3×7 and 1000 = 2³×5³, they share no common factors, so it's already in lowest terms.

What if the decimal has trailing zeros like 0.210?

Trailing zeros after the decimal point do matter for place value! 0.210 has 3 decimal places, so it becomes $\frac{210}{1000} = \frac{21}{100}$ after simplifying.

How can I double-check my answer?

Divide the numerator by the denominator using long division or a calculator. If you get back to your original decimal, your conversion is correct!

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