Convert 0.630 to a Simplified Fraction: Step-by-Step Solution

Q: Why do I put 630 over 1000 for 0.630?

The decimal 0.630 has 3 digits after the decimal point, so the denominator is 10³ = 1000. The numerator is the decimal without the decimal point: 630.

Q: How do I find the greatest common divisor (GCD)?

List the factors of both numbers or use the division method. For 630 and 1000: both divide by 10, giving $ \frac{63}{100} $. Since 63 and 100 share no common factors, we're done!

Q: What if the decimal ends in zeros like 0.630?

Treat trailing zeros like any other digit! 0.630 still has 3 decimal places, so use 1000 as denominator. The simplification step will handle any unnecessary complexity.

Q: Can I remove the zero from 0.630 to make it 0.63?

Yes! 0.630 and 0.63 represent the same value. You can work with 0.63 = $ \frac{63}{100} $ directly, which is already simplified.

Decimal to Fraction with Simplification

Write the following decimal fraction as a simple fraction and simplify:

$0.630$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's start by writing the number as a simple fraction.

00:11 Next, divide each digit after the decimal point by the value it represents, like tenths or hundredths.

00:19 Now, place the correct denominator to match that value.

00:24 Finally, reduce the fraction as much as possible by dividing both the numerator and denominator by their greatest common factor.

00:39 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following decimal fraction as a simple fraction and simplify:

$0.630$

Step-by-step solution

Since there are three digits after the decimal point, we divide 630 by 1000:

$\frac{630}{1000}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 10, so:

$\frac{630:10}{1000:10}=\frac{63}{100}$

Final Answer

$\frac{63}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Count decimal places to determine denominator power of 10
Technique: 0.630 = 630/1000, then find GCD of 630 and 1000
Check: Verify 63/100 = 0.63 by dividing 63 ÷ 100 = 0.63 ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction completely
Don't stop at 630/1000 without simplifying = unsimplified answer! This leaves the fraction in its most complex form when a simpler equivalent exists. Always find the GCD and divide both numerator and denominator by it.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

Why do I put 630 over 1000 for 0.630?

The decimal 0.630 has 3 digits after the decimal point, so the denominator is 10³ = 1000. The numerator is the decimal without the decimal point: 630.

How do I find the greatest common divisor (GCD)?

List the factors of both numbers or use the division method. For 630 and 1000: both divide by 10, giving $\frac{63}{100}$ . Since 63 and 100 share no common factors, we're done!

What if the decimal ends in zeros like 0.630?

Treat trailing zeros like any other digit! 0.630 still has 3 decimal places, so use 1000 as denominator. The simplification step will handle any unnecessary complexity.

Can I remove the zero from 0.630 to make it 0.63?

Yes! 0.630 and 0.63 represent the same value. You can work with 0.63 = $\frac{63}{100}$ directly, which is already simplified.

How do I check if my fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator have no common factors except 1. For $\frac{63}{100}$ , since 63 = 3² × 7 and 100 = 2² × 5², they share no common factors.

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