Convert 0.350 to a Simplified Fraction: Step-by-Step Solution

Q: How do I know what power of 10 to use in the denominator?

Count the decimal places! For 0.350, there are 3 decimal places, so use 1000 (which is $ 10^3 $). For 2 decimal places, use 100.

Q: What if the decimal ends in zero like 0.350?

The trailing zero doesn't change the value! 0.350 = 0.35, so you can ignore it. Just remember to count all digits when placing over the power of 10.

Q: Can I simplify step by step instead of finding the GCD?

Yes! Divide by small common factors first: $ \frac{350}{1000} = \frac{35}{100} = \frac{7}{20} $. Just make sure you reach the simplest form.

Q: How do I check if my fraction is fully simplified?

The numerator and denominator should have no common factors except 1. For $ \frac{7}{20} $, 7 is prime and doesn't divide 20, so it's fully simplified!

Decimal to Fraction with Simplification

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

$0.350$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's write this as a simple and reduced fraction.

00:11 To begin, divide each digit after the decimal by the place value it represents.

00:17 Next, write the fraction with the correct denominator.

00:23 Now, reduce it as much as possible by dividing both the numerator and the denominator.

00:36 And there you have it, that's the solution!

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:

$0.350$

Step-by-step solution

Since there are three digits after the decimal point, we divide 350 by 1000:

$\frac{350}{1000}$

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

In this case, the number is 50, so:

$\frac{350:50}{1000:50}=\frac{7}{20}$

Final Answer

$\frac{7}{20}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place decimal digits over power of ten based on decimal places
Technique: 0.350 = 350/1000, then find GCD of 350 and 1000
Check: Verify 7/20 = 0.35 by dividing 7 ÷ 20 = 0.35 ✓

Common Mistakes

Avoid these frequent errors

Stopping at the unsimplified fraction
Don't leave your answer as 350/1000 = it's not fully simplified! This makes your fraction unnecessarily complex and won't match answer choices. 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

How do I know what power of 10 to use in the denominator?

Count the decimal places! For 0.350, there are 3 decimal places, so use 1000 (which is $10^3$ ). For 2 decimal places, use 100.

What if the decimal ends in zero like 0.350?

The trailing zero doesn't change the value! 0.350 = 0.35, so you can ignore it. Just remember to count all digits when placing over the power of 10.

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

List the factors of both numbers and find the largest one they share. For 350 and 1000: factors include 2, 5, 10, 25, 50... The GCD is 50.

Can I simplify step by step instead of finding the GCD?

Yes! Divide by small common factors first: $\frac{350}{1000} = \frac{35}{100} = \frac{7}{20}$ . Just make sure you reach the simplest form.

How do I check if my fraction is fully simplified?

The numerator and denominator should have no common factors except 1. For $\frac{7}{20}$ , 7 is prime and doesn't divide 20, so it's fully simplified!

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