Convert Decimal 0.35 to Simplified Fraction Form

Q: How do I know what denominator to use for the decimal?

Count the decimal places! 0.35 has 2 decimal places, so it goes over 100 (which has 2 zeros). One decimal place = 10, two decimal places = 100, three = 1000, and so on.

Q: Can I convert the decimal a different way?

Yes! You could think of 0.35 as 35 cents out of 100 cents, which is $ \frac{35}{100} $. The place value method always works for any decimal.

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

Divide the numerator by the denominator: $ 7 ÷ 20 = 0.35 $. If you get back to your original decimal, you're right!

Q: What if the GCD is 1?

If the GCD is 1, the fraction is already in simplest form! This means the numerator and denominator have no common factors other than 1.

Decimal Conversion with GCD Simplification

Write 0.35 as a fraction and reduce.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's convert this to a simple fraction.

00:07 First, place the numbers as the numerator.

00:12 Move the decimal point to the right until the number is whole.

00:16 We moved it two times, so the denominator is one hundred.

00:25 Now, let's reduce the fraction as much as we can.

00:34 Factor thirty-five into five and seven, and one hundred into five and twenty.

00:40 Reduce the fraction by canceling common factors.

00:47 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write 0.35 as a fraction and reduce.

Step-by-step solution

To solve this problem, we need to convert the decimal $0.35$ into a fraction and simplify it:

Step 1: Convert the decimal to a fraction. The decimal $0.35$ means that 35 is in the hundredths place. Thus, we write it as $\frac{35}{100}$ .
Step 2: Simplify the fraction $\frac{35}{100}$ by finding the greatest common divisor (GCD) of 35 and 100. The factors of 35 are 1, 5, 7, 35, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common divisor is 5.
Step 3: Divide both the numerator and the denominator by 5:
$\frac{35}{100} = \frac{35 \div 5}{100 \div 5} = \frac{7}{20}$

Therefore, the simplified fraction of $0.35$ is $\frac{7}{20}$ .

Final Answer

$\frac{7}{20}$

Key Points to Remember

Essential concepts to master this topic

Place Value: 0.35 equals 35 hundredths or $\frac{35}{100}$
GCD Method: Find common factors: 35 = 5×7, 100 = 5×20
Verify: Check $\frac{7}{20} = 0.35$ by dividing 7÷20 ✓

Common Mistakes

Avoid these frequent errors

Stopping at the unsimplified fraction
Don't write $\frac{35}{100}$ as your final answer = incomplete solution! The question asks to reduce, so you must find the GCD. Always simplify by dividing both numerator and denominator by their greatest common divisor.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

How do I know what denominator to use for the decimal?

Count the decimal places! 0.35 has 2 decimal places, so it goes over 100 (which has 2 zeros). One decimal place = 10, two decimal places = 100, three = 1000, and so on.

What if I can't find the GCD easily?

Start by listing factors of both numbers, or try dividing by small primes like 2, 3, 5. For $\frac{35}{100}$ , both end in 5 or 0, so try dividing by 5 first!

Can I convert the decimal a different way?

Yes! You could think of 0.35 as 35 cents out of 100 cents, which is $\frac{35}{100}$ . The place value method always works for any decimal.

How do I check if my simplified fraction is correct?

Divide the numerator by the denominator: $7 ÷ 20 = 0.35$ . If you get back to your original decimal, you're right!

What if the GCD is 1?

If the GCD is 1, the fraction is already in simplest form! This means the numerator and denominator have no common factors other than 1.

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