Convert Decimal 0.75 to Simplified Fraction Form

Q: How do I know what number to put in the denominator?

Count the decimal places! One decimal place = 10, two decimal places = 100, three decimal places = 1000. Since 0.75 has two decimal places, use 100 as your denominator.

Q: What's the easiest way to find the GCD of 75 and 100?

List the factors! 75: 1, 3, 5, 15, 25, 75 and 100: 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common factor is 25.

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

Divide the numerator by denominator: 3 ÷ 4 = 0.75. If you get back your original decimal, you're right!

Q: What if the decimal has more than 2 places?

0.375 has 3 places → $ \frac{375}{1000} $0.1234 has 4 places → $ \frac{1234}{10000} $Then simplify by finding the GCD!

Decimal to Fraction with Simplification

Write the following decimal as a fraction and simplify:

$0.75$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's change it to a simple fraction and reduce as much as possible.

00:10 Take the digits after the decimal point and write them as a whole number.

00:15 Now, count these digits to find out what the denominator should be.

00:20 Since there are two digits after the decimal point, our denominator is one hundred.

00:25 Next, divide the fraction by its greatest common factor.

00:30 Remember to divide both the numerator and the denominator by this number.

00:35 Now, calculate the quotients to simplify the fraction.

00:39 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following decimal as a fraction and simplify:

$0.75$

Step-by-step solution

Since there are two digits after the decimal point, we divide 75 by 100:

$\frac{75}{100}$

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

In this case, the number is 25, so:

$\frac{75:25}{100:25}=\frac{3}{4}$

Final Answer

$\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Decimal places determine the denominator power of ten
Technique: Two decimal places means divide by 100: $\frac{75}{100}$
Check: Verify by dividing: $\frac{3}{4} = 0.75$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction
Don't leave $\frac{75}{100}$ as your final answer = unsimplified fraction! This isn't wrong but incomplete, like leaving 6/8 instead of 3/4. Always find the GCD and divide both numerator and denominator by it.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I know what number to put in the denominator?

Count the decimal places! One decimal place = 10, two decimal places = 100, three decimal places = 1000. Since 0.75 has two decimal places, use 100 as your denominator.

What's the easiest way to find the GCD of 75 and 100?

List the factors! 75: 1, 3, 5, 15, 25, 75 and 100: 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common factor is 25.

Can I convert 0.75 to a fraction differently?

Yes! You could recognize that 0.75 = 75 cents = 3 quarters = $\frac{3}{4}$ of a dollar. But the standard method using place value works for any decimal.

How do I check if my simplified fraction is correct?

Divide the numerator by denominator: 3 ÷ 4 = 0.75. If you get back your original decimal, you're right!

What if the decimal has more than 2 places?

0.375 has 3 places → $\frac{375}{1000}$
0.1234 has 4 places → $\frac{1234}{10000}$
Then simplify by finding the GCD!

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Convert Decimal 0.75 to Simplified Fraction Form

Decimal to Fraction with Simplification

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know what number to put in the denominator?

What's the easiest way to find the GCD of 75 and 100?

Can I convert 0.75 to a fraction differently?

How do I check if my simplified fraction is correct?

What if the decimal has more than 2 places?

🌟 Unlock Your Math Potential

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