Convert Decimal 0.45 to Simplified Fraction Form

Q: How do I know what denominator to use when converting a decimal?

Count the decimal places! For 0.45, there are 2 decimal places, so use $ \frac{45}{100} $ (10² = 100). For 0.375, use $ \frac{375}{1000} $ since there are 3 places.

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

Divide the numerator by the denominator! $ \frac{9}{20} = 9 ÷ 20 = 0.45 $. If you get back to your original decimal, your simplification is correct.

Q: What if the decimal has more than 2 places, like 0.125?

Same process! 0.125 has 3 decimal places, so start with $ \frac{125}{1000} $. Then find the GCD (which is 125) to simplify to $ \frac{1}{8} $.

Q: Why can't I just use the decimal as my answer?

The question specifically asks for a fraction form. Decimals and fractions are different ways to represent the same value, and math problems often require you to express answers in a specific format.

Decimal Conversion with Fraction Simplification

Write 0.45 as a fraction and reduce.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple and reduced fraction

00:03 Place the digits in the numerator

00:09 Move the decimal point right until the number is whole and not decimal

00:12 We moved 2 times, so the denominator will equal 100

00:18 Now let's reduce as much as possible

00:23 Factorize 45 into factors 5 and 9, and 100 into factors 5 and 20

00:27 Reduce what we can

00:32 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

Write 0.45 as a fraction and reduce.

Step-by-step solution

To convert the decimal 0.45 to a fraction, we follow these steps:

Step 1: Express the Decimal as a Fraction
The decimal 0.45 can be expressed as $\frac{45}{100}$ because moving the decimal two places to the right makes the numerator 45, with 100 as the denominator since there are two decimal places.
Step 2: Simplify the Fraction
Identify the greatest common divisor (GCD) of 45 and 100. The divisors of 45 are 1, 3, 5, 9, 15, 45, and the divisors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common divisor is 5.
Step 3: Divide by the GCD
Divide both the numerator and denominator by 5:
$\frac{45}{100} = \frac{45 \div 5}{100 \div 5} = \frac{9}{20}$

Therefore, the simplified fraction corresponding to the decimal 0.45 is $\frac{9}{20}$ .

The correct answer from the choices provided is $\frac{9}{20}$ , which corresponds to choice 2.

Final Answer

$\frac{9}{20}$

Key Points to Remember

Essential concepts to master this topic

Conversion: Place decimal over power of 10 based on decimal places
Technique: For 0.45, use $\frac{45}{100}$ then find GCD of 45 and 100
Check: Convert back: $\frac{9}{20} = 0.45$ by dividing 9 ÷ 20 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction after conversion
Don't leave $\frac{45}{100}$ as your final answer = not fully simplified! The question asks to reduce, and leaving it unsimplified loses points. Always find the GCD and divide both numerator and denominator by it to get the simplest form.

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 when converting a decimal?

Count the decimal places! For 0.45, there are 2 decimal places, so use $\frac{45}{100}$ (10² = 100). For 0.375, use $\frac{375}{1000}$ since there are 3 places.

What's the easiest way to find the GCD of two numbers?

List the factors of both numbers and find the largest one they share. For 45 and 100: factors of 45 are 1, 3, 5, 9, 15, 45 and factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common factor is 5.

How can I check if my simplified fraction is correct?

Divide the numerator by the denominator! $\frac{9}{20} = 9 ÷ 20 = 0.45$ . If you get back to your original decimal, your simplification is correct.

What if the decimal has more than 2 places, like 0.125?

Same process! 0.125 has 3 decimal places, so start with $\frac{125}{1000}$ . Then find the GCD (which is 125) to simplify to $\frac{1}{8}$ .

Why can't I just use the decimal as my answer?

The question specifically asks for a fraction form. Decimals and fractions are different ways to represent the same value, and math problems often require you to express answers in a specific format.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime