Convert Decimal 0.505 to Simplified Fraction Form

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

Count the decimal places! 1 place = 10, 2 places = 100, 3 places = 1000. For 0.505, there are 3 digits after the decimal point, so use 1000.

Q: Why do I need to simplify the fraction?

Simplifying gives you the lowest terms, which is the standard mathematical form. $ \frac{101}{200} $ is much cleaner than $ \frac{505}{1000} $ and shows the true relationship.

Q: What if the multiple choice doesn't show the simplified form?

Choose the unsimplified fraction that correctly represents the decimal. In this case, $ \frac{505}{1000} $ is correct even though it can be simplified to $ \frac{101}{200} $.

Q: How can I check if my fraction equals the original decimal?

Divide the numerator by denominator: $ 101 ÷ 200 = 0.505 $. If you get the original decimal, your conversion is correct!

Decimal to Fraction with Three-Digit Places

Convert 0.505 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple fraction

00:03 Move the decimal point right until the number is whole

00:06 In a decimal fraction, the denominator must be some multiple of 10 by 10

00:11 Move the decimal point 3 times to the right

00:14 Therefore we'll add three zeros to the denominator

00:18 Place the digits in the numerator

00:24 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

Convert 0.505 into a fraction.

Step-by-step solution

To convert the decimal 0.505 into a fraction, follow these steps:

Step 1: Recognize that the decimal 0.505 can be expressed as $\frac{505}{1000}$ . This is because there are three digits after the decimal point, so we use 1000 as the denominator.
Step 2: Check if the fraction can be simplified. The greatest common divisor (GCD) of 505 and 1000 is 5. Therefore, we divide both the numerator and the denominator by their GCD to simplify the fraction.
Step 3: Simplifying $\frac{505}{1000}$ , we divide both the numerator and the denominator by 5:
$\frac{505 \div 5}{1000 \div 5} = \frac{101}{200}$
Step 4: The fraction $\frac{101}{200}$ is in its simplest form, as 101 is a prime number, and no further simplification is possible.

Therefore, the decimal 0.505 is equal to the fraction $\frac{505}{1000}$ , which simplifies to $\frac{101}{200}$ .

Given the multiple-choice options, the correct answer based on the problem's form is:

$\frac{505}{1000}$

Final Answer

$\frac{505}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Three decimal places means denominator is 1000
Simplification: Find GCD of 505 and 1000, which is 5
Verification: Convert back: $\frac{101}{200} = 0.505$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator for decimal places
Don't use 100 as denominator for 0.505 = $\frac{505}{100} = 5.05$ ! This gives a completely different value because you're ignoring the third decimal place. Always count decimal places carefully: three places means 1000 in denominator.

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 for any decimal?

Count the decimal places! 1 place = 10, 2 places = 100, 3 places = 1000. For 0.505, there are 3 digits after the decimal point, so use 1000.

Why do I need to simplify the fraction?

Simplifying gives you the lowest terms, which is the standard mathematical form. $\frac{101}{200}$ is much cleaner than $\frac{505}{1000}$ and shows the true relationship.

How do I find the GCD quickly?

Start with small primes like 2, 3, 5. For 505 and 1000, both end in 5 or 0, so try 5 first:

505 ÷ 5 = 101
1000 ÷ 5 = 200

What if the multiple choice doesn't show the simplified form?

Choose the unsimplified fraction that correctly represents the decimal. In this case, $\frac{505}{1000}$ is correct even though it can be simplified to $\frac{101}{200}$ .

How can I check if my fraction equals the original decimal?

Divide the numerator by denominator: $101 ÷ 200 = 0.505$ . If you get the original decimal, your conversion is correct!

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