Convert 36.105 to a Simplified Decimal Fraction: Step-by-Step Solution

Q: How do I know what denominator to use?

Count the decimal places! In 36.105, there are 3 digits after the decimal point, so use 1000 as your denominator. The pattern is: 1 place = 10, 2 places = 100, 3 places = 1000.

Q: Why do we need to simplify the fraction?

Simplifying gives you the lowest terms, which is the standard form. $ \frac{105}{1000} $ and $ \frac{21}{200} $ are equal, but $ \frac{21}{200} $ is simpler and preferred.

Q: How do I find the GCD to simplify?

Find the greatest number that divides both the numerator and denominator. For 105 and 1000: try 5 (both divisible), so $ \frac{105÷5}{1000÷5} = \frac{21}{200} $.

Q: What if I can't find the GCD easily?

Start with small prime numbers like 2, 3, 5. Try dividing both numbers by each until you find one that works. You can also use the Euclidean algorithm for larger numbers.

Q: Can I check my answer without doing division?

Yes! Convert back to decimal: $ 36\frac{21}{200} $ should equal 36.105. Since $ \frac{21}{200} = \frac{21×5}{200×5} = \frac{105}{1000} = 0.105 $, you get 36.105 ✓

Decimal Conversion with Three-Digit Precision

Convert into a mixed fraction:

$36.105$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's write this as a simplified fraction.

00:09 Divide each number after the decimal by the proper value for each place.

00:16 Next, choose the right denominator to match.

00:20 And don't forget to add thirty-six to it.

00:28 Simplify by dividing both the top and bottom as much as you can.

00:46 And that's how we find the answer.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into a mixed fraction:

$36.105$

Step-by-step solution

Let's write the decimal fraction as a mixed fraction.

Since there are 3 digits after the decimal point, we'll divide 105 by 1000 and 36, as follows:

$36+\frac{105}{1000}$

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 5:

$36+\frac{105:4}{1000:4}=36+\frac{21}{200}=36\frac{21}{200}$

Final Answer

$36\frac{21}{200}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Three decimal digits means denominator is 1000
Technique: Convert 36.105 = 36 + 105/1000, then simplify by GCD
Check: Verify 21/200 = 0.105 by division: 21 ÷ 200 = 0.105 ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator for decimal places
Don't use 100 as denominator for 36.105 = wrong fraction 36 105/100! Three decimal places requires 1000, not 100. Always count decimal digits: 1 digit = 10, 2 digits = 100, 3 digits = 1000.

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 denominator to use?

Count the decimal places! In 36.105, there are 3 digits after the decimal point, so use 1000 as your denominator. The pattern is: 1 place = 10, 2 places = 100, 3 places = 1000.

Why do we need to simplify the fraction?

Simplifying gives you the lowest terms, which is the standard form. $\frac{105}{1000}$ and $\frac{21}{200}$ are equal, but $\frac{21}{200}$ is simpler and preferred.

How do I find the GCD to simplify?

Find the greatest number that divides both the numerator and denominator. For 105 and 1000: try 5 (both divisible), so $\frac{105÷5}{1000÷5} = \frac{21}{200}$ .

What if I can't find the GCD easily?

Start with small prime numbers like 2, 3, 5. Try dividing both numbers by each until you find one that works. You can also use the Euclidean algorithm for larger numbers.

Can I check my answer without doing division?

Yes! Convert back to decimal: $36\frac{21}{200}$ should equal 36.105. Since $\frac{21}{200} = \frac{21×5}{200×5} = \frac{105}{1000} = 0.105$ , you get 36.105 ✓

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