Convert 2.6 to a Simplified Fraction: Step-by-Step Solution

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

Count the decimal places! For 2.6, there's 1 decimal place, so use 10. For 2 decimal places (like 2.65), use 100. The pattern is: 1 place = 10, 2 places = 100, 3 places = 1000, etc.

Q: Why do I need to simplify the fraction?

Simplifying gives the simplest form of the fraction, which is the standard way to express answers. $ \frac{6}{10} $ and $ \frac{3}{5} $ are equal, but $ \frac{3}{5} $ is preferred because it uses smaller numbers.

Q: What if the decimal has more than one digit after the decimal point?

The same process works! For example, 3.25 becomes $ 3\frac{25}{100} $, then simplify by dividing both 25 and 100 by their GCD of 25 to get $ 3\frac{1}{4} $.

Q: Can I check my answer by converting back to decimal?

Absolutely! Convert $ 2\frac{3}{5} $ back: divide 3 ÷ 5 = 0.6, then add 2 + 0.6 = 2.6. This matches the original decimal, so your answer is correct!

Decimal to Mixed Fraction with Simplification

Convert into a mixed fraction:

$2.6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Write as a reduced and simplified fraction

00:03 Divide each digit after the decimal point by the division amount it represents

00:08 Place the appropriate denominator

00:11 Remember to add 2

00:17 Reduce as much as possible, make sure to divide both numerator and denominator

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

Convert into a mixed fraction:

$2.6$

Step-by-step solution

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

Since there is one digit after the decimal point, we divide 6 by 10 and add 2, as follows:

$2+\frac{6}{10}$

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 2:

$2+\frac{6:2}{10:2}=2+\frac{3}{5}=2\frac{3}{5}$

Final Answer

$2\frac{3}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place decimal digits over power of 10 based on place value
Technique: Convert $2.6 = 2\frac{6}{10}$ then simplify using GCD
Check: Convert back: $2\frac{3}{5} = 2.6$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fractional part
Don't leave $2\frac{6}{10}$ as final answer = incomplete solution! The fraction 6/10 can be reduced further by dividing both numerator and denominator by their GCD of 2. Always simplify fractions to lowest terms: $\frac{6}{10} = \frac{3}{5}$ .

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 for the decimal part?

Count the decimal places! For 2.6, there's 1 decimal place, so use 10. For 2 decimal places (like 2.65), use 100. The pattern is: 1 place = 10, 2 places = 100, 3 places = 1000, etc.

Why do I need to simplify the fraction?

Simplifying gives the simplest form of the fraction, which is the standard way to express answers. $\frac{6}{10}$ and $\frac{3}{5}$ are equal, but $\frac{3}{5}$ is preferred because it uses smaller numbers.

How do I find the greatest common divisor (GCD)?

List the factors of both numbers and find the largest one they share. For 6 and 10: factors of 6 are 1, 2, 3, 6 and factors of 10 are 1, 2, 5, 10. The largest common factor is 2.

What if the decimal has more than one digit after the decimal point?

The same process works! For example, 3.25 becomes $3\frac{25}{100}$ , then simplify by dividing both 25 and 100 by their GCD of 25 to get $3\frac{1}{4}$ .

Can I check my answer by converting back to decimal?

Absolutely! Convert $2\frac{3}{5}$ back: divide 3 ÷ 5 = 0.6, then add 2 + 0.6 = 2.6. This matches the original decimal, so your answer is correct!

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