Convert 6.9 to a Simplified Fraction: Decimal to Fraction Exercise

Q: What if the decimal has more digits after the decimal point?

Count the decimal places! For example, 6.75 has two decimal places, so write it as $ 6\frac{75}{100} $, then simplify to $ 6\frac{3}{4} $.

Q: How do I know what denominator to use?

The denominator is always a power of 10 based on decimal places: 1 place = 10, 2 places = 100, 3 places = 1000, and so on.

Q: Can I write this as an improper fraction instead?

Yes! $ 6\frac{9}{10} $ equals $ \frac{69}{10} $. Multiply the whole number by the denominator and add the numerator: 6 × 10 + 9 = 69.

Q: What's the difference between a mixed number and improper fraction?

A mixed number like $ 6\frac{9}{10} $ shows the whole and fractional parts separately. An improper fraction like $ \frac{69}{10} $ has a numerator larger than the denominator.

Decimal to Fraction with Mixed Numbers

Write the following decimal fraction as an imaginary fraction and simplify:

$6.9$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's start by writing it as a reduced and simplified fraction.

00:11 Now, divide each digit after the decimal point by what it represents.

00:16 Then, place the correct denominator.

00:19 Don't forget to add six.

00:22 And that's the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following decimal fraction as an imaginary fraction and simplify:

$6.9$

Step-by-step solution

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

Since there is one digit after the decimal point, we'll divide 9 by 10 and add 6, as follows:

$6+\frac{9}{10}$

Since it can't be simplified further, the answer is:

$6\frac{9}{10}$

Final Answer

$6\frac{9}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place decimal digits over appropriate power of ten
Technique: For 6.9, separate whole part 6 and write 9/10
Check: Convert back: 6 + 9/10 = 6.9 ✓

Common Mistakes

Avoid these frequent errors

Trying to simplify 9/10
Don't try to reduce 9/10 to a smaller fraction = impossible and wrong! Since 9 and 10 share no common factors (9 = 3×3, 10 = 2×5), the fraction is already in simplest form. Always check if numerator and denominator have common factors before simplifying.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

Why can't I simplify 9/10 further?

To simplify a fraction, the numerator and denominator must share a common factor. Since 9 = 3 × 3 and 10 = 2 × 5, they have no shared factors, so $\frac{9}{10}$ is already simplified!

What if the decimal has more digits after the decimal point?

Count the decimal places! For example, 6.75 has two decimal places, so write it as $6\frac{75}{100}$ , then simplify to $6\frac{3}{4}$ .

How do I know what denominator to use?

The denominator is always a power of 10 based on decimal places: 1 place = 10, 2 places = 100, 3 places = 1000, and so on.

Can I write this as an improper fraction instead?

Yes! $6\frac{9}{10}$ equals $\frac{69}{10}$ . Multiply the whole number by the denominator and add the numerator: 6 × 10 + 9 = 69.

What's the difference between a mixed number and improper fraction?

A mixed number like $6\frac{9}{10}$ shows the whole and fractional parts separately. An improper fraction like $\frac{69}{10}$ has a numerator larger than the denominator.

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