Complete the Expression: Finding Values Equal to 2.4

Q: Why is the denominator 10 and not 4?

The denominator comes from the decimal place position, not the digit value. Since 4 is in the tenths place, we write it as $\frac{4}{10}$. The digit 4 becomes the numerator!

Q: Do I need to simplify the fraction?

You can simplify $\frac{4}{10}$ to $\frac{2}{5}$, but both forms are correct. The question shows $2\frac{4}{10}$ as the answer, so either form works.

Q: How do I know which part is the whole number?

The whole number part is everything to the left of the decimal point. In 2.4, that's 2. The decimal part (0.4) becomes the fraction part of the mixed number.

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

Use the rightmost decimal place to determine the denominator. For example, 2.35 would be $2\frac{35}{100}$ because 5 is in the hundredths place.

Q: Why can't the answer be 1 and 42/10?

That would equal $1 + \frac{42}{10} = 1 + 4.2 = 5.2$, not 2.4! Always check that your mixed number equals the original decimal when you add the parts together.

Decimal to Mixed Number Conversion

$2.4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's convert this to a mixed number.

00:06 First, break the number into a whole number and its remainder.

00:11 Now, change the remainder into a fraction.

00:16 Combine both parts to create the mixed number.

00:21 And there you have it! That's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2.4=$

Step-by-step solution

To solve this problem, we'll convert the decimal $2.4$ into a mixed number:

Step 1: Identify the integer part and the decimal part of $2.4$ .
The integer part is $2$ , and the decimal part is $0.4$ .
Step 2: Convert the decimal $0.4$ to a fraction.
Decimal $0.4$ is equivalent to $\frac{4}{10}$ because the digit $4$ is in the tenth position.
Step 3: Combine the integer part with the fraction.
The mixed number is $2\frac{4}{10}$ .

Therefore, when $2.4$ is expressed as a mixed number, it is $2\frac{4}{10}$ .

Final Answer

$2\frac{4}{10}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Decimal places determine the denominator of the fraction
Technique: Convert 0.4 to $\frac{4}{10}$ using tenths position
Check: Verify $2\frac{4}{10} = 2 + 0.4 = 2.4$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on digit value
Don't use the digit 4 as the denominator to get $\frac{4}{4}$ = wrong fraction! The decimal position determines the denominator, not the digit itself. Always use 10 for tenths place, 100 for hundredths place.

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

Why is the denominator 10 and not 4?

The denominator comes from the decimal place position, not the digit value. Since 4 is in the tenths place, we write it as $\frac{4}{10}$ . The digit 4 becomes the numerator!

Do I need to simplify the fraction?

You can simplify $\frac{4}{10}$ to $\frac{2}{5}$ , but both forms are correct. The question shows $2\frac{4}{10}$ as the answer, so either form works.

How do I know which part is the whole number?

The whole number part is everything to the left of the decimal point. In 2.4, that's 2. The decimal part (0.4) becomes the fraction part of the mixed number.

What if the decimal has more than one digit?

Use the rightmost decimal place to determine the denominator. For example, 2.35 would be $2\frac{35}{100}$ because 5 is in the hundredths place.

Why can't the answer be 1 and 42/10?

That would equal $1 + \frac{42}{10} = 1 + 4.2 = 5.2$ , not 2.4! Always check that your mixed number equals the original decimal when you add the parts together.

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