Complete the Numerical Expression: 7.3 = ?

Q: How do I know what denominator to use?

The decimal place position tells you! The first digit after the decimal point is tenths, so use 10 as your denominator. The second digit would be hundredths (denominator 100).

Q: Why is 7.3 not equal to 7 3/100?

Because 7.3 means seven and three-tenths, not three-hundredths! $ \frac{3}{100} = 0.03 $, which is much smaller than $ \frac{3}{10} = 0.3 $.

Q: Do I need to simplify the fraction part?

Yes, always simplify when possible! However, $ \frac{3}{10} $ is already in lowest terms since 3 and 10 share no common factors except 1.

Q: Can I convert this back to check my answer?

Absolutely! Convert $ 7\frac{3}{10} $ back: 7 + 3 ÷ 10 = 7 + 0.3 = 7.3. This confirms your mixed number is correct!

Q: What if the decimal has more digits like 7.35?

Count the decimal places! 7.35 has two decimal places, so it becomes $ 7\frac{35}{100} $, which simplifies to $ 7\frac{7}{20} $.

Decimal to Mixed Number Conversion

$7.3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed fraction

00:03 Break down the number into whole number and remainder

00:07 Convert the remainder to a fraction

00:13 Combine into mixed fraction

00:18 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$7.3=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the decimal and its components.
Step 2: Convert the decimal part to a fraction.
Step 3: Combine the whole number and fraction into a mixed number.

Now, let's work through each step:
Step 1: The given decimal is $7.3$ . This can be separated into the whole number $7$ and the decimal fraction $.3$ .
Step 2: To convert $.3$ into a fraction, we observe that it represents three tenths, which is $\frac{3}{10}$ .
Step 3: Combine the whole number and the fractional part to form a mixed number. Thus, $7.3$ becomes $7\frac{3}{10}$ as a mixed number.

Therefore, the solution to the problem is $7\frac{3}{10}$ .

Final Answer

$7\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Decimal position determines the fraction denominator
Technique: Convert 0.3 to 3/10 by reading three-tenths
Check: Verify $7\frac{3}{10} = 7 + \frac{3}{10} = 7.3$ ✓

Common Mistakes

Avoid these frequent errors

Misreading decimal place values
Don't convert 7.3 to 7 3/100 = 7.03! This happens when you confuse tenths and hundredths place values. Always read the decimal carefully - 0.3 is in the tenths place, so it equals 3/10.

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?

The decimal place position tells you! The first digit after the decimal point is tenths, so use 10 as your denominator. The second digit would be hundredths (denominator 100).

Why is 7.3 not equal to 7 3/100?

Because 7.3 means seven and three-tenths, not three-hundredths! $\frac{3}{100} = 0.03$ , which is much smaller than $\frac{3}{10} = 0.3$ .

Do I need to simplify the fraction part?

Yes, always simplify when possible! However, $\frac{3}{10}$ is already in lowest terms since 3 and 10 share no common factors except 1.

Can I convert this back to check my answer?

Absolutely! Convert $7\frac{3}{10}$ back: 7 + 3 ÷ 10 = 7 + 0.3 = 7.3. This confirms your mixed number is correct!

What if the decimal has more digits like 7.35?

Count the decimal places! 7.35 has two decimal places, so it becomes $7\frac{35}{100}$ , which simplifies to $7\frac{7}{20}$ .

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