Complete the Decimal Expression: 1.3 = ?

Q: Why is the denominator 10 and not 100?

The denominator depends on the place value of the last digit! Since 3 is in the tenths place (first digit after decimal), the denominator is 10. If it were in hundredths place, then you'd use 100.

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

The whole number part is everything before the decimal point. In 1.3, the whole number is 1. In 5.7, it would be 5. Easy!

Q: Do I need to simplify the fraction?

Yes! Always check if you can simplify. In this case, $ \frac{3}{10} $ is already in lowest terms because 3 and 10 share no common factors other than 1.

Q: What if the decimal has more digits like 1.25?

Count the decimal places! 1.25 has two decimal places, so it becomes $ 1\frac{25}{100} = 1\frac{1}{4} $ after simplifying.

Q: Can I convert any decimal to a mixed number?

Yes! Any decimal with a whole number part greater than 1 can become a mixed number. Just remember: whole part + decimal part as a fraction.

Decimal to Mixed Number Conversion

$1.3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Let's change it to a mixed number.

00:05 First, separate the whole number from the remainder.

00:09 Now, turn that remainder into a fraction.

00:13 Next, put them together to form a mixed number.

00:17 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1.3=$

Step-by-step solution

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

Step 1: Identify the integer and decimal parts of $1.3$ .
Step 2: Convert the decimal $0.3$ to a fraction.
Step 3: Combine the integer and fractional parts into a mixed number.

Let’s work through each step:
Step 1: The integer part of $1.3$ is $1$ , and the decimal part is $0.3$ .
Step 2: The decimal $0.3$ can be converted to the fraction $\frac{3}{10}$ because it signifies three-tenths.
Step 3: Combining the integer part with the fractional part, we get the mixed number $1\frac{3}{10}$ .

Therefore, the solution to the problem is $1\frac{3}{10}$ .

Final Answer

$1\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Separate decimal into whole number and fractional parts
Technique: Convert 0.3 to $\frac{3}{10}$ using place value
Check: Verify $1\frac{3}{10} = 1 + \frac{3}{10} = 1.3$ ✓

Common Mistakes

Avoid these frequent errors

Writing the decimal digits directly as numerator over 100
Don't write 1.3 as $1\frac{30}{100}$ or $1\frac{30}{10}$ = wrong fraction! The decimal 0.3 means 3 tenths, not 30 tenths. Always use the place value: tenths place means denominator 10.

Practice Quiz

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How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

Why is the denominator 10 and not 100?

The denominator depends on the place value of the last digit! Since 3 is in the tenths place (first digit after decimal), the denominator is 10. If it were in hundredths place, then you'd use 100.

How do I know what the whole number part is?

The whole number part is everything before the decimal point. In 1.3, the whole number is 1. In 5.7, it would be 5. Easy!

Do I need to simplify the fraction?

Yes! Always check if you can simplify. In this case, $\frac{3}{10}$ is already in lowest terms because 3 and 10 share no common factors other than 1.

What if the decimal has more digits like 1.25?

Count the decimal places! 1.25 has two decimal places, so it becomes $1\frac{25}{100} = 1\frac{1}{4}$ after simplifying.

Can I convert any decimal to a mixed number?

Yes! Any decimal with a whole number part greater than 1 can become a mixed number. Just remember: whole part + decimal part as a fraction.

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