Convert Decimal to Fraction: Writing 1.3 as a Proper Fraction

Q: Why is the denominator 10 and not 3?

The denominator comes from the place value, not the digit itself! Since 0.3 has one decimal place, it represents tenths, so the denominator is 10.

Q: What if I had 1.13 instead?

With two decimal places, you'd have hundredths! So 1.13 = $ 1\frac{13}{100} $. The number of decimal places tells you the denominator.

Q: Do I need to simplify the fraction?

$ \frac{3}{10} $ is already in simplest form since 3 and 10 share no common factors. Always check if you can reduce your fraction!

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

Yes! $ 1\frac{3}{10} = \frac{13}{10} $. To convert: multiply the whole number by the denominator, then add the numerator: 1 × 10 + 3 = 13.

Q: How do I remember which place value to use?

Count the decimal places! 1 place = tenths (10), 2 places = hundredths (100), 3 places = thousandths (1000), and so on.

Decimal to Mixed Number Conversion

Write the following as a fraction:

$1.3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's convert the whole number into a mixed fraction.

00:12 Next, change the remainder to a fraction of the same denominator.

00:19 Now, add this fraction back to the mixed number.

00:23 That's it! We have successfully solved the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the following as a fraction:

$1.3=$

Step-by-step solution

To solve this problem, we will convert the decimal $1.3$ into a fraction.

Step 1: Identify the whole number and decimal component. The number $1.3$ consists of the whole number $1$ and the decimal $0.3$ .

Step 2: Convert the decimal $0.3$ to a fraction. The decimal $0.3$ means three-tenths, which is expressed as the fraction $\frac{3}{10}$ .

Step 3: Combine the whole number and the fractional part into a mixed number. The number $0.3$ is converted to $\frac{3}{10}$ , and adding the whole number $1$ gives us the mixed number $1 \frac{3}{10}$ .

Therefore, when the decimal $1.3$ is expressed as a fraction, it is written as $1 \frac{3}{10}$ .

Final Answer

$1\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: The decimal 0.3 means 3 in the tenths place
Technique: Convert 0.3 to $\frac{3}{10}$ then add whole number 1
Check: Convert back: $1\frac{3}{10} = 1 + 0.3 = 1.3$ ✓

Common Mistakes

Avoid these frequent errors

Writing the decimal digit as the denominator
Don't write 1.3 as $1\frac{1}{3}$ = wrong fraction! The 3 in 1.3 is in the tenths place, not thirds. Always use the place value (tenths = 10) as your denominator.

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 3?

The denominator comes from the place value, not the digit itself! Since 0.3 has one decimal place, it represents tenths, so the denominator is 10.

What if I had 1.13 instead?

With two decimal places, you'd have hundredths! So 1.13 = $1\frac{13}{100}$ . The number of decimal places tells you the denominator.

Do I need to simplify the fraction?

$\frac{3}{10}$ is already in simplest form since 3 and 10 share no common factors. Always check if you can reduce your fraction!

Can I write this as an improper fraction instead?

Yes! $1\frac{3}{10} = \frac{13}{10}$ . To convert: multiply the whole number by the denominator, then add the numerator: 1 × 10 + 3 = 13.

How do I remember which place value to use?

Count the decimal places! 1 place = tenths (10), 2 places = hundredths (100), 3 places = thousandths (1000), and so on.

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