Convert Decimal 0.3 to Fraction: Step-by-Step Solution

Q: Why is the denominator 10 and not 100?

The denominator depends on the number of decimal places. Since 0.3 has one decimal place, it's in the tenths position, so we use 10 as the denominator.

Q: How do I remember which denominator to use?

Count the decimal places: 1 place = 10, 2 places = 100, 3 places = 1000. Each additional place adds another zero to the denominator!

Q: Should I simplify the fraction further?

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

Q: What if I get confused between 3/10 and 30/10?

Remember: $ \frac{30}{10} = 3 $ (a whole number), but $ \frac{3}{10} = 0.3 $ (a decimal). The numerator should match the digits after the decimal point.

Q: Can I convert back to check my answer?

Yes! Divide the numerator by denominator: 3 ÷ 10 = 0.3. If you get back your original decimal, your fraction is correct!

Decimal to Fraction with Place Value

Convert 0.3 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's convert this decimal into a simple fraction.

00:06 Move the decimal point right until the number becomes whole.

00:10 Remember, for a decimal fraction, the bottom number or denominator, is a power of ten.

00:17 We moved the decimal one place, so we add one zero to the denominator.

00:22 Next, write the digits of the number on the top or numerator.

00:27 And there you have it, that's how you find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert 0.3 into a fraction.

Step-by-step solution

To solve this problem, let's convert the decimal 0.3 into a fraction:

Step 1: Identify the place value of 0.3.
Since the decimal 0.3 has one digit after the decimal point, it is in the tenths place. This means that 0.3 is equivalent to 3 tenths, or $\frac{3}{10}$ .
Step 2: Write the fraction based on the place value:
The decimal 0.3 is expressed as $\frac{3}{10}$ , where 3 is the numerator and 10 is the denominator, reflective of the tenths place.
Step 3: Verify the answer using multiple-choice options:
Among the choices provided, $\frac{3}{10}$ is the correct match, which corresponds to choice 3.

Therefore, the correct fraction representation for 0.3 is $\frac{3}{10}$ .

Final Answer

$\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: One decimal place means tenths denomination
Technique: 0.3 = 3 tenths = $\frac{3}{10}$
Check: Divide 3 ÷ 10 = 0.3 to verify fraction is correct ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on numerator value
Don't use 100 as denominator just because you see 3 in the numerator = $\frac{3}{100}$ = 0.03, not 0.3! The denominator must match the decimal place value. Always use 10 for one decimal place, 100 for two decimal places.

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 100?

The denominator depends on the number of decimal places. Since 0.3 has one decimal place, it's in the tenths position, so we use 10 as the denominator.

How do I remember which denominator to use?

Count the decimal places: 1 place = 10, 2 places = 100, 3 places = 1000. Each additional place adds another zero to the denominator!

Should I simplify the fraction further?

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

What if I get confused between 3/10 and 30/10?

Remember: $\frac{30}{10} = 3$ (a whole number), but $\frac{3}{10} = 0.3$ (a decimal). The numerator should match the digits after the decimal point.

Can I convert back to check my answer?

Yes! Divide the numerator by denominator: 3 ÷ 10 = 0.3. If you get back your original decimal, your fraction is correct!

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