Convert Fraction to Decimal: Finding the Decimal Form of 3/10

Q: Why is 0.30 marked as incorrect when it equals 0.3?

While 0.30 mathematically equals 0.3, the question asks for the decimal form. In standard decimal notation, we don't include unnecessary trailing zeros. 0.3 is the simplest correct form.

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

Count the zeros! 10 has 1 zero = 1 decimal place (tenths), 100 has 2 zeros = 2 decimal places (hundredths), and so on. The numerator goes in that decimal place.

Q: What if the fraction doesn't have 10, 100, or 1000 in the denominator?

You'll need to use long division instead. Divide the numerator by the denominator: $ \frac{3}{4} $ means 3 ÷ 4 = 0.75.

Q: Can I always convert fractions to decimals?

Most fractions convert to decimals, but some create repeating decimals like $ \frac{1}{3} = 0.333... $. Fractions with denominators of 10, 100, 1000 always give terminating decimals.

Fraction to Decimal with Powers of Ten

Convert to decimal fraction $\frac{3}{10}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Based on the number of zeros in the denominator, we'll know how many places to move the decimal point to the left:

00:06 There is one zero in the denominator, so we'll move the decimal point one place to the left

00:09 Place the numerator in the appropriate position after the decimal point

00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert to decimal fraction $\frac{3}{10}$

Step-by-step solution

To solve this problem, let's convert the fraction $\frac{3}{10}$ into a decimal.

First, identify the given fraction: $\frac{3}{10}$ .

Since the denominator is 10, a power of 10, the conversion to a decimal is straightforward. The fraction $\frac{3}{10}$ can be interpreted as dividing 3 by 10.

Perform the division: $3 \div 10 = 0.3$ .

This results in the decimal number $0.3$ .

Therefore, the decimal conversion of the fraction $\frac{3}{10}$ is $\mathbf{0.3}$ .

Final Answer

0.3

Key Points to Remember

Essential concepts to master this topic

Rule: When denominator is 10, 100, 1000, decimal conversion is direct
Technique: Place numerator 3 in tenths place to get 0.3
Check: Verify 0.3 × 10 = 3, confirming $\frac{3}{10} = 0.3$ ✓

Common Mistakes

Avoid these frequent errors

Placing digits in wrong decimal places
Don't put 3 in hundredths place to get 0.03! This makes the value 10 times smaller than correct. Always remember: tenths place for denominator 10, hundredths for 100.

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 0.30 marked as incorrect when it equals 0.3?

While 0.30 mathematically equals 0.3, the question asks for the decimal form. In standard decimal notation, we don't include unnecessary trailing zeros. 0.3 is the simplest correct form.

How do I remember which decimal place to use?

Count the zeros! 10 has 1 zero = 1 decimal place (tenths), 100 has 2 zeros = 2 decimal places (hundredths), and so on. The numerator goes in that decimal place.

What if the fraction doesn't have 10, 100, or 1000 in the denominator?

You'll need to use long division instead. Divide the numerator by the denominator: $\frac{3}{4}$ means 3 ÷ 4 = 0.75.

Can I always convert fractions to decimals?

Most fractions convert to decimals, but some create repeating decimals like $\frac{1}{3} = 0.333...$ . Fractions with denominators of 10, 100, 1000 always give terminating decimals.

How do I check if my decimal conversion is correct?

Multiply your decimal answer by the original denominator. If you get the numerator back, you're correct! For example: 0.3 × 10 = 3 ✓

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