Convert Mixed Number to Decimal: 2⅕ Step-by-Step

Q: Why do I multiply both numerator and denominator by 2?

To convert $ \frac{1}{5} $ to decimal form easily, we need a denominator of 10 or 100. Since 5 × 2 = 10, multiplying by 2 gives us $ \frac{2}{10} = 0.2 $.

Q: What if the fraction doesn't convert to a nice decimal?

Some fractions like $ \frac{1}{3} $ give repeating decimals (0.333...). You can either round to a specific number of decimal places or use long division to find the exact decimal representation.

Q: Can I just divide 1 by 5 instead?

Absolutely! Dividing 1 ÷ 5 = 0.2 gives the same result. Both methods work - choose whichever feels easier for you.

Q: How do I know which answer choice is correct?

Calculate the decimal conversion step by step: $ 2\frac{1}{5} = 2 + \frac{1}{5} = 2 + 0.2 = 2.2 $. Then match your result to the given choices.

Q: What's the difference between 2.1 and 2.2?

The difference is 0.1! 2.1 would come from $ 2\frac{1}{10} $, while 2.2 comes from $ 2\frac{1}{5} $. Always double-check your fraction conversion.

Mixed Number Conversion with Decimal Form

$2\frac{1}{5}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's start by converting to a decimal fraction.

00:07 Break it down into a whole number and a fraction.

00:11 We'll change the bottom number, the denominator, to ten.

00:15 Remember to multiply both the top number, the numerator, and the bottom number.

00:24 Now, let's convert the fraction to a decimal.

00:31 Add everything up.

00:40 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2\frac{1}{5}=$

Step-by-step solution

The goal is to convert the mixed number $2\frac{1}{5}$ into its decimal form.

We'll focus first on converting the fractional part, $\frac{1}{5}$ , to a decimal. To do so, it's useful to express $\frac{1}{5}$ as an equivalent fraction with a denominator of 10. Since $5 \times 2 = 10$ , multiply both the numerator and the denominator by 2:

$\frac{1 \times 2}{5 \times 2} = \frac{2}{10}$

This fraction, $\frac{2}{10}$ , can be expressed directly as the decimal $0.2$ .

Now, combine this decimal with the whole number part of the mixed number:

$2 + 0.2 = 2.2$

Therefore, the decimal equivalent of $2\frac{1}{5}$ is $2.2$ .

When comparing with the provided choices, choice 2 correctly corresponds to the decimal $2.2$ .

Final Answer

$2.2$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fraction to decimal then add to whole number
Technique: Express $\frac{1}{5}$ as $\frac{2}{10} = 0.2$
Check: Verify 2 + 0.2 = 2.2 matches the decimal form ✓

Common Mistakes

Avoid these frequent errors

Adding the numerator directly to the whole number
Don't add 2 + 1 = 3! This treats the fraction like a whole number, giving completely wrong results. Always convert the fraction to decimal first, then add: 2 + 0.2 = 2.2.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why do I multiply both numerator and denominator by 2?

To convert $\frac{1}{5}$ to decimal form easily, we need a denominator of 10 or 100. Since 5 × 2 = 10, multiplying by 2 gives us $\frac{2}{10} = 0.2$ .

What if the fraction doesn't convert to a nice decimal?

Some fractions like $\frac{1}{3}$ give repeating decimals (0.333...). You can either round to a specific number of decimal places or use long division to find the exact decimal representation.

Can I just divide 1 by 5 instead?

Absolutely! Dividing 1 ÷ 5 = 0.2 gives the same result. Both methods work - choose whichever feels easier for you.

How do I know which answer choice is correct?

Calculate the decimal conversion step by step: $2\frac{1}{5} = 2 + \frac{1}{5} = 2 + 0.2 = 2.2$ . Then match your result to the given choices.

What's the difference between 2.1 and 2.2?

The difference is 0.1! 2.1 would come from $2\frac{1}{10}$ , while 2.2 comes from $2\frac{1}{5}$ . Always double-check your fraction conversion.

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