Convert Decimal 1.2: Finding All Equivalent Representations

Q: How do I know if the denominator should be 10 or 100?

Look at the rightmost digit after the decimal point! In 1.2, the digit 2 is in the tenths place (first position), so use denominator 10. If it were 1.20, you'd still use 10 because trailing zeros don't change the value.

Q: Can I simplify the fraction 2/10?

Yes! $ \frac{2}{10} = \frac{1}{5} $ when you divide both numerator and denominator by 2. So $ 1\frac{2}{10} = 1\frac{1}{5} $, but both answers are correct!

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

Count the decimal places! 1.25 has 2 decimal places, so the denominator is 100: $ 1.25 = 1\frac{25}{100} $. The number of decimal places tells you the denominator.

Q: How can I check if my mixed number is right?

Convert it back to a decimal! $ 1\frac{2}{10} $ means 1 + 2÷10 = 1 + 0.2 = 1.2. If you get the original decimal, you're correct!

Decimal to Mixed Number with Tenths

$1.2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Alright, let's convert this to a mixed number.

00:05 First, separate the number into a whole part and a remainder. Ready?

00:11 Next, turn the remainder into a fraction. You can do it!

00:16 Now, combine them to form a mixed number.

00:20 Great job! That's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1.2=$

Step-by-step solution

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

Step 1: Identify the parts of the decimal number $1.2$ .
Step 2: Convert the decimal part to a fraction.
Step 3: Form a mixed number using the integer and the fractional parts.

Now, let's work through each step:
Step 1: The decimal number $1.2$ consists of an integer part $1$ and a decimal part $0.2$ .
Step 2: The decimal $0.2$ translates to the fraction $\frac{2}{10}$ , since the digit 2 is in the tenths place.
Step 3: Combine the integer part $1$ with the fractional part $\frac{2}{10}$ to form the mixed number $1\frac{2}{10}$ .

Therefore, the solution to the problem is $1\frac{2}{10}$ .

Final Answer

$1\frac{2}{10}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: The decimal 0.2 has 2 in the tenths place
Conversion Method: Write 1.2 as 1 + 0.2 = 1 + 2/10
Verification: Convert back: 1 2/10 = 10/10 + 2/10 = 12/10 = 1.2 ✓

Common Mistakes

Avoid these frequent errors

Confusing place value positions when converting decimals
Don't put 0.2 as 2/100 instead of 2/10 = wrong denominator! The digit 2 is in the tenths place (first position after decimal), not hundredths. Always identify the rightmost digit's place value to determine the correct denominator.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

How do I know if the denominator should be 10 or 100?

Look at the rightmost digit after the decimal point! In 1.2, the digit 2 is in the tenths place (first position), so use denominator 10. If it were 1.20, you'd still use 10 because trailing zeros don't change the value.

Why isn't 1 21/10 the correct answer?

That would equal 1 + 21/10 = 1 + 2.1 = 3.1, not 1.2! The fractional part should only represent the decimal portion, which is 0.2 = 2/10.

Can I simplify the fraction 2/10?

Yes! $\frac{2}{10} = \frac{1}{5}$ when you divide both numerator and denominator by 2. So $1\frac{2}{10} = 1\frac{1}{5}$ , but both answers are correct!

What if the decimal has more digits, like 1.25?

Count the decimal places! 1.25 has 2 decimal places, so the denominator is 100: $1.25 = 1\frac{25}{100}$ . The number of decimal places tells you the denominator.

How can I check if my mixed number is right?

Convert it back to a decimal! $1\frac{2}{10}$ means 1 + 2÷10 = 1 + 0.2 = 1.2. If you get the original decimal, you're correct!

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