Complete the Decimal Expression: Finding the Value of 1.9

Q: How do I know what denominator to use?

Look at the decimal place! One digit after the decimal point = tenths = denominator 10. Two digits = hundredths = denominator 100. The 9 in 1.9 is in the tenths place, so use 10.

Q: What if the fraction can be simplified?

Always simplify! For example, if you got $ \frac{5}{10} $, reduce it to $ \frac{1}{2} $. But $ \frac{9}{10} $ is already in lowest terms since 9 and 10 share no common factors.

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

Yes! $ 1.9 = 1\frac{9}{10} = \frac{19}{10} $. To convert: multiply whole number by denominator, then add numerator: (1 × 10) + 9 = 19, so $ \frac{19}{10} $.

Q: How do I check my answer is correct?

Convert your mixed number back to decimal: $ 1\frac{9}{10} = 1 + \frac{9}{10} = 1 + 0.9 = 1.9 $ ✓. If you get the original decimal, you're right!

Decimal to Mixed Number with Tenths

$1.9=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Let's convert this to a mixed fraction.

00:05 First, break the number into a whole number and a remainder.

00:09 Now, turn the remainder into a fraction.

00:17 Add this fraction to the whole number to make a mixed fraction.

00:22 Great job! That's the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1.9=$

Step-by-step solution

We are tasked with converting the decimal number $1.9$ into a mixed number.

Step 1: Identify the whole number part of $1.9$ . The digit to the left of the decimal point is $1$ .
Step 2: Identify the fractional part of $1.9$ . The digit to the right of the decimal point is $9$ . This represents $\frac{9}{10}$ .
Step 3: Combine the whole number and the fractional part to form a mixed number. Therefore, $1.9 = 1\frac{9}{10}$ .

Hence, the mixed number equivalent of the decimal $1.9$ is $1\frac{9}{10}$ .

Final Answer

$1\frac{9}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Whole number stays same, decimal becomes fraction over power of 10
Technique: 0.9 means 9 tenths, so write as $\frac{9}{10}$
Check: Convert back: $1\frac{9}{10} = 1 + 0.9 = 1.9$ ✓

Common Mistakes

Avoid these frequent errors

Writing the decimal digits as any fraction denominator
Don't write 1.9 as $1\frac{9}{100}$ or $1\frac{9}{9}$ = wrong value! The decimal place determines the denominator: tenths place means denominator 10. Always use the place value: 0.9 is 9 tenths, so $\frac{9}{10}$ .

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

How do I know what denominator to use?

Look at the decimal place! One digit after the decimal point = tenths = denominator 10. Two digits = hundredths = denominator 100. The 9 in 1.9 is in the tenths place, so use 10.

What if the fraction can be simplified?

Always simplify! For example, if you got $\frac{5}{10}$ , reduce it to $\frac{1}{2}$ . But $\frac{9}{10}$ is already in lowest terms since 9 and 10 share no common factors.

Can I write this as an improper fraction instead?

Yes! $1.9 = 1\frac{9}{10} = \frac{19}{10}$ . To convert: multiply whole number by denominator, then add numerator: (1 × 10) + 9 = 19, so $\frac{19}{10}$ .

Why isn't the answer just 1 or 19?

Because 1.9 is between 1 and 2! The whole number part is 1, but there's still 0.9 left over. That leftover becomes the fraction $\frac{9}{10}$ , giving us $1\frac{9}{10}$ .

How do I check my answer is correct?

Convert your mixed number back to decimal: $1\frac{9}{10} = 1 + \frac{9}{10} = 1 + 0.9 = 1.9$ ✓. If you get the original decimal, you're right!

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