Express 1.09: Converting Decimal to Different Number Forms

Q: How do I know which denominator to use?

Count the decimal places! One decimal place means tenths (denominator 10), two decimal places means hundredths (denominator 100). Since 1.09 has two decimal places, use 100.

Q: Why is the answer not 1 3/10?

Because 0.09 is not the same as 0.3! The digit 9 is in the hundredths place, making it $ \frac{9}{100} $, not $ \frac{3}{10} $.

Q: How can I double-check my answer?

Convert your mixed number back to decimal: $ 1\frac{9}{100} = 1 + \frac{9}{100} = 1 + 0.09 = 1.09 $. If you get the original decimal, you're correct!

Q: What if the decimal has more places, like 1.009?

Use the same method! Count decimal places: three places means thousandths, so 1.009 = $ 1\frac{9}{1000} $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's convert the number to a mixed fraction.

00:06 First, divide to find the whole number and the remainder.

00:10 Next, turn the remainder into a fraction.

00:17 Now, add them together to get a mixed fraction.

00:21 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$1.09=$

2

Step-by-step solution

To solve the problem of converting the decimal $1.09$ into a mixed number, we proceed with the following steps:

Step 1: Identify that the whole number part is $1$ .
Step 2: Convert the decimal part $0.09$ to a fraction. As the digit 9 is in the hundredth place, $0.09$ is equivalent to $\frac{9}{100}$ .
Step 3: Combine the whole number and fractional parts to form the mixed number: $1 \frac{9}{100}$ .

Consequently, by converting $1.09$ into a mixed number, we obtain the result: $1\frac{9}{100}$ .

Among the provided choices, the correct answer is:

$1\frac{9}{100}$

3

Final Answer

$1\frac{9}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Identify whole number and decimal parts separately
Technique: Convert 0.09 to $\frac{9}{100}$ using hundredths place
Check: Verify $1\frac{9}{100} = 1 + 0.09 = 1.09$ ✓

Common Mistakes

Avoid these frequent errors

Converting decimal part to wrong denominator
Don't convert 0.09 to $\frac{9}{10}$ = wrong place value! The 9 is in the hundredths place, not tenths, so it represents 9 out of 100 parts. Always count decimal places to determine the correct denominator.

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 which denominator to use?

+

Count the decimal places! One decimal place means tenths (denominator 10), two decimal places means hundredths (denominator 100). Since 1.09 has two decimal places, use 100.

Why is the answer not 1 3/10?

+

Because 0.09 is not the same as 0.3! The digit 9 is in the hundredths place, making it $\frac{9}{100}$ , not $\frac{3}{10}$ .

Do I need to simplify the fraction 9/100?

+

Check if 9 and 100 have common factors. Since 9 = 3×3 and 100 = 4×25, they share no common factors, so $\frac{9}{100}$ is already in simplest form.

How can I double-check my answer?

+

Convert your mixed number back to decimal: $1\frac{9}{100} = 1 + \frac{9}{100} = 1 + 0.09 = 1.09$ . If you get the original decimal, you're correct!

What if the decimal has more places, like 1.009?

+

Use the same method! Count decimal places: three places means thousandths, so 1.009 = $1\frac{9}{1000}$ .

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Express 1.09: Converting Decimal to Different Number Forms

Decimal to Mixed Number with Hundredths

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