Convert Decimal 7.09: Express in Alternative Number Forms

Q: Why is 0.09 equal to 9/100 and not 9/10?

The decimal 0.09 has two decimal places, which means hundredths. Think of it as 9 out of 100 parts. If it were 9/10, it would be written as 0.9 (one decimal place).

Q: How do I know which denominator to use?

Count the decimal places! One decimal place = tenths (10), two decimal places = hundredths (100), three decimal places = thousandths (1000), and so on.

Q: Can I simplify 9/100 to a smaller fraction?

Yes! Since 9 and 100 share no common factors other than 1, $ \frac{9}{100} $ is already in simplest form. But you could write it as a decimal: 0.09.

Q: What if I need to convert a longer decimal like 7.125?

Same process! 7.125 has three decimal places, so convert 0.125 to $ \frac{125}{1000} $, then simplify to get $ 7\frac{1}{8} $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed number

00:03 Break down the number into whole number and remainder

00:09 Convert the remainder to fraction

00:14 Add to mixed number

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$7.09=$

2

Step-by-step solution

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

Step 1: Identify the whole number part of 7.09.
Step 2: Convert the decimal part to a fraction with a denominator of 100.
Step 3: Combine both parts to form a mixed number.

Now, let's work through each step:

Step 1: The whole number part is 7.

Step 2: Convert the decimal part, 0.09, into a fraction. Since 0.09 is equivalent to 9 hundredths, it can be expressed as $\frac{9}{100}$ .

Step 3: Combine the whole number and the fraction to form the mixed number, which is $7\frac{9}{100}$ .

Therefore, the solution to the problem is $\mathbf{7\frac{9}{100}}$ .

3

Final Answer

$7\frac{9}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Read decimal 7.09 as seven and nine hundredths
Technique: Convert 0.09 directly to $\frac{9}{100}$ using place value
Check: Verify $7\frac{9}{100} = 7 + 0.09 = 7.09$ ✓

Common Mistakes

Avoid these frequent errors

Converting 0.09 to the wrong fraction
Don't convert 0.09 to $\frac{9}{10}$ = wrong place value! This ignores that 0.09 means 9 hundredths, not 9 tenths. Always match the decimal places to the denominator: 2 decimal places = hundredths = 100.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why is 0.09 equal to 9/100 and not 9/10?

+

The decimal 0.09 has two decimal places, which means hundredths. Think of it as 9 out of 100 parts. If it were 9/10, it would be written as 0.9 (one decimal place).

How do I know which denominator to use?

+

Count the decimal places! One decimal place = tenths (10), two decimal places = hundredths (100), three decimal places = thousandths (1000), and so on.

Can I simplify 9/100 to a smaller fraction?

+

Yes! Since 9 and 100 share no common factors other than 1, $\frac{9}{100}$ is already in simplest form. But you could write it as a decimal: 0.09.

What if I need to convert a longer decimal like 7.125?

+

Same process! 7.125 has three decimal places, so convert 0.125 to $\frac{125}{1000}$ , then simplify to get $7\frac{1}{8}$ .

Is there a shortcut for converting decimals to fractions?

+

Yes! Write the decimal digits as the numerator and use a denominator with the same number of zeros as decimal places. Then simplify if possible.

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Convert Decimal 7.09: Express in Alternative Number Forms

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