Convert Decimal 4.27 to a Fraction: Step-by-Step Solution

Q: How do I know what denominator to use?

Count the decimal places! One decimal place (like 0.3) uses 10, two decimal places (like 0.27) uses 100, three places uses 1000, and so on.

Q: What's the difference between a mixed number and improper fraction?

A mixed number like $ 4\frac{27}{100} $ shows the whole number separately. An improper fraction would be $ \frac{427}{100} $ - both are correct!

Q: What if the decimal has more than 2 places?

Same process! For example, 4.275 becomes $ 4\frac{275}{1000} $ because there are 3 decimal places, so the denominator is 1000.

Q: Can I write this as just a fraction without the whole number?

Absolutely! $ 4\frac{27}{100} $ equals $ \frac{427}{100} $. To convert: multiply whole number by denominator, then add numerator: (4 × 100) + 27 = 427.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's change it into a mixed fraction.

00:09 First, convert it to a fraction.

00:13 Remember, the denominator is based on how many digits are after the decimal point.

00:19 Since there are two digits, the denominator is one hundred.

00:23 Now, place the digits as a whole number in the numerator.

00:28 Let's break down four hundred twenty-seven into four hundred plu s twenty-seven.

00:33 Next, split the fraction into two fractions: the whole part and the re mainder.

00:44 Reduce the fractions as much as you can.

00:54 Combine them into a mixed fraction.

00:59 And that's how you find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Convert 4.27 into a fraction.

2

Step-by-step solution

To convert the decimal 4.27 into a fraction, follow these steps:

Step 1: Identify the whole number and decimal separately.
The given number is 4.27, where 4 is the whole number, and 0.27 is the decimal part.
Step 2: Convert the decimal part into a fraction.
The decimal 0.27 can be written as $\frac{27}{100}$ because the "7" is in the hundredths place. Therefore, 0.27 is equivalent to $\frac{27}{100}$ .
Step 3: Combine the whole number and the fraction.
Since the whole number is 4, the mixed number combining these components is $4\frac{27}{100}$ .

Therefore, 4.27 as a fraction is $4\frac{27}{100}$ .

The correct answer among the choices provided is choice 1: $4\frac{27}{100}$ .

3

Final Answer

$4\frac{27}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Identify decimal places to determine denominator power
Technique: 4.27 = 4 + 0.27 = 4 + 27/100
Check: Convert back: 4 27/100 = 4.27 ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator for decimal place
Don't put 0.27 as 27/10 = wrong place value! The 7 is in hundredths place, not tenths, giving you 2.7 instead of 0.27. Always count decimal places: one place = tenths, two places = hundredths.

Practice Quiz

Test your knowledge with interactive questions

What part of the whole does the shaded (blue) area represent?

FAQ

Everything you need to know about this question

How do I know what denominator to use?

+

Count the decimal places! One decimal place (like 0.3) uses 10, two decimal places (like 0.27) uses 100, three places uses 1000, and so on.

What's the difference between a mixed number and improper fraction?

+

A mixed number like $4\frac{27}{100}$ shows the whole number separately. An improper fraction would be $\frac{427}{100}$ - both are correct!

Do I need to simplify the fraction part?

+

Yes, if possible! Check if the numerator and denominator share common factors. For $\frac{27}{100}$ , since 27 and 100 don't share factors, it's already simplified.

What if the decimal has more than 2 places?

+

Same process! For example, 4.275 becomes $4\frac{275}{1000}$ because there are 3 decimal places, so the denominator is 1000.

Can I write this as just a fraction without the whole number?

+

Absolutely! $4\frac{27}{100}$ equals $\frac{427}{100}$ . To convert: multiply whole number by denominator, then add numerator: (4 × 100) + 27 = 427.

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Convert Decimal 4.27 to a Fraction: Step-by-Step Solution

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