Convert Decimal 1.543 to Simplified Fraction Form

Q: How do I know what denominator to use?

Count the decimal places! 1.543 has 3 decimal places, so use 1000 as denominator. Remember: 1 place = 10, 2 places = 100, 3 places = 1000.

Q: Should I simplify the fraction?

Always check if you can simplify! For $ \frac{543}{1000} $, find the GCD of 543 and 1000. If they share no common factors, it's already in simplest form.

Q: What's the difference between improper and mixed fractions?

A mixed number like $ 1\frac{543}{1000} $ shows whole and fractional parts separately. An improper fraction would be $ \frac{1543}{1000} $ - both are correct!

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

Yes! $ 1.543 = \frac{1543}{1000} $ is also correct. However, the question asks for the answer given, which is the mixed number form.

Q: How can I check if my answer is right?

Convert back to decimal! $ 1\frac{543}{1000} = 1 + \frac{543}{1000} = 1 + 0.543 = 1.543 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's change the decimal into a mixed fraction.

00:07 First, split the number into a whole number and a remainder.

00:11 Next, let's convert that remainder into a fraction.

00:15 Remember, the denominator is based on how many digits follow the decimal.

00:21 Here, we have three digits, so the denominator is one thousand.

00:28 Place those digits in the numerator as a single number.

00:33 Now, combine them together into a mixed fraction.

00:38 And there you have it! That's how you solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Convert 1.543 into a fraction.

2

Step-by-step solution

To convert the decimal 1.543 into a fraction, we'll proceed with the following steps:

Step 1: Identify the fractional part of the number. Here, the number is 1.543, where 1 is the whole number and 0.543 is the decimal part.
Step 2: Convert the decimal part to a fraction. The decimal 0.543 can be expressed as $\frac{543}{1000}$ because it is equivalent to 543 thousandths.
Step 3: Combine the whole number with the fractional part to express the entire decimal as a mixed number. Thus, 1.543 becomes $1\frac{543}{1000}$ .

Therefore, the decimal 1.543 is equivalent to $1\frac{543}{1000}$ as a fraction.

3

Final Answer

$1\frac{543}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Three decimal places means denominator of 1000
Method: Write 1.543 as $1\frac{543}{1000}$ using place value
Check: Convert back: $1\frac{543}{1000} = 1 + 0.543 = 1.543$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't use 100 as denominator for three decimal places = $\frac{1543}{100} = 15.43$ ! This ignores place value rules. Always count decimal places: 3 places means denominator 1000.

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 what denominator to use?

+

Count the decimal places! 1.543 has 3 decimal places, so use 1000 as denominator. Remember: 1 place = 10, 2 places = 100, 3 places = 1000.

Should I simplify the fraction?

+

Always check if you can simplify! For $\frac{543}{1000}$ , find the GCD of 543 and 1000. If they share no common factors, it's already in simplest form.

What's the difference between improper and mixed fractions?

+

A mixed number like $1\frac{543}{1000}$ shows whole and fractional parts separately. An improper fraction would be $\frac{1543}{1000}$ - both are correct!

Can I write this as just an improper fraction?

+

Yes! $1.543 = \frac{1543}{1000}$ is also correct. However, the question asks for the answer given, which is the mixed number form.

How can I check if my answer is right?

+

Convert back to decimal! $1\frac{543}{1000} = 1 + \frac{543}{1000} = 1 + 0.543 = 1.543$ ✓

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