Convert Decimal to Fraction: Transforming 56.043 into Rational Form

Q: How do I know what denominator to use?

Count the number of digits after the decimal point. In 56.043, there are 3 digits after the decimal, so use thousandths which is 1000 as the denominator.

Q: Do I need to simplify the fraction?

Yes, always check if you can simplify! For $ \frac{43}{1000} $, since 43 is prime and doesn't share factors with 1000, it's already in simplest form.

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

A mixed number like $ 56\frac{43}{1000} $ separates the whole and fractional parts. An improper fraction would be $ \frac{56043}{1000} $. Both are correct!

Q: Can I convert this to a simpler fraction?

Since 43 and 1000 share no common factors (43 is prime), $ 56\frac{43}{1000} $ is already in its simplest form. Always check for common factors first!

Q: How can I check my answer is correct?

Convert back to decimal: $ 56\frac{43}{1000} = 56 + \frac{43}{1000} = 56 + 0.043 = 56.043 $. If you get the original decimal, you're right!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a complex fraction

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

00:14 Convert the remainder to a fraction

00:18 The denominator depends on the number of digits after the decimal point

00:21 There are 3 digits, so the denominator will be 1000

00:28 Place the digits in the numerator as a number

00:32 Combine into a complex fraction

00:37 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

Convert 56.043 into a fraction.

2

Step-by-step solution

To convert the decimal number $56.043$ into a fraction, we'll follow these steps:

Step 1: Isolate the integer and fractional parts of the number.
Step 2: Convert the fractional part to a fraction.
Step 3: Combine the integer and fractional parts into a mixed number.

Let's proceed through these steps:

Step 1: Identify the integer part as $56$ and the decimal part as $0.043$ .

Step 2: Convert $0.043$ to a fraction. Since $0.043$ has three digits after the decimal, this suggests thousandths: $0.043 = \frac{43}{1000}$

Step 3: Combine the integer $56$ with the fractional part: $56 + \frac{43}{1000} = 56\frac{43}{1000}$

Therefore, the solution to the problem is $56\frac{43}{1000}$ .

3

Final Answer

$56\frac{43}{1000}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Count decimal places to determine the denominator power
Technique: Three decimal places means thousandths, so 0.043 = $\frac{43}{1000}$
Check: Verify by converting back: $56\frac{43}{1000} = 56 + 0.043 = 56.043$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't count decimal places incorrectly and use 100 instead of 1000 = $56\frac{43}{100} = 56.43$ not 56.043! The number of decimal places determines the denominator: 3 places means thousandths (1000). Always count carefully: one place = tenths, two places = hundredths, three places = thousandths.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{1}{100}=$

FAQ

Everything you need to know about this question

How do I know what denominator to use?

+

Count the number of digits after the decimal point. In 56.043, there are 3 digits after the decimal, so use thousandths which is 1000 as the denominator.

Do I need to simplify the fraction?

+

Yes, always check if you can simplify! For $\frac{43}{1000}$ , since 43 is prime and doesn't share factors with 1000, it's already in simplest form.

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

+

A mixed number like $56\frac{43}{1000}$ separates the whole and fractional parts. An improper fraction would be $\frac{56043}{1000}$ . Both are correct!

Can I convert this to a simpler fraction?

+

Since 43 and 1000 share no common factors (43 is prime), $56\frac{43}{1000}$ is already in its simplest form. Always check for common factors first!

How can I check my answer is correct?

+

Convert back to decimal: $56\frac{43}{1000} = 56 + \frac{43}{1000} = 56 + 0.043 = 56.043$ . If you get the original decimal, you're right!

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Convert Decimal to Fraction: Transforming 56.043 into Rational Form

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