To express the decimal number [tex]\( 3.56 \)[/tex] as a fraction, we need to follow the process of converting it and then simplifying the fraction if necessary.
### Step-by-Step Solution:
1. Understanding the decimal:
The decimal number given is [tex]\( 3.56 \)[/tex].
2. Separate the integer and decimal parts:
[tex]\( 3.56 \)[/tex] can be separated into its integer part [tex]\( 3 \)[/tex] and its decimal part [tex]\( 0.56 \)[/tex].
3. Express the decimal part as a fraction:
To convert [tex]\( 0.56 \)[/tex] into a fraction, consider it has two decimal places.
Therefore, [tex]\( 0.56 \)[/tex] can be written as:
[tex]\[
0.56 = \frac{56}{100}
\][/tex]
4. Simplify the fraction:
We need to simplify [tex]\(\frac{56}{100}\)[/tex] by finding the greatest common divisor (GCD) of 56 and 100.
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The greatest common divisor is 4.
Dividing the numerator and the denominator by their GCD, we get:
[tex]\[
\frac{56 \div 4}{100 \div 4} = \frac{14}{25}
\][/tex]
5. Combine the integer part and the simplified fraction:
Adding the integer part back, we have:
[tex]\[
3 + \frac{14}{25} = \frac{3 \times 25 + 14}{25} = \frac{75 + 14}{25} = \frac{89}{25}
\][/tex]
Thus, the decimal number 3.56 expressed as a fraction in its simplest form is [tex]\(\frac{89}{25}\)[/tex].
To confirm, among the given options:
- [tex]\(\frac{25}{89}\)[/tex]
- [tex]\(\frac{89}{50}\)[/tex]
- [tex]\(\frac{178}{25}\)[/tex]
- [tex]\(\frac{89}{25}\)[/tex]
The correct answer is [tex]\(\frac{89}{25}\)[/tex].
