Certainly! Let's convert the fraction [tex]\( \frac{1}{4} \)[/tex] into its decimal form, step by step.
1. Write the fraction [tex]\(\frac{1}{4}\)[/tex].
2. Set up the long division problem of dividing 1 by 4. This means we want to see how many times 4 goes into 1. We will use decimal places to find an exact answer since 1 is smaller than 4.
[tex]\[
4 \longdiv { 1 . 0 }
\][/tex]
3. Since 4 does not go into 1, we add a decimal point and a zero, making it 10. How many times does 4 fit into 10?
It fits 2 times (since [tex]\( 4 \times 2 = 8 \)[/tex]).
[tex]\[
0.
\][/tex]
[tex]\[
4 \longdiv { 1 . 0 }\\
- 8\\
\][/tex]
Subtract 8 from 10: [tex]\( 10 - 8 = 2 \)[/tex].
4. Bring down another 0, making it 20. How many times does 4 fit into 20?
It fits 5 times (since [tex]\( 4 \times 5 = 20 \)[/tex]).
[tex]\[
0.2
\][/tex]
[tex]\[
4 \longdiv { 1 . 0 0 } \\
- 8\\
200\\
- 200
\][/tex]
Subtract 20 from 20: [tex]\( 20 - 20 = 0 \)[/tex].
5. Since the remainder is now 0, we have completed the division. The quotient we obtained is [tex]\( 0.25 \)[/tex].
Therefore, the fraction [tex]\(\frac{1}{4}\)[/tex] expressed as a decimal is [tex]\( 0.25 \)[/tex].
