To solve the problem of converting the fraction [tex]\(\frac{13}{75}\)[/tex] to its decimal equivalent, follow these steps:
1. Understand the Fraction: The fraction given is [tex]\(\frac{13}{75}\)[/tex]. This means you are dividing 13 by 75.
2. Set Up the Division: You can set this up as a division problem where 13 is the dividend (the number to be divided) and 75 is the divisor (the number you are dividing by).
3. Perform the Division:
- Start by adding a decimal point and zeros to the dividend (13.0000...).
- Divide 130 by 75. This fits 1 time.
- Subtract 75 from 130 to get a remainder of 55.
- Bring down the next zero to make it 550.
- Divide 550 by 75. This fits 7 times.
- Subtract 525 (75 7) from 550 to get a remainder of 25.
- Bring down the next zero to make it 250.
- Divide 250 by 75. This fits 3 times.
- Subtract 225 (75 3) from 250 to get a remainder of 25.
- Bring down another zero to make it 250 again.
- This process repeats, resulting in a recurring pattern.
4. Identify the Recurring Decimal:
- The result is a non-terminating decimal with a repeating sequence.
- The decimal equivalent of [tex]\(\frac{13}{75}\)[/tex] is [tex]\(0.1733333...\)[/tex] where the digit 3 repeats indefinitely.
Therefore, the decimal that is equivalent to [tex]\(\frac{13}{75}\)[/tex] is approximately:
[tex]\[ 0.17333333333333334 \][/tex]
This decimal representation accurately reflects the division of 13 by 75.
