Convert this fraction into the decimal form: 17/12
The Correct Answer and Explanation is:
Decimal Form of 17/12:
The fraction 17/12 is equal to 1.4166… or 1.4167 (rounded to 4 decimal places). It is a repeating decimal.
Explanation
To convert a fraction to its decimal form, divide the numerator (top number) by the denominator (bottom number). In this case, we divide 17 by 12.
Start with long division:
12 goes into 17 once, since 12 × 1 = 12.
17 – 12 = 5, so the remainder is 5.
We now add a decimal point and a zero to continue.
Bring down a zero: 50
12 goes into 50 four times (12 × 4 = 48)
50 – 48 = 2
Bring down another zero: 20
12 goes into 20 once (12 × 1 = 12)
20 – 12 = 8
Bring down another zero: 80
12 goes into 80 six times (12 × 6 = 72)
80 – 72 = 8
Bring down another zero: 80 again
You will see that from here, the same pattern continues with 80 repeating, so 6 keeps repeating.
Therefore, the full decimal form is:
1.41666…
The digit 6 repeats forever. We write it as 1.416̅ or approximate it as 1.4167 for practical rounding.
This type of decimal is called a repeating decimal, since it does not terminate (stop), but follows a repeating pattern.
Fractions where the denominator does not have only 2 or 5 as prime factors (like 12, which has 2 and 3), often result in repeating decimals. If the denominator can be expressed as a product of only 2s and 5s (like 10, 20, 100), then the decimal terminates.
In this case, since 12 includes the factor 3, the decimal repeats. Understanding this helps in math, especially when converting between fractions and decimals, comparing numbers, or solving real-world problems that involve measurements and finances.
