Write 25/6 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeat.
The Correct Answer and Explanation is:
Decimal Form of 25/6:
The fraction 25/6 as a decimal is:
4.1̅6, which means 4.1666…, where the 6 repeats forever.
Explanation
To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). In this case, we are converting 25/6 to decimal form.
Let’s begin the long division:
- Divide 25 by 6:
- 6 goes into 25 4 times (because 6 × 4 = 24)
- Subtract 24 from 25, we get 1 as remainder
So far, we have:
25 ÷ 6 = 4 remainder 1
- Now, add a decimal point and continue dividing:
- Bring down a 0 after the decimal point, making the new number 10
- 6 goes into 10 1 time (6 × 1 = 6), remainder 4
Now we have:
4.1
- Bring down another 0 to make 40
- 6 goes into 40 6 times (6 × 6 = 36), remainder 4
We notice a pattern starting:
- Every time we bring down a zero, we get 40 again, and dividing 40 by 6 gives 6 with a remainder of 4
- This cycle will repeat forever
So, the decimal becomes:
4.1666…
To express the repeating part, we use a bar over the digit that repeats:
4.1̅6
This bar notation means that the 6 repeats endlessly.
Why Does the 6 Repeat?
This happens because the remainder becomes the same again (4), which causes the same digit (6) to be produced repeatedly. When a remainder repeats in division, the digits in the quotient will also repeat, creating a repeating decimal.
Summary:
- 25/6 = 4.1̅6
- The digit 6 repeats forever.
- This is a repeating decimal, not a terminating one.
- Repeating decimals are common when the denominator doesn’t evenly divide into a power of 10.
