Question

find the quotient.

\\(3 \overline{) 752}\\)

\\(\bigcirc\\) 234

\\(\bigcirc\\) 250.6

\\(\bigcirc\\) 250.\bar{6}\\)

\\(\bigcirc\\) 256.\bar{6}\\)

Explanation:

Identify the division problem

We need to find the quotient of \(752 \div 3\). This involves dividing a three-digit integer by a single-digit divisor.

Divide the hundreds and tens

Using Long Division Steps, we divide the first digit:

• \(7 \div 3 = 2\) with a remainder of \(1\).
• Bring down the \(5\) to make \(15\).
• \(15 \div 3 = 5\) with a remainder of \(0\).

Divide the ones

• Bring down the \(2\).
• \(2 \div 3 = 0\) with a remainder of \(2\).
• This gives us a whole number quotient of \(250\) and a remainder of \(2\).

Convert the remainder to a decimal

To continue dividing, place a decimal point after \(250\) and add a zero to the remainder:

• \(20 \div 3 = 6\) with a remainder of \(2\).
• Adding another zero gives \(20 \div 3 = 6\) with a remainder of \(2\).
• This pattern repeats infinitely.

Identify the repeating decimal

Using Repeating Decimals, we write the repeating digit \(6\) with a bar over it:

• The quotient is \(250.666...\), which is written as \(250.\bar{6}\).

Answer:

• (A) 234
• (B) 250.6
• (C) \(250.\bar{6}\) (Correct answer)
• (D) \(256.\bar{6}\)