use long division to convert 2 3/8

Answer 1

To convert the mixed number \(2 \frac{3}{8}\) into a decimal using long division, follow these steps:

1. Convert the mixed number to an improper fraction: \[ 2 \frac{3}{8} = \frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8} \]

2. Divide 19 by 8 using long division:

   • 8 goes into 19 twice (since \(8 \times 2 = 16\)).
   • Subtract 16 from 19, which gives us 3.
   • Bring down a 0 (making it 30) since we want to continue dividing.
   • 8 goes into 30 three times (since \(8 \times 3 = 24\)).
   • Subtract 24 from 30, which gives us 6.
   • Bring down another 0 (making it 60).
   • 8 goes into 60 seven times (since \(8 \times 7 = 56\)).
   • Subtract 56 from 60, which gives us 4.
   • Bring down another 0 (making it 40).
   • 8 goes into 40 five times (since \(8 \times 5 = 40\)).
   • Subtract 40 from 40, which gives us 0.

Putting it all together, we have:

• The quotient is 2 (from \(19 \div 8\)), then we have a decimal part \(0.375\).

Thus, \(2 \frac{3}{8}\) converts to \(2.375\).