Ask a New Question
Menu

Use long division to convert 2 7/16

to a decimal.(1 point)
Responses

2.2857
2.2857

0.4375
0.4375

2.716
2.716

2.4375

1 answer

To convert the mixed number \( 2 \frac{7}{16} \) to a decimal, we first need to focus on the fractional part \( \frac{7}{16} \).

We will use long division to divide 7 by 16:

  1. Set up the division: We want to divide 7 by 16. Since 7 is less than 16, we start by adding a decimal and a zero. So we divide 7.000 by 16.

  2. Divide the first part:

    • 16 goes into 70 four times (since \( 16 \times 4 = 64 \)).
    • Write 4 above the line. Subtract \( 64 \) from \( 70 \) which gives \( 6 \).

  3. Bring down the next zero:

    • Now we have 60.
    • 16 goes into 60 three times (since \( 16 \times 3 = 48 \)).
    • Write 3 above the line. Subtract \( 48 \) from \( 60 \) which gives \( 12 \).

  4. Bring down the next zero:

    • Now we have 120.
    • 16 goes into 120 seven times (since \( 16 \times 7 = 112 \)).
    • Write 7 above the line. Subtract \( 112 \) from \( 120 \) which gives \( 8 \).

  5. Bring down the next zero:

    • Now we have 80.
    • 16 goes into 80 five times (since \( 16 \times 5 = 80 \)).
    • Write 5 above the line. Subtract \( 80 \) from \( 80 \) which gives \( 0 \).

Now, we have completed our long division, yielding \( 0.4375 \) from \( \frac{7}{16} \).

  1. Now combine it with the whole number:
    • Since \( 2 \frac{7}{16} = 2 + 0.4375 \), we combine these: \[ 2 + 0.4375 = 2.4375 \]

Thus, the decimal equivalent of \( 2 \frac{7}{16} \) is \( 2.4375 \).

Therefore, the correct response is:

2.4375.