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Use long division to convert 316

to a decimal.(1 point)
$$

3 answers

To convert the whole number \( 316 \) to a decimal using long division, you can think of it as dividing \( 316 \) by \( 1 \). However, if you want to express \( 316 \) as a decimal, you simply write it as:

\[ 316.0 \]

If you are looking to express \( 316 \) in a different format, such as converting it to a decimal with more precision, you can consider division by a number that changes its format.

But if we're performing long division to show how it behaves with decimal points, let's go through the process of dividing a larger number by \( 1 \):

  1. Set up the long division where \( 316 \) is the dividend and \( 1 \) is the divisor: \[ \begin{array}{r|l} 1 & 316.0 \ \end{array} \]

  2. Perform the division:

    • \( 1 \) goes into \( 3 \) (the first digit of \( 316 \)) \( 3 \) times. Multiply \( 1 \) by \( 3 \) getting \( 3 \).
    • Subtract \( 3 \) from \( 3 \) which equals \( 0 \).
    • Bring down the next digit, which is \( 1 \), making it \( 01 \).
    • \( 1 \) goes into \( 01 \) \( 0 \) times, subtract \( 0 \) from \( 1 \) resulting in \( 1 \).
    • Bring down the next digit, which is \( 6 \), making it \( 16 \).
    • \( 1 \) goes into \( 16 \) \( 16 \) times.
    • Multiply \( 1 \) by \( 16 \), getting \( 16 \).
    • Subtract \( 16 \) from \( 16 \) resulting in \( 0 \).

So, combining all the results, we have:

\[ \begin{align*} 316 \div 1 & = 316 \ \end{align*} \]

Thus, simply put, \( 316 \) as a decimal is:

\[ 316.0 \]

However, if you meant to convert something else into a decimal or perform a different operation, please clarify!

as written, the question makes no sense. It should be clear that they meant
3/16 = 0.1875

Thank you for the clarification! If you are looking to convert \( \frac{3}{16} \) to a decimal using long division, let's go through that process.

Long Division of \( 3 \div 16 \):

  1. Set Up the Division: Write \( 3 \) as the dividend and \( 16 \) as the divisor.
  ______________
16 |  3.000000

  1. Determine How Many Times 16 Goes into 3:

    • \( 16 \) goes into \( 3 \) \( 0 \) times, so we write \( 0 \) in the quotient. Since we need decimal division, we add a decimal point and bring down zeros.

  2. Add Decimal Point and 0s:

    • Write a decimal point in the quotient and add \( 0 \)s to the dividend (i.e., consider \( 3.000000 \)). Now looking at \( 30 \).
  0.1__________
16 |  3.000000
  1. Divide 30 by 16:
    • \( 16 \) goes into \( 30 \) \( 1 \) time. Write \( 1 \) in the quotient.
    • Multiply \( 1 \) by \( 16 \) and write \( 16 \) below \( 30 \).
  0.1__________
16 |  3.000000
     -16
    ________
      14
  1. Bring Down the Next 0:
    • Bring down the next \( 0 \), making the new dividend \( 140 \).
  0.1__________
16 |  3.000000
     -16
    ________
      140
  1. Divide 140 by 16:
    • \( 16 \) goes into \( 140 \) \( 8 \) times. Write \( 8 \) in the quotient.
    • Multiply \( 8 \) by \( 16 \) getting \( 128 \) and write it below \( 140 \).
  0.18_______
16 |  3.000000
     -16
    ________
      140
     -128
    ________
       12
  1. Bring Down Another 0:
    • Bring down another \( 0 \), making the new dividend \( 120 \).
  0.18________
16 |  3.000000
     -16
    ________
      140
     -128
    ________
       120
  1. Divide 120 by 16:
    • \( 16 \) goes into \( 120 \) \( 7 \) times. Write \( 7 \) in the quotient.
    • Multiply \( 7 \) by \( 16 \) getting \( 112 \) and write it below \( 120 \).
  0.187______
16 |  3.000000
     -16
    ________
      140
     -128
    ________
       120
      -112
    ________
         8
  1. Bring Down Another 0:
    • Bring down another \( 0 \), making the new dividend \( 80 \).
  0.187______
16 |  3.000000
     -16
    ________
      140
     -128
    ________
       120
      -112
    ________
         80
  1. Divide 80 by 16:
    • \( 16 \) goes into \( 80 \) \( 5 \) times. Write \( 5 \) in the quotient.
    • Multiply \( 5 \) by \( 16 \) getting \( 80 \) and write it below \( 80 \).
  0.1875____
16 |  3.000000
     -16
    ________
      140
     -128
    ________
       120
      -112
    ________
         80
        -80
    ________
          0

The remainder becomes \( 0 \), meaning the division is complete.

Final Result:

From the long division, we find that

\[ \frac{3}{16} = 0.1875 \]

So the decimal representation of \( \frac{3}{16} \) is \( 0.1875 \). Thank you for your patience, and let me know if you need further assistance!