Question

use long divison to convert 5 3/1/6 to a decimal

Answer 1

To convert the mixed fraction \(5 \frac{3}{16}\) into a decimal using long division, we first need to express it as an improper fraction.

1. Convert \(5 \frac{3}{16}\) to an improper fraction:
\[
5 \frac{3}{16} = \frac{5 \times 16 + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16}
\]

2. Now, we need to divide \(83\) by \(16\) using long division.

**Step 1:** Set up the division.

```
83 ÷ 16
```

**Step 2:** Determine how many times \(16\) can go into \(83\).

- \(16 \times 5 = 80\) (which is less than \(83\)).
- \(16 \times 6 = 96\) (which is more than \(83\)).

So, \(16\) goes into \(83\) a total of \(5\) times.

**Step 3:** Multiply and subtract.

```
83
-80 (16 × 5)
----
3
```

**Step 4:** Bring down a \(0\) to \(3\) (so we have \(30\)).

**Step 5:** Divide again:

Now we need to determine how many times \(16\) goes into \(30\).

- \(16 \times 1 = 16\)
- \(16 \times 2 = 32\) (too much)

So, \(16\) goes into \(30\) \(1\) time.

**Step 6:** Multiply and subtract again.

```
30
-16 (16 × 1)
----
14
```

**Step 7:** Bring down another \(0\) (now we have \(140\)).

**Step 8:** Divide \(140\) by \(16\):

- \(16 \times 8 = 128\) (which is less than \(140\)).
- \(16 \times 9 = 144\) (which is more than \(140\)).

So, \(16\) goes into \(140\) \(8\) times.

**Step 9:** Multiply and subtract again.

```
140
-128 (16 × 8)
----
12
```

**Step 10:** Bring down another \(0\) (now we have \(120\)).

**Step 11:** Divide \(120\) by \(16\):

- \(16 \times 7 = 112\) (which is less than \(120\)).
- \(16 \times 8 = 128\) (which is more than \(120\)).

So, \(16\) goes into \(120\) \(7\) times.

**Step 12:** Multiply and subtract again.

```
120
-112 (16 × 7)
----
8
```

**Step 13:** Bring down another \(0\) (now you have \(80\)).

**Step 14:** Divide \(80\) by \(16\):

- \(16 \times 5 = 80\) (which is exactly \(80\)).

So, \(16\) goes into \(80\) \(5\) times.

**Step 15:** Multiply and subtract.

```
80
-80 (16 × 5)
----
0
```

Since there is no remainder, we can write the decimal conversion as follows:

\[ 5 \frac{3}{16} = 5.1875 \]

Thus, the decimal representation of \(5 \frac{3}{16}\) is **5.1875**.