Question

45.77 x 32.1 show your work

Answer 1

To multiply 45.77 by 32.1, we can follow the standard multiplication algorithm. Here’s a step-by-step breakdown:

1. **Multiply without decimals:**
- Ignore the decimals for now and multiply \(4577\) (which is 45.77 without the decimal) by \(321\) (which is 32.1 without the decimal).

```
4577
x 321
_________
4577 (4577 x 1)
9154 (4577 x 2, shifted one position to the left)
+ 9154 (4577 x 3, shifted two positions to the left)
_________
```

We can calculate each part separately:

- \(4577 \times 1 = 4577\)
- \(4577 \times 2 = 9154\), but remember to shift this one position left, which gives \(9154\)00.
- \(4577 \times 3 = 13731\), but remember to shift this two positions left, which gives \(1373100\).

Now, we can add them together:

```
4577
9154
+ 1373100
__________
1464157
```

2. **Adjust for decimals:**
- Now, we need to adjust for the decimals. When you multiply \(45.77\) by \(32.1\), there are a total of \(3\) decimal places to consider (2 from \(45.77\) and 1 from \(32.1\)).

Therefore, we move the decimal point in the result \(1464157\) three places to the left:

\[
1464157 \rightarrow 1464.157
\]

So, the final answer is:

\[
\boxed{1464.157}
\]