Question

Find the value of 321 base 5 × 21 base 5

Answer 1

To multiply these two numbers together, we can use the same method as multiplying in base 10. Let's break it down step by step:

```
321
x 21
-------
```

First, we multiply the units digit of the second number (1) with every digit in the first number:

```
321
x 21
-------
321
+ 3210
-------
```

Now we multiply the tens digit of the second number (2) with every digit in the first number:

```
321
x 21
-------
321
+ 3210
+642
-------
```

Finally, we multiply the hundreds digit of the second number (0) with every digit in the first number:

```
321
x 21
-------
321
+ 3210
+ 642
-------
321
+ 3210
+ 6420
-------
```

By summing all the partial products, we get:

```
321
x 21
-------
10011
+ 32100
+ 32100
-------
100211
-------
```

Therefore, the value of 321 base 5 × 21 base 5 is 100211 base 5.