Convert the following base 5 numbers into base 10.
(1) 20(5)
(2) 44(5)
(3) 304(5)
(4) 403(5)
(5) 1042(5)
(6) 2010(5)
(7) 2000(5)
(8) 2341(5)
Convert the following base 5 numbers into base 10.
(1) 20(5)
(2) 44(5)
(3) 304(5)
(4) 403(5)
(5) 1042(5)
(6) 2010(5)
(7) 2000(5)
(8) 2341(5)
(1) 20(5)
51
50
2
0
∴20(5) = 2 × 51 + 0 × 50 = 2 × 5 + 0 × 1 = 10 + 0 = 10
(2) 44(5)
51
50
4
4
∴44(5) = 4 × 51 + 4 × 50 = 4 × 5 + 4× 1= 20 + 4 = 24
(3) 304(5)
52
51
50
3
0
4
∴304(5) = 3 × 52 + 0 × 51 + 4 × 50 = 3 × 25 + 0 × 5 + 4 × 1 = 75 + 0+ 4 = 79
(4) 403(5)
52
51
50
4
0
3
∴403(5) = 4 × 52 + 0 × 51 + 3 × 50 = 4 × 25 + 0 × 5 + 3 × 1 = 100 + 0 + 3 = 103
(5) 1042(5)
53
52
51
50
1
0
4
2
∴1042(5) = 1 ×53 + 0 × 52 + 4 × 51 + 2 × 50
= 1 × 125 + 0 × 25 + 4 × 5 + 2 × 1
= 125 + 0 + 20 + 2
= 147
(6) 2010(5)
53
52
51
50
2
0
1
0
∴ 2010(5) = 2 × 53 + 0 × 52 + 1 × 51 + 0 × 50
= 2 × 125 + 0 × 25 + 1 × 5 + 0 × 1
= 250 + 0+ 5 + 0
= 255
(7) 2000(5)
53
52
51
50
2
0
0
0
∴ 2000(5) = 2 × 53 + 0 × 52 + 0 × 51 + 0 × 50
= 2 × 125 + 0 × 25 + 0 × 5 + 0 × 1
= 250 + 0+ 0 + 0
= 250
(8) 2341(5)
53
52
51
50
2
3
4
1
∴ 2341(5) = 2 × 53 + 3 × 52 + 4 × 51 + 1 × 50
= 2 × 125 + 3 × 25 + 4 × 5 + 1 × 1
= 250 + 75 + 20 + 1
= 346
(1) 20(5)
|
51 |
50 |
|
2 |
0 |
∴20(5) = 2 × 51 + 0 × 50 = 2 × 5 + 0 × 1 = 10 + 0 = 10
(2) 44(5)
|
51 |
50 |
|
4 |
4 |
∴44(5) = 4 × 51 + 4 × 50 = 4 × 5 + 4× 1= 20 + 4 = 24
(3) 304(5)
|
52 |
51 |
50 |
|
3 |
0 |
4 |
∴304(5) = 3 × 52 + 0 × 51 + 4 × 50 = 3 × 25 + 0 × 5 + 4 × 1 = 75 + 0+ 4 = 79
(4) 403(5)
|
52 |
51 |
50 |
|
4 |
0 |
3 |
∴403(5) = 4 × 52 + 0 × 51 + 3 × 50 = 4 × 25 + 0 × 5 + 3 × 1 = 100 + 0 + 3 = 103
(5) 1042(5)
|
53 |
52 |
51 |
50 |
|
1 |
0 |
4 |
2 |
∴1042(5) = 1 ×53 + 0 × 52 + 4 × 51 + 2 × 50
= 1 × 125 + 0 × 25 + 4 × 5 + 2 × 1
= 125 + 0 + 20 + 2
= 147
(6) 2010(5)
|
53 |
52 |
51 |
50 |
|
2 |
0 |
1 |
0 |
∴ 2010(5) = 2 × 53 + 0 × 52 + 1 × 51 + 0 × 50
= 2 × 125 + 0 × 25 + 1 × 5 + 0 × 1
= 250 + 0+ 5 + 0
= 255
(7) 2000(5)
|
53 |
52 |
51 |
50 |
|
2 |
0 |
0 |
0 |
∴ 2000(5) = 2 × 53 + 0 × 52 + 0 × 51 + 0 × 50
= 2 × 125 + 0 × 25 + 0 × 5 + 0 × 1
= 250 + 0+ 0 + 0
= 250
(8) 2341(5)
|
53 |
52 |
51 |
50 |
|
2 |
3 |
4 |
1 |
∴ 2341(5) = 2 × 53 + 3 × 52 + 4 × 51 + 1 × 50
= 2 × 125 + 3 × 25 + 4 × 5 + 1 × 1
= 250 + 75 + 20 + 1
= 346
