Study the number pattern.
- In 57 what is the digit in the ones place?
- What is the sum of the last three digits in 515?
- What is the sum of the last four digits in 5100?
| Pattern |
|
|
| 51 |
5 |
= 5 |
| 52 |
5 x 5 |
= 25 |
| 53 |
5 x 5 x 5 |
= 125 |
| 54 |
5 x 5 x 5 x 5 |
= 625 |
| 55 |
5 x 5 x 5 x 5 x 5 |
= 3125 |
| 56 |
5 x 5 x 5 x 5 x 5 x 5 |
= 15625 |
| 57 |
5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 78125 |
| 58 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 390625 |
| 59 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 1953125 |
| 510 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 9765625 |
| 511 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 48828125 |
| 512 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 244140625 |
| 513 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 1220703125 |
| 514 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 6103515625 |
| 515 |
5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 |
= 30517578125 |
(a)
Digit in the ones place in 5
7 = 5
(b)
Last three digits in odd-numbered powers is
1, 2 and
5.
Sum of the last three digits in 5
15 = 1 + 2 + 5
= 8
(c)
For even-numbered powers from 5
6 onwards
Formula:
(1) If even-numbered powers ÷ 2 has an odd-numbered quotient, the last four digits is
5, 6, 2 and
5.(2) If even-numbered powers ÷ 2 has an even-numbered quotient, the last four digits is
0, 6, 2 and
5.100 ÷ 4 = 25 r 0
Since the remainder is 0, the sum of the last four digits in 5
100 = 0 + 6 + 2 + 5
= 13
Answer(s): (a) 5; (b) 8; (c) 13
