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Question
The multiplicative inverse of 10–100 is ______.
Options
10
100
10100
10–100
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Solution
The multiplicative inverse of 10–100 is 10100.
Explanation:
For multiplicative inverse, let a be the multiplicative inverse of 10–100.
So, a × b = 1
∴ a × 10–100 = 1
⇒ `a = 1/10^-100 xx 1/(1/10^100)` ...`[∵ a^-m = 1/a^m]`
= 10100
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| Powers Table | ||||||||||
| x | 1x | 2x | 3x | 4x | 5x | 6x | 7x | 8x | 9x | 10x |
| 1 | 1 | 2 | ||||||||
| 2 | 1 | 4 | ||||||||
| 3 | 1 | 8 | ||||||||
| 4 | 1 | 16 | ||||||||
| 5 | 1 | 32 | ||||||||
| 6 | 1 | 64 | ||||||||
| 7 | 1 | 128 | ||||||||
| 8 | 1 | 256 | ||||||||
| Ones Digits of the Powers |
1 | 2, 4, 8, 6 | ||||||||
- Describe patterns you see in the ones digits of the powers.
- Predict the ones digit in the following:
- 412
- 920
- 317
- 5100
- 10500
- Predict the ones digit in the following:
- 3110
- 1210
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