Answer:
413_7
Step-by-step explanation:
Convert the following to base 7:
206_10
Hint: | Starting with zero, raise 7 to increasingly larger integer powers until the result exceeds 206.
Determine the powers of 7 that will be used as the places of the digits in the base-7 representation of 206:
Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value
3 | 7^3 | 343
2 | 7^2 | 49
1 | 7^1 | 7
0 | 7^0 | 1
Hint: | The powers of 7 (in ascending order) are associated with the places from right to left.
Label each place of the base-7 representation of 206 with the appropriate power of 7:
Place | | | 7^2 | 7^1 | 7^0 |
| | | ↓ | ↓ | ↓ |
206_10 | = | ( | __ | __ | __ | )_(_7)
Hint: | Divide 206 by 7 and find the remainder. The remainder is the first digit from the right.
Determine the value of the first digit from the right of 206 in base 7:
206/7=29 with remainder 3
Place | | | 7^2 | 7^1 | 7^0 |
| | | ↓ | ↓ | ↓ |
206_10 | = | ( | __ | __ | 3 | )_(_7)
Hint: | Divide the whole number part of the previous quotient, 29, by 7 and find the remainder. The remainder is the next digit.
Determine the value of the next digit from the right of 206 in base 7:
29/7=4 with remainder 1
Place | | | 7^2 | 7^1 | 7^0 |
| | | ↓ | ↓ | ↓ |
206_10 | = | ( | __ | 1 | 3 | )_(_7)
Hint: | Divide the whole number part of the previous quotient, 4, by 7 and find the remainder. The remainder is the last digit.
Determine the value of the last remaining digit of 206 in base 7:
4/7=0 with remainder 4
Place | | | 7^2 | 7^1 | 7^0 |
| | | ↓ | ↓ | ↓ |
206_10 | = | ( | 4 | 1 | 3 | )_(_7)
Hint: | Express 206_10 in base 7.
The number 206_10 is equivalent to 413_7 in base 7.
Answer: 206_10 =413_7
