base eight: 4 flats, 0 longs, 5 units
In base eight, 4 flats, 0 longs, and 5 units can be represented as 405.
To convert the base-eight number 405 into base-ten, you need to calculate the decimal equivalent of the number:
Step 1: Write down the given base-eight number: 405.
Step 2: Identify the place values of each digit in the base-eight number. The rightmost digit is in the units place, the second digit is in the longs place, and the leftmost digit is in the flats place.
Step 3: Convert each digit to its base-ten equivalent. In base eight, the digit 5 is equivalent to 5 in base ten, the digit 0 is equivalent to 0 in base ten, and the digit 4 is equivalent to 4 in base ten.
Step 4: Multiply each digit by its respective place value. Starting from the right, multiply 5 (units place) by 8^0 to get 5, multiply 0 (longs place) by 8^1 (8) to get 0, and multiply 4 (flats place) by 8^2 (64) to get 256.
Step 5: Add up the results from step 4. 5 + 0 + 256 equals 261.
Therefore, the base-eight number 405 is equivalent to 261 in base ten.