In a base-7 system, what is the base-10 equivalent of the base-7 number 345?
Practice Questions
Q1
In a base-7 system, what is the base-10 equivalent of the base-7 number 345?
150
170
180
190
Questions & Step-by-Step Solutions
In a base-7 system, what is the base-10 equivalent of the base-7 number 345?
Step 1: Identify the base-7 number you want to convert, which is 345.
Step 2: Break down the base-7 number into its digits: 3, 4, and 5.
Step 3: Assign each digit a power of 7 based on its position from right to left, starting at 0: 3 is in the 2nd position (7^2), 4 is in the 1st position (7^1), and 5 is in the 0th position (7^0).
Step 4: Calculate the value of each digit multiplied by its corresponding power of 7: 3 * 7^2, 4 * 7^1, and 5 * 7^0.
Step 5: Calculate 3 * 7^2 = 3 * 49 = 147.
Step 6: Calculate 4 * 7^1 = 4 * 7 = 28.
Step 7: Calculate 5 * 7^0 = 5 * 1 = 5.
Step 8: Add all the results together: 147 + 28 + 5.
Step 9: The final result is 180, which is the base-10 equivalent of the base-7 number 345.
