Find the product of 214 base 5 and 102 base 5
214*102
= 214*100 + 214*2
= 21400 + 433
= 22333
Why did the mathematician become an acrobat? Because he wanted to add some decimal points! 🤡
To find the product of 214 base 5 and 102 base 5, let's first convert them to base 10.
214 base 5 = (2 * 5^2) + (1 * 5^1) + (4 * 5^0) = 2 * 25 + 1 * 5 + 4 * 1 = 50 + 5 + 4 = 59.
102 base 5 = (1 * 5^2) + (0 * 5^1) + (2 * 5^0) = 1 * 25 + 0 * 5 + 2 * 1 = 25 + 0 + 2 = 27.
Now, let's multiply 59 by 27:
59 * 27 = 1593.
So, the product of 214 base 5 and 102 base 5 is 1593.
To find the product of 214 base 5 and 102 base 5, we need to perform multiplication using base 5 arithmetic.
First, let's align the numbers properly:
214 base 5
x 102 base 5
_____________
To proceed with multiplication, we start by multiplying the units place digits, which are 4 and 2. The product is 4 times 2, which equals 8.
8
214 base 5
x 102 base 5
_____________
Next, we proceed to the tens place digit of the bottom number, which is 0. We multiply it by each digit in the top number.
For the digit 0 in the tens place, the product is 0 times each of the digits in 214, which will result in a 0 in the next row.
0
8
214 base 5
x 102 base 5
_____________
Lastly, we move to the hundreds place digit of the bottom number, which is 1. We multiply it by each digit in the top number.
For the digit 1 in the hundreds place, we multiply it by each digit in 214: 1 times 4, 1 times 1, and 1 times 2.
1 1 1
0 8
______
+ 8 4
214 base 5
x 102 base 5
_____________
Now, we add up the products in each row:
111
0
+ 8 4
___________
22014 base 5
Therefore, the product of 214 base 5 and 102 base 5 is 22014 base 5.
To find the product of two numbers in base 5, we can use the standard multiplication method. Let's break it down step by step.
Step 1: Convert the numbers to base 10.
To multiply two numbers in base 5, we first need to convert them to base 10.
214 base 5 = (2 * 5^2) + (1 * 5^1) + (4 * 5^0) = 2 * 25 + 1 * 5 + 4 * 1 = 50 + 5 + 4 = 59
102 base 5 = (1 * 5^2) + (0 * 5^1) + (2 * 5^0) = 1 * 25 + 0 * 5 + 2 * 1 = 25 + 0 + 2 = 27
So, 214 base 5 is equal to 59 in base 10, and 102 base 5 is equal to 27 in base 10.
Step 2: Multiply the numbers in base 10.
Now that we have converted the numbers to base 10, we can multiply them as regular base 10 numbers:
59 * 27 = 1593
Step 3: Convert the product back to base 5.
Finally, we need to convert the product back to base 5.
1593 base 10 = (1 * 5^3) + (1 * 5^2) + (3 * 5^1) + (3 * 5^0) = 1 * 125 + 1 * 25 + 3 * 5 + 3 * 1 = 125 + 25 + 15 + 3 = 168
So, the product of 214 base 5 and 102 base 5 is 168 base 5.