Convert each number from base 10 to the desired base. 83 83 into base 8 8

Welcome back. For this problem, we'd like to convert 83 from base 10 into base 8. Our first step is to find the base and place values that we're converting to. Now, we're converting to base 8, and the place values in base 8 are powers of 8. We start with 1, then we have 88 squared, 8 cubed, 84, and so on and so forth, just increasing the power on 8 by 1 as we move to the next highest place value. Now for step two, we want to identify the relevant place values, which are just the powers of our base that are less than or equal to our starting number. So here we want to find the powers of 8 that are less than or equal to 83. 1 and 8 are clearly less than or equal to 83. 82 is 64, which is also less than or equal to 83, but 8 cubed is 512, which is not less than or equal to 83. So, we're not going to need 8 cubed or any of the other higher powers of 8. The only place values that will appear in our numeral when we represent 83 in base eight, are going to be the place value for 8 squared. 8 and 1. And I do like to write these little lines here, because in step 3, which we will be going to next, we're going to find the digits 1 at a time and place values, and it's helpful to just have a place to just slot them right into. Step 2 is all set here. We move on to step 3. For each place value from step 2, starting with the highest, we're going to divide our base 10 number by the place value. So here we're going to take that 83, and we're going to divide it by the highest place value, which in this case is 82. So, I'm gonna come over here, I'm gonna do 83 divided by 82, which is 64. Now, 64 does not go into 8, but it does go into 83 1 time. So we can subtract 83 minus 64, and we end up getting 19. Now, the quotient, which is this number up top, is going to be the digit in that place value. So this one will be the digit in the 8 squared place. The remainder is going to become the new base 10 number that we will use when we follow this step again for the next highest place value. So, I'm going to take this remainder of 19, and I want to divide it by the next highest place value, 8. Now 8 does not go into 1, but it does go into 19 2 times. We can subtract 8 times 2, which is 16, and we end up getting a remainder of 3. Now, we're going to take the quotient to the number up top, and it will be the digit in the 8th place. The remainder is going to be the new base 10 number that we'll use when following the step for the next highest place value. So we'll take this 3 and divide it by 1. Now, 1 goes into 33 times, and when we subtract, we end up getting 0. Now, the number up top, the quotient, is going to be the digit in the 1's place, so we'll put it here. And we got a remainder of 0, which means that we are done. And we also know that we're done because we did fill in a digit into each of our place values. So, just to end this off, I'm going to rewrite my number, 123, and make sure that I add the subscript for the base, which is 8. Now I have my answer 123 base 8, which is the quantity 83 represented in base 8. Great work.