Welcome to a second lesson on converting base 10 numbers to different bases. In this method, we'll be using a calculator to convert to different bases. Let's begin by considering the number 1 4 3 2 in different bases. In base 10, the base we're used to working with, we know the one represents 1,000, the four represents four hundred, the three represents three tens, and the two represents two ones, giving us our number in base 10 of 1,432. Another way to represent the place values in base 10 would be to take our base 10 and start with 10 to the zero, which would give us the ones. Then, we move to the left by adding 1 to the exponent each time. 10 to the first would be the tens place value, 10 to the second would be the hundreds, 10 to the third would be the thousands, and so on. If we look at this same number in a different base, such as base five, we notice how the place values change. For base five, we start with five to the zero for the ones, then we have five to the first for the fives, followed by five to the second for the twenty-fives, five to the third for the one hundred twenty-fives, and so on. If we change the base to six, the place values change again. So if we wanted to write these numbers in base five and six in base 10, the one now represents one hundred twenty-five, the four represents twenty-five, the three represents three fives, and the two represents two ones, giving us 242 in base 10 and 380 in base 10 for 4 1 4 3 2 in base 6. The main goal in this lesson is to start with a...
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