Express 550 and 1645 in the scale of 2, 5, 6, and 9.
2+5+6+9 = 22
550/22 = 25, so multiply all the values by 25.
1645 done that way will give fractional values.
Ahh I see you meant base, not scale.
550 = 10001001102
550 = 6719
what do you get for the others?
To express the numbers 550 and 1645 in the scale of 2, 5, 6, and 9, we need to determine the place value of each digit in each number.
Let's start with 550:
- The digit 5 is in the hundreds place.
- The digit 5 is in the tens place.
- The digit 0 is in the ones place.
To express 550 in the given scale, we would write it as: 259.
Now let's move on to 1645:
- The digit 1 is in the thousands place.
- The digit 6 is in the hundreds place.
- The digit 4 is in the tens place.
- The digit 5 is in the ones place.
To express 1645 in the given scale, we would write it as: 6959.
To express numbers in a different base or scale, we need to understand the concept of place values. Each digit in a number represents a specific value depending on its position.
In the given question, we need to express the numbers 550 and 1645 in the scale of 2, 5, 6, and 9. This means that each digit in the numbers can only be 0, 1, 2, 3, 4, or 5.
Let's start with 550:
To express this number in the given scale, we need to find the equivalent digits for each place value.
Starting from the rightmost digit, which is the units place, the available digits in the scale are 0, 1, 2, 3, 4, and 5. Since we have 0 available in the scale, we can use that as the digit for the units place, giving us the number 0.
Moving to the next place value, which is the tens place, the available digits in the scale are 0, 1, 2, 3, 4, and 5. We can use the available digit 5 as the digit for the tens place, giving us the number 5.
Finally, let's consider the hundreds place. The available digits in the scale are 0, 1, 2, 3, 4, and 5. Since we want to express the number 550, we need all three digits in the scale. Therefore, we can use 5, 5, and 0 as the digits for the hundreds, tens, and units places, respectively. Thus, in the scale of 2, 5, 6, and 9, the number 550 is represented as 550.
Now, let's move on to expressing 1645:
Similarly, starting from the rightmost digit, which is the units place, the available digits in the scale are 0, 1, 2, 3, 4, and 5. We can use the available digit 5 as the digit for the units place, giving us the number 5.
Moving to the next place value, which is the tens place, the available digits in the scale are 0, 1, 2, 3, 4, and 5. We can use the available digit 4 as the digit for the tens place, giving us the number 4.
The next place value is the hundreds place. The available digits in the scale are 0, 1, 2, 3, 4, and 5. We can use the available digit 6 as the digit for the hundreds place. However, since 6 is not available in the scale, we need to use the next highest available digit, which is 5. Therefore, we use 5 as the digit for the hundreds place.
Lastly, let's consider the thousands place. The available digits in the scale are 0, 1, 2, 3, 4, and 5. We can use the available digit 1 as the digit for the thousands place, giving us the number 1.
Thus, in the scale of 2, 5, 6, and 9, the number 1645 is represented as 1545.