# Write 17 x 4^4 with respect to base 4

• MHB
• ketanco
In summary, converting a number from one base to another involves understanding the place value system of the new base and breaking down the number into its digit components. When writing a number, it is important to specify the base to avoid confusion and ensure accuracy. For example, converting 17 x 4^4 to base 4 results in the final answer of 20201, which can also be written as 521 in base 10. An example of converting a number to base 4 is converting 45 to 3011.
ketanco
how can i write 17 x 4^4 with respect to base 4?

here is what i did:
i divide 17 by 4 twice and get 101 on base 4, and then say 1 x 4^6 + 1 x 4 ^ 4

is it correct?

ketanco said:
how can i write 17 x 4^4 with respect to base 4?

here is what i did:
i divide 17 by 4 twice and get 101 on base 4, and then say 1 x 4^6 + 1 x 4 ^ 4

is it correct?
It is correct as far as at goes, but I think that it is not yet the answer that is expected.

In base 4, $4^4$ is $10000$; and $4^6$ is $1000000$.

## 1. What does "Write 17 x 4^4 with respect to base 4" mean?

This is a mathematical expression that is asking you to rewrite the number 17 x 4^4 (which is the same as 17 x 256) in a different base, specifically base 4.

## 2. How do I convert a number from one base to another?

To convert a number from one base to another, you need to understand the place value system of that base. In base 4, for example, the digits represent multiples of powers of 4 (1, 4, 16, 64, etc.). To convert a number, you need to break it down into its digit components, multiply each digit by the corresponding power of the base, and then sum them up.

## 3. What is the final answer when writing 17 x 4^4 with respect to base 4?

The final answer is 20201, which represents 2 x 4^4 + 2 x 4^1 + 1 x 4^0 in base 10. This can also be written as 2 x 256 + 2 x 4 + 1 = 512 + 8 + 1 = 521.

## 4. Why is it important to specify the base when writing a number?

Different bases represent numbers in different ways, so it is important to specify the base when writing a number in order to avoid confusion and ensure accuracy. For example, 142 in base 10 is not the same as 142 in base 2 (which is 1000110).

## 5. Can you provide an example of converting a number to base 4?

Sure, let's convert the number 45 to base 4. First, we break down 45 into its digit components: 45 = 3 x 10 + 5. Next, we convert each digit to base 4: 3 = 3 x 4^1 + 0 x 4^0 = 30, 5 = 1 x 4^1 + 1 x 4^0 = 11. Finally, we combine the two digits to get the final answer in base 4: 45 = 30 + 11 = 3011.

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