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Convert the number [tex]\( 210_{\text{four}} \)[/tex] to the base-ten system.

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GinnyAnswer
To convert the base-four number [tex]\(210_{\text{four}}\)[/tex] into a base-ten number, we follow these steps:

1. Identify the place values in the base-four number. Starting from the right, the place values are [tex]\(4^0\)[/tex], [tex]\(4^1\)[/tex], [tex]\(4^2\)[/tex], etc.

2. Each digit in the base-four number is multiplied by its corresponding power of 4.

So, we have:

[tex]\(2 \times 4^2 + 1 \times 4^1 + 0 \times 4^0\)[/tex]

3. Calculate the value of each term:

- [tex]\(2 \times 4^2 = 2 \times 16 = 32\)[/tex]
- [tex]\(1 \times 4^1 = 1 \times 4 = 4\)[/tex]
- [tex]\(0 \times 4^0 = 0 \times 1 = 0\)[/tex]

4. Sum these values:

[tex]\[32 + 4 + 0 = 36\][/tex]

Therefore, [tex]\(210_{\text{four}} = 36_{\text{ten}}\)[/tex].
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