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The hundredth's place is the second number after the decimal. In order to round to such place, you look at the number after it. For example, the number in the hundredth's place in 47.9025 is 0. In order to round, you must look at the number after it, in this case 2. Since 2 is less than 5, the 0 will not be rounded up and remain 0. The answer to your particular question is 12.58. 

12.5829 rounded to the nearest hundredth is 12.58.

This is because the thousandths place is a number of 4 or less, which means in rounding to the nearest hundredths place, the value of the hundredths place stays the same.
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