In mathematics, every digit in a number has a place value. A place value system enables us to assign values to digits in a number based on the location of the digit in the number. In mathematics, we use the decimal or base-ten place value system to help us to determine the values of various numbers.

In the decimal place value system, the place values of numbers increase from right to left. The first place before the decimal point is the ones place. It is followed by the tens, hundreds, thousands, ten thousands, and so on, as we move towards the left. Meanwhile, the first place after the decimal point as we move towards the right is the tenths, followed by the hundredths, thousandths, and so on. As such, each position in the decimal place value system has a value that is a power of 10. For example, ones is `10^{0}` , tens is `10^{1}` , and hundreds is `10^{2}` , whereas tenths is `10^{-1} = \frac{1}{10}` and hundredths is `10^{-2} = \frac{1}{100}` .

Against this background, therefore, the total value of a digit is the product of the digit and its place value. For example, the total value of 5 in the number 1.56 is 5 (the digit) x `\frac{1}{10}` (place value) = `\frac{5}{10}` .

To answer how many hundredths are there in one-tenth, we first determine the total value of one-tenth, i.e., 1 (digit) x `\frac{1}{10}` (place value) = `\frac{1}{10}` , and the total value of one-hundredth, i.e., 1 x `\frac{1}{100}` = `\frac{1}{100}` . In other words, we want to solve the equation `\frac{1}{100} \times b = \frac{1}{10}` , where b denotes the number of hundredths that are in one-tenth. (what must one-hundredth be multiplied with to obtain one-tenth?).

Solving the equation, we obtain `\frac{b}{100} = \frac{1}{10}` , and 10b = 100 (cross multiplication), so that b = 10.

Thus, there are ten hundredths in one-tenth.

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