Q:

# Why is one column in a hundredths grid equal to one column in a tenths grid?

A:

One column in a hundredths grid is equal to one column in a tenths grid because in each case, the selected column composes one-tenth of the grid in total. The number of blocks is different, but the proportion of space filled is the same.

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In a hundredths grid, there is a total of 100 equally sized blocks arranged in a 10-by-10 format. One column (or one row, for that matter) has 10 of these blocks. The fraction 10/100 is the same proportion as one-tenth, as both are equal to 10 percent.

In the case of the tenths grid, there are 10 columns of just one block each, leading to 10 blocks in total. Selecting one of those columns is choosing one-tenth of the space in the grid, which is the same fraction as the 10 blocks that comprise the column in the hundredths grid. In a tenths grid, each column is said to have a value of 10, though usually the column is illustrated as one entity (without the individual 10 boxes marked off).

It is important to note that, while a hundredths grid is composed of 100 squares in a 10-by-10 larger square, a tenths grid is one square composed of 10 rectangles. This difference in composition allows for their columns to be equal in terms of proportion.

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