Explain why one column in a hundredths grid is equal to one column in a tenths grid?
To understand why one column in a hundredths grid is equal to one column in a tenths grid, we need to visualize what these grids represent.
A hundredths grid is a visual representation of numbers that are divided into 100 equal parts. It is often used to represent decimal numbers where each square represents 1/100 or 0.01. The grid typically has 10 rows and 10 columns.
A tenths grid is a visual representation of numbers that are divided into 10 equal parts. It is also used to represent decimal numbers, where each square represents 1/10 or 0.1. The grid typically has 10 rows and 1 column.
Now, to compare the columns in these grids, let's focus on the concept of place value. In decimal numbers, each digit has a specific place value based on its location in the number. The rightmost digit represents the ones place, the next digit to the left represents the tens place, the digit to the left of that represents the hundreds place, and so on.
In the hundredths grid, each column represents a power of ten. The rightmost column represents 1/100, the second column represents 1/10 of 1/100 or 1/1000, the third column represents 1/10 of 1/1000 or 1/10,000, and so on.
In the tenths grid, each column also represents a power of ten. The only difference is that it starts at 1/10 (tenth) instead of 1/100 (hundredth). The rightmost column represents 1/10, the second column represents 1/10 of 1/10 or 1/100, the third column represents 1/10 of 1/100 or 1/1000, and so on.
From this comparison, we can see that the leftmost column in both grids represents the same place value, which is 1/100 or 0.01. Therefore, we can conclude that one column in a hundredths grid is equal to one column in a tenths grid.