Question

which expression can be represented by the model?
81 × 0.01
81 × 0.1
81 × 100
80 × 10

Explanation:

Step1: Analyze the grid model

The grid appears to be a 10x10 grid (since it's a square with 10 columns and 10 rows, total of 100 small squares). The blue shaded area has 81 small squares (let's assume: 9 columns fully shaded (9*10 = 90? Wait, no, maybe 9 columns and 9 rows? Wait, no, looking at the model, the blue part: let's count. Wait, the grid is 10 columns and 10 rows, so total 100 squares. The blue area: let's see, 9 columns (each with 10 squares) is 90, but then 1 more square? Wait, no, maybe 9 rows and 9 columns? Wait, no, the model shows a blue region that is 9 columns (each 10 squares) and 1 row with 1 square? Wait, no, maybe the grid is 10x10, so each small square is 0.01 of the whole (since 1/100 = 0.01). Wait, no, if the whole grid is 1 unit, then each small square is 0.01 (since 10x10=100 squares, so 1/100=0.01). But the blue area has 81 squares. So the blue area is 81 * 0.01? Wait, no, wait: maybe the grid is representing a decimal multiplication. Wait, let's think again.

Wait, the expressions are 81×0.01, 81×0.1, 81×100, 80×10.

Wait, if the grid is 10x10, so 100 squares. Each square is 0.01 (since 1/100 = 0.01). So 81 squares would be 81×0.01. But wait, maybe the grid is a 10x10 grid where each column is 0.1 (since 10 columns, so each column is 1/10 = 0.1). Wait, no, let's check the expressions.

Wait, 81×0.01 = 0.81, 81×0.1 = 8.1, 81×100 = 8100, 80×10 = 800.

Looking at the model, the blue area: if the grid is 10 columns (each 0.1) and 8 rows? No, wait, the model shows a blue region that is 9 columns (each 10 squares) and 1 row with 1 square? Wait, no, maybe the grid is 10x10, so 100 squares. The blue area has 81 squares. So if each square is 0.01 (since 1/100 = 0.01), then the blue area is 81×0.01. But wait, let's check the expressions. Wait, 81×0.01 is 0.81, which would be 81 hundredths. If the grid is 100 squares, each 0.01, then 81 squares is 81×0.01. But wait, maybe I made a mistake. Wait, another approach: the model is a decimal grid, where each square is 0.01 (since 10x10 grid, so 0.1 per column, 0.1 per row, so each square is 0.1×0.1=0.01). So 81 squares would be 81×0.01. But wait, let's check the expressions. Wait, 81×0.01 is 0.81, which is 81 hundredths. The other expressions: 81×0.1=8.1 (too big), 81×100=8100 (way too big), 80×10=800 (way too big). So the correct expression should be 81×0.01? Wait, no, wait, maybe the grid is 10 columns (each 0.1) and 8 rows? No, the model shows a blue area that is 9 columns (each 10 squares) and 1 row with 1 square? Wait, maybe the grid is 10x10, so 100 squares. The blue area is 81 squares. So 81×0.01. But let's confirm.

Wait, the model: the blue part is 9 columns (each 10 squares) is 90, but then 1 square? No, maybe 9 rows and 9 columns? No, 9×9=81. Oh! Wait, 9 rows and 9 columns: 9×9=81 squares. So the grid is 10x10, but the blue area is 9x9? No, 9x9 is 81. So each square is 0.01 (since 10x10=100, so 1/100=0.01). So 81 squares would be 81×0.01. But wait, the expressions: 81×0.01 is 0.81, which is 81 hundredths. The other options: 81×0.1=8.1 (which would be 81 tenths, requiring 81 squares each of 0.1, but 0.1 per square would mean 10 squares make 1, so 81×0.1 would be 8.1, which is 81 tenths, but the grid is 10x10, so 100 squares, each 0.01. So 81 squares is 81×0.01. So the correct expression is 81×0.01? Wait, no, wait, maybe I messed up. Wait, the problem is "Which expression can be represented by the model?" Let's check the model again. The model is a grid with 10 columns and 10 rows (100 squares). The blue area has 81 squares. So each square is 0.01 (since 1/100=0.01). So 81 squares is 81×0.01. So the correct option is 81×0.01.

Wait, but let's check the expressions again:

- 81×0.01 = 0.81 (81 hundredths)
- 81×0.1 = 8.1 (81 tenths)
- 81×100 = 8100 (81 times 100)
- 80×10 = 800 (80 times 10)

The model shows a blue area that is less than 1 (since it's a part of the 10x10 grid, which is 1 unit). So 0.81 is less than 1, 8.1 is more than 1, 8100 and 800 are way more. So the correct expression is 81×0.01.

Wait, but maybe the grid is a 10x10 grid where each column is 0.1 (so each column is 1/10 of the grid). So 9 columns would be 9×0.1=0.9, and 1 square in the 10th column. Wait, no, the 10th column has 10 squares, so 1 square in the 10th column is 1×0.01 (since 1/10 of 0.1 is 0.01). So total blue area is 9×0.1 + 1×0.01 = 0.9 + 0.01 = 0.91? No, that doesn't match. Wait, maybe I miscounted the blue squares. Let's look at the model: the blue part is 9 columns (each with 10 squares) and 1 square in the 10th column? Wait, no, the image shows a blue region that is 9 columns (each 10 squares) and 1 row with 1 square? Wait, maybe the grid is 10 rows and 10 columns, so 100 squares. The blue area: let's count the number of blue squares. From the image, it looks like 9 columns (each 10 squares) is 90, and 1 square in the 10th column, 1st row? No, the bottom right has 1 blue square. Wait, maybe 9 rows and 9 columns: 9×9=81. Yes, 9 rows and 9 columns: 81 squares. So each square is 0.01 (since 10x10=100, so 1/100=0.01). So 81 squares is 81×0.01=0.81. So the expression is 81×0.01.

Step2: Match with the expressions

The expression 81×0.01 gives 0.81, which matches the blue area being 81 out of 100 squares (since each square is 0.01). The other expressions are too large (81×0.1=8.1, 81×100=8100, 80×10=800) and do not represent a part of the 10x10 grid (which is 1 unit).

Answer:

\boxed{81 \times 0.01}