When students first start learning about decimals, teachers may use shaded graphs to help demonstrate how they work. The whole graph represents the number 1, and it is divided into a number of equal parts. It may be divided into 10 parts, 100 parts or 1,000 parts. Teachers use these graphs to teach place value in decimals. They first show their students a 10-square graph, then a 100-square graph, then a 1,000-square graph. They shade different amounts of the graphs to represent different decimals.

Note that 1 shaded square on a 10 graph, 10 shaded squares on a 100 graph and 100 shaded squares on a 1,000 graph are all the same size. This is because .1, .10 and .100 are all the same value. One square on a 10 graph is one tenth. One square on a 100 graph is one hundredth. One square on a 1,000 graph is one thousandth.

Identify the graph. See if it has 10 squares, 100 squares or 1,000 squares.

Count the number of shaded squares. If the graph has 100 squares, count each fully-shaded row as 10, then count the individual squares in a partially-shaded row. If the graph has 1,000 squares, count each fully-shaded box as 100, then each left-over fully-shaded row as 10, then each left-over individual shaded square.

Count the zeros in the total number of squares (10 has one zero; 100 has two zeros; 1,000 has three zeros). Write down the number of shaded squares, and use the same number of digits as the zeros you just counted. For example, if you counted three shaded squares in a 10 graph, write "3," with only one digit; for three shaded squares in a 100 graph, write "03," with two digits; for three shaded squares in a 1,000 graph, write "003," with three digits.

Put a decimal point on the left of the number, before any zeros you added. For example, for three shaded squares on a 1,000 graph, write .003.

#### Tips

References

Tips

- Note that 1 shaded square on a 10 graph, 10 shaded squares on a 100 graph and 100 shaded squares on a 1,000 graph are all the same size. This is because .1, .10 and .100 are all the same value.
- One square on a 10 graph is one tenth. One square on a 100 graph is one hundredth. One square on a 1,000 graph is one thousandth.

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