# Calculating Products of Decimals

Warmup

Activity #1

Multiply Small Decimal Numbers by 10.

• Enter a decimal number between 0.01 and 0.4.​
• Without click the mouse or pressing the Enter key, try to solve the problem on paper.​
• Press the Enter key to see the answer.​
• Check the two boxes to see the model.

Activity #2

Multiply Decimals by Powers of 10.

• Check the box “Extend this concept”.
• Attempt to solve the problem before checking the answer.
• Check “Explain” to see the general rule.
• Uncheck the boxes and then use the slider to multiply by different powers of 10.
• Click and click .
• Follow the same steps as above.

Activity #3

Review Rules Multiply Decimals.

• Follow the Six Rules to Multiply Decimals in the applet below.

Challenge #1

Use the area diagram below to multiply the numbers, (4.6) · (0.9). First decompose each number into its base ten units and write them in the boxes on each side of the rectangle. Write the area of each lettered region in the diagram. Then find the area of the entire rectangle.

Challenge #2

Here are an unfinished calculation of (0.54) · (3.8) and 0.54-by-3.8 rectangle.

(1.) Which part of the rectangle has an area of 0.432? Which part of the rectangle has an area of 1.62? Show your reasoning in the applet above.

(2.) What is (0.54) · (3.8)?

Challenge #3

Explain how the product of 3 and 65 could be used to find (0.03) · (0.065)?

Challenge #3