Algebra: Patterns in Decimal Factors and Products

Schimmel

MCC5.NBT.2 – Explain patterns in the number of zeros of the product when multiplying a number by powers of ten, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

Essential Question:How are the products affected when multiplying decimals by powers of 10?

When you multiply a decimal number by 10, 100, or 1,000, move the decimal point to the right because the product will be greater than the original factor.

When you multiply a decimal number by 0.1 and 0.01 move the decimal point to the left because the product will be less than the original factor.

Example #10.98 x 1 = 0.98

Example #124.5 x 1 = 24.5

0.98 x 10 = 9.8 24.5 x 0.1 = 2.45

0.98 x 100 = 98. 24.5 x 0.01 = 0.2450.98 x 1,000 = 980.

When you multiply a decimal number by 10, 100, or 1,000, move the decimal point to the right because the product will be greater than the original factor.

When you multiply a decimal number by 0.1 and 0.01 move the decimal point to the left because the product will be less than the original factor.

Example #20.478 x 1 = 0.478

Example #20.4 x 1 = 0.4

0.478 x 10 = 4.78 0.4 x 0.1 = 0.04

0.478 x 100 = 47.8 0.4 x 0.01 = 0.0040.478 x 1,000 = 478.

When you multiply a decimal number by 10, 100, or 1,000, move the decimal point to the right because the product will be greater than the original factor.

When you multiply a decimal number by 0.1 and 0.01 move the decimal point to the left because the product will be less than the original factor.

Example #3$3.25 x 1 = $3.25

Example #30.88 x 1 = 0.88

$3.25 x 10 = $32.50 0.88 x 0.1 = 0.088

$3.25 x 100 = $325.00 0.88 x 0.01 = 0.0088$3.25 x 1,000 = $3,250.00

Guided Practice

1 x 0.3 = 0.310 x 0.3 = 3

100 x 0.3 = _____1,000 x 0.3 = _____

1 x 2.845 = 2.84510 x 2.845 = 28.45

100 x 2.845 = _______1,000 x 2.845 = 2,845

1 x 0.3459 = 0.345910 x 0.3459 = _______100 x 0.3459 = 34.59

1,000 x 0.3459 = 345.9

0.5 x 1 = 0.50.5 x 0.1 = _____0.5 x 0.01 = 0.005

3.82 x 1 = 3.823.82 x 0.1 = _____

3.82 x 0.01 = 0.0382

7.2 x 1 = _____7.2 x 0.1 = 0.72

7.2 x 0.01 = ____

What is the value of n?

10 x 0.009 = n

What is the value of n?

n x 0.08 = 0.8

What is the value of n?

100 x n = 4.5

Your Turn

1 x 0.005 = 0.00510 x 0.005 = _____100 x 0.005 = 0.51,000 x 0.005 = 5

1 x 4.761 = 4.76110 x 4.761 = 47.61

100 x 4.761 = _____1,000 x 4.761 = ______

1 x 0.45 = 0.4510 x 0.45 = _____

100 x 0.45 = _____1,000 x 0.45 = ______

1 x 0.9 = ______0.1 x 0.9 = 0.09

0.01 x 0.9 = _____

1 x 8.2 = 8.20.1 x 8.2 = 0.82

0.01 x 8.2 = _____

1 x 9.8 = ______0.1 x 9.8 = _____0.01 x 9.8 = 0.098

What is the value of n?

1.5 x n = 0.15

What is the value of n?

n x 3.8 = 0.038

What is the value of n?

0.07 x n = 0.007

Word Problems

A half dollar is 0.50 of a dollar. What is the value of 100 half dollars? Of 1,000 half dollars?

Mario used up 0.1 bottle of vanilla that held 2.5 ounces. How

many ounces did he use?

A package contains 100 small pieces of candy. The package contains 12.5

grams of fat. How many grams of fat are in each piece of candy?

At the school dance, 100 people bought candy bars. Each candy bar

cost $0.65. What was the total amount collected from the ice cream sales?

Jason learned that Native earth houses 45 feet long. He built a

model that is 0.01 times as long. How long is Jason’s model?