algebra: patterns in decimal factors and products schimmel
TRANSCRIPT
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Algebra: Patterns in Decimal Factors and Products
Schimmel
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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.
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Essential Question:How are the products affected when multiplying decimals by powers of 10?
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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.
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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.
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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
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Guided Practice
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1 x 0.3 = 0.310 x 0.3 = 3
100 x 0.3 = _____1,000 x 0.3 = _____
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1 x 2.845 = 2.84510 x 2.845 = 28.45
100 x 2.845 = _______1,000 x 2.845 = 2,845
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1 x 0.3459 = 0.345910 x 0.3459 = _______100 x 0.3459 = 34.59
1,000 x 0.3459 = 345.9
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0.5 x 1 = 0.50.5 x 0.1 = _____0.5 x 0.01 = 0.005
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3.82 x 1 = 3.823.82 x 0.1 = _____
3.82 x 0.01 = 0.0382
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7.2 x 1 = _____7.2 x 0.1 = 0.72
7.2 x 0.01 = ____
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What is the value of n?
10 x 0.009 = n
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What is the value of n?
n x 0.08 = 0.8
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What is the value of n?
100 x n = 4.5
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Your Turn
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1 x 0.005 = 0.00510 x 0.005 = _____100 x 0.005 = 0.51,000 x 0.005 = 5
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1 x 4.761 = 4.76110 x 4.761 = 47.61
100 x 4.761 = _____1,000 x 4.761 = ______
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1 x 0.45 = 0.4510 x 0.45 = _____
100 x 0.45 = _____1,000 x 0.45 = ______
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1 x 0.9 = ______0.1 x 0.9 = 0.09
0.01 x 0.9 = _____
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1 x 8.2 = 8.20.1 x 8.2 = 0.82
0.01 x 8.2 = _____
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1 x 9.8 = ______0.1 x 9.8 = _____0.01 x 9.8 = 0.098
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What is the value of n?
1.5 x n = 0.15
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What is the value of n?
n x 3.8 = 0.038
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What is the value of n?
0.07 x n = 0.007
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Word Problems
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A half dollar is 0.50 of a dollar. What is the value of 100 half dollars? Of 1,000 half dollars?
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Mario used up 0.1 bottle of vanilla that held 2.5 ounces. How
many ounces did he use?
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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?
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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?
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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?