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**Algebra: Patterns in Decimal Factors, Products & Quotients**

Schimmel Algebra: Patterns in Decimal Factors, Products & Quotients

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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 quotients affected when dividing decimals by powers of 10?

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When you divide a decimal number by 10, 100, or 1,000, move the decimal point to the left because the quotient will be less than the dividend. When you divide a decimal number by 0.1 and 0.01 move the decimal point to the right because the greater will be greater than the dividend. Example #1 0.98 ÷ 1 = 0.98 24.5 ÷ 1 = 24.5 0.98 ÷ 10 = 0.098 24.5 ÷ 0.1 = 245 0.98 ÷ 100 = 24.5 ÷ 0.01 = 2,450 0.98 ÷ 1,000 = 24.5 ÷ = 24,500

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When you divide a decimal number by 10, 100, or 1,000, move the decimal point to the left because the quotient will be less than the dividend. When you divide a decimal number by 0.1 and 0.01 move the decimal point to the right because the greater will be greater than the dividend. Example #2 0.478 ÷ 1 = 0.478 0.4 ÷ 1 = 0.4 0.478 ÷ 10 = 0.478 0.4 ÷ 0.1 = 4 0.478 ÷ 100 = 0.4 ÷ 0.01 = 40 0.478 ÷ 1,000 = 0.4 ÷ = 400

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Guided Practice

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0.3 ÷ 1 = 0.3 0.3 ÷ 10 = 0.03 0.3 ÷ 100 = _____ 0.3 ÷ 1000 = _____

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2.845 ÷ 1 = 2.845 2.845 ÷ 10 = 2.845 ÷ 100 = _______ 2.845 ÷ 1,000 =

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0.5 ÷ 1 = 0.5 0.5 ÷ 0.1 = ______ 0.5 ÷ 0.01 = ______

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3.82 ÷ 1 = 3.82 3.82 ÷ 0.1 = ________ 3.82 ÷ 0.01 = ________

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7.2 ÷ 1 = _______ 7.2 ÷ 0.1 = ______ 7.2 ÷ 0.01 = ______

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Your Turn

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0.9 ÷ 1 = 0.9 0.9 ÷ 0.1 = _______ 0.9 ÷ 0.01 = _______ 0.9 ÷ = ________ 0.9 ÷ = _______

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8.2 x 1 = 8.2 8.2 ÷ 0.1 = ________ 8.2 ÷ 0.01 = ________ 8.2 ÷ = ________ 8.2 ÷ = _______

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9.8 ÷ 1 = _______ 9.8 ÷ 0.1 = _______ 9.8 ÷ 0.01 = _______ 9.8 ÷ = _______ 9.8 ÷ = _______

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