1. Algebra: Patterns in Decimal Factors, Products & Quotients
Schimmel
Algebra: Patterns in Decimal Factors, Products & Quotients

2. 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.

3. Essential Question:
How are the quotients affected when dividing decimals by powers of 10?

4. 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

5. 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

6. Guided Practice

7. 0.3 ÷ 1 = 0.3
0.3 ÷ 10 = 0.03
0.3 ÷ 100 = _____
0.3 ÷ 1000 = _____

8. 2.845 ÷ 1 = 2.845
2.845 ÷ 10 =
2.845 ÷ 100 = _______
2.845 ÷ 1,000 =

11. 0.5 ÷ 1 = 0.5
0.5 ÷ 0.1 = ______
0.5 ÷ 0.01 = ______

12. 3.82 ÷ 1 = 3.82
3.82 ÷ 0.1 = ________
3.82 ÷ 0.01 = ________

13. 7.2 ÷ 1 = _______
7.2 ÷ 0.1 = ______
7.2 ÷ 0.01 = ______

14. Your Turn

18. 0.9 ÷ 1 = 0.9
0.9 ÷ 0.1 = _______
0.9 ÷ 0.01 = _______
0.9 ÷ = ________
0.9 ÷ = _______

19. 8.2 x 1 = 8.2
8.2 ÷ 0.1 = ________
8.2 ÷ 0.01 = ________
8.2 ÷ = ________
8.2 ÷ = _______

20. 9.8 ÷ 1 = _______
9.8 ÷ 0.1 = _______
9.8 ÷ 0.01 = _______
9.8 ÷ = _______
9.8 ÷ = _______