Algebra: Patterns in Decimal Factors, Products & Quotients

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 quotients affected when dividing decimals by powers of 10?

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 #10.98 ÷ 1 = 0.98

Example #124.5 ÷ 1 = 24.5

0.98 ÷ 10 = 0.098 24.5 ÷ 0.1 = 245

0.98 ÷ 100 = 0.0098 24.5 ÷ 0.01 = 2,450

0.98 ÷ 1,000 = 0.00098 24.5 ÷ 0.001 = 24,500

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 #20.478 ÷ 1 = 0.478

Example #20.4 ÷ 1 = 0.4

0.478 ÷ 10 = 0.478 0.4 ÷ 0.1 = 4

0.478 ÷ 100 = 0.00478 0.4 ÷ 0.01 = 400.478 ÷ 1,000 = 0.000478 0.4 ÷ 0.001 = 400

Guided Practice

0.3 ÷ 1 = 0.30.3 ÷ 10 = 0.03

0.3 ÷ 100 = _____ 0.3 ÷ 1000 = _____

2.845 ÷ 1 = 2.8452.845 ÷ 10 = 0.2845

2.845 ÷ 100 = _______2.845 ÷ 1,000 = 0.002845

 

 

0.5 ÷ 1 = 0.50.5 ÷ 0.1 = ______

0.5 ÷ 0.01 = ______

3.82 ÷ 1 = 3.823.82 ÷ 0.1 = ________

3.82 ÷ 0.01 = ________

7.2 ÷ 1 = _______7.2 ÷ 0.1 = ______

7.2 ÷ 0.01 = ______

Your Turn

 

 

 

0.9 ÷ 1 = 0.90.9 ÷ 0.1 = _______

0.9 ÷ 0.01 = _______0.9 ÷ 0.001 = ________0.9 ÷ 0.0001 = _______

8.2 x 1 = 8.28.2 ÷ 0.1 = ________

8.2 ÷ 0.01 = ________8.2 ÷ 0.001 = ________8.2 ÷ 0.0001 = _______

9.8 ÷ 1 = _______9.8 ÷ 0.1 = _______

9.8 ÷ 0.01 = _______9.8 ÷ 0.001 = _______

9.8 ÷ 0.0001 = _______