Question

complete each table. use patterns to help.

number	÷ 10	÷ 100	÷ 1000
8.9
165
0.72

number	÷ 10	÷ 100	÷ 1000
56.29
0.286
126.93

divide.

1. $8 \div 10 = \underline{\quad\quad}$
2. $93 \div 10 = \underline{\quad\quad}$
3. $0.47 \div 10 = \underline{\quad\quad}$
4. $2.54 \div 100 = \underline{\quad\quad}$
5. $0.08 \div 100 = \underline{\quad\quad}$
6. $3427.1 \div 100 = \underline{\quad\quad}$
7. $1 \div 1000 = \underline{\quad\quad}$
8. $3.006 \div 1000 = \underline{\quad\quad}$
9. $82.45 \div 1000 = \underline{\quad\quad}$

find the value of the variable.

1. $0.14 \div a = 0.014$ $\underline{\quad\quad}$
2. $7.6 \div n = 0.076$ $\underline{\quad\quad}$
3. $21 \div b = 0.021$ $\underline{\quad\quad}$
4. $d \div 1000 = 3.175$ $\underline{\quad\quad}$
5. $m \div 100 = 7.253$ $\underline{\quad\quad}$
6. $y \div 100 = 0.32$ $\underline{\quad\quad}$

Explanation:

Step1: Divide by 10 (shift decimals left 1)

For 16.2: $16.2 \div 10 = 1.62$
For 8.9: $8.9 \div 10 = 0.89$
For 165: $165 \div 10 = 16.5$
For 0.72: $0.72 \div 10 = 0.072$
For 1679: $1679 \div 10 = 167.9$
For 56.29: $56.29 \div 10 = 5.629$
For 0.286: $0.286 \div 10 = 0.0286$
For 126.93: $126.93 \div 10 = 12.693$
For 8: $8 \div 10 = 0.8$
For 93: $93 \div 10 = 9.3$
For 0.47: $0.47 \div 10 = 0.047$

Step2: Divide by 100 (shift decimals left 2)

For 16.2: $16.2 \div 100 = 0.162$
For 8.9: $8.9 \div 100 = 0.089$
For 165: $165 \div 100 = 1.65$
For 0.72: $0.72 \div 100 = 0.0072$
For 1679: $1679 \div 100 = 16.79$
For 56.29: $56.29 \div 100 = 0.5629$
For 0.286: $0.286 \div 100 = 0.00286$
For 126.93: $126.93 \div 100 = 1.2693$
For 2.54: $2.54 \div 100 = 0.0254$
For 0.08: $0.08 \div 100 = 0.0008$
For 3427.1: $3427.1 \div 100 = 34.271$

Step3: Divide by 1000 (shift decimals left 3)

For 16.2: $16.2 \div 1000 = 0.0162$
For 8.9: $8.9 \div 1000 = 0.0089$
For 165: $165 \div 1000 = 0.165$
For 0.72: $0.72 \div 1000 = 0.00072$
For 1679: $1679 \div 1000 = 1.679$
For 56.29: $56.29 \div 1000 = 0.05629$
For 0.286: $0.286 \div 1000 = 0.000286$
For 126.93: $126.93 \div 1000 = 0.12693$
For 1: $1 \div 1000 = 0.001$
For 3.006: $3.006 \div 1000 = 0.003006$
For 82.45: $82.45 \div 1000 = 0.08245$

Step4: Solve for variables (reverse division)

For 18: $a = \frac{0.14}{0.014} = 10$
For 19: $n = \frac{7.6}{0.076} = 100$
For 20: $b = \frac{21}{0.021} = 1000$
For 21: $d = 3.175 \times 1000 = 3175$
For 22: $m = 7.253 \times 100 = 725.3$
For 23: $y = 0.32 \times 100 = 32$

Answer:

Completed Tables:

Number	$\div 10$	$\div 100$	$\div 1000$
8.9	0.89	0.089	0.0089
165	16.5	1.65	0.165
0.72	0.072	0.0072	0.00072

Number	$\div 10$	$\div 100$	$\div 1000$
56.29	5.629	0.5629	0.05629
0.286	0.0286	0.00286	0.000286
126.93	12.693	1.2693	0.12693

Divide Section:

1. $0.8$
2. $9.3$
3. $0.047$
4. $0.0254$
5. $0.0008$
6. $34.271$
7. $0.001$
8. $0.003006$
9. $0.08245$

Variable Section:

1. $a=10$
2. $n=100$
3. $b=1000$
4. $d=3175$
5. $m=725.3$
6. $y=32$