Question

a pattern for multiplying decimals
rewrite a decimal problem as fractions to find the pattern.
\

$$\begin{array}{r} 0.6\\\\ \\times 0.3\\\\ \\hline \\end{array}$$

\quad \

$$\begin{array}{r} 0.24\\\\ \\times 0.4\\\\ \\hline \\end{array}$$

\quad \

$$\begin{array}{r} 0.09\\\\ \\times 0.04\\\\ \\hline \\end{array}$$

\frac{6}{10} \times \frac{3}{10} = \frac{18}{100} \quad \frac{4}{10} \times \frac{24}{100} = \frac{96}{1000} \quad \frac{9}{100} \times \frac{4}{100} = \frac{36}{10000}
0.6 \times 0.3 = 0.18 \quad 0.4 \times 0.24 = 0.096 \quad 0.09 \times 0.04 = 0.0036
the pattern: multiply as with whole numbers. the product will have the same number of decimal places as the total decimal places of the factors.
find the products.

1. \

$$\begin{array}{r} 3.25\\\\ \\times \\quad 3\\\\ \\hline 9.75\\\\ \\end{array}$$

\underline{\quad} decimal places \underline{\quad} decimal places \underline{\quad} decimal places

1. \

$$\begin{array}{r} 3.2\\\\ \\times \\quad 8\\\\ \\hline 25.6\\\\ \\end{array}$$

\underline{\quad} decimal places \underline{\quad} decimal places \underline{\quad} decimal places

1. \

$$\begin{array}{r} 29.8\\\\ \\times \\quad.06\\\\ \\hline \\end{array}$$

\underline{\quad} decimal places \underline{\quad} decimal places \underline{\quad} decimal places

1. \

$$\begin{array}{r} .32\\\\ \\times \\quad.06\\\\ \\hline \\end{array}$$

\underline{\quad} decimal places \underline{\quad} decimal places \underline{\quad} decimal places

1. \

$$\begin{array}{r} .5\\\\ \\times \\quad.3\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} .23\\\\ \\times \\quad.4\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} .27\\\\ \\times \\quad.04\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} .19\\\\ \\times \\quad 6\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} .014\\\\ \\times \\quad.4\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} .17\\\\ \\times \\quad.07\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} 4.9\\\\ \\times \\quad 5\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} 2.7\\\\ \\times \\quad.6\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} 3.5\\\\ \\times \\quad.04\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} 65.1\\\\ \\times \\quad.03\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} 2.3\\\\ \\times \\quad.6\\\\ \\hline \\end{array}$$

1. \

$$\begin{array}{r} 59.8\\\\ \\times \\quad.05\\\\ \\hline \\end{array}$$

1. gina’s mother walks 2.75 kilometers each day. how many kilometers does she walk in one week?
2. your home uses 8.4 kilowatts of electricity each day. how much would be used in 0.5 of a day?

Explanation:

Step1: Count decimal places (Q1)

3.25: 2 places; 3: 0 places; Total: $2+0=2$
Calculate product: $325 \times 3 = 975$ → place decimal: $9.75$

Step2: Count decimal places (Q2)

3.2: 1 place; 8: 0 places; Total: $1+0=1$
Calculate product: $32 \times 8 = 256$ → place decimal: $25.6$

Step3: Count decimal places (Q3)

29.8:1 place; 0.06:2 places; Total: $1+2=3$
Calculate product: $298 \times 6 = 1788$ → place decimal: $1.788$

Step4: Count decimal places (Q4)

0.32:2 places; 0.06:2 places; Total: $2+2=4$
Calculate product: $32 \times 6 = 192$ → place decimal: $0.0192$

Step5: Calculate Q5 product

0.5 (1 place) ×0.3 (1 place); Total places: 2
$5 \times 3 =15$ → $0.15$

Step6: Calculate Q6 product

0.23 (2 places) ×0.4 (1 place); Total places:3
$23 \times 4=92$ → $0.092$

Step7: Calculate Q7 product

0.27 (2 places) ×0.04 (2 places); Total places:4
$27 \times 4=108$ → $0.0108$

Step8: Calculate Q8 product

0.19 (2 places) ×6 (0 places); Total places:2
$19 \times 6=114$ → $1.14$

Step9: Calculate Q9 product

0.014 (3 places) ×0.4 (1 place); Total places:4
$14 \times 4=56$ → $0.0056$

Step10: Calculate Q10 product

0.17 (2 places) ×0.07 (2 places); Total places:4
$17 \times 7=119$ → $0.0119$

Step11: Calculate Q11 product

4.9 (1 place) ×5 (0 places); Total places:1
$49 \times 5=245$ → $24.5$

Step12: Calculate Q12 product

2.7 (1 place) ×0.6 (1 place); Total places:2
$27 \times 6=162$ → $1.62$

Step13: Calculate Q13 product

3.5 (1 place) ×0.04 (2 places); Total places:3
$35 \times 4=140$ → $0.140=0.14$

Step14: Calculate Q14 product

65.1 (1 place) ×0.03 (2 places); Total places:3
$651 \times 3=1953$ → $1.953$

Step15: Calculate Q15 product

2.3 (1 place) ×0.6 (1 place); Total places:2
$23 \times 6=138$ → $1.38$

Step16: Calculate Q16 product

59.8 (1 place) ×0.05 (2 places); Total places:3
$598 \times 5=2990$ → $2.990=2.99$

Step17: Solve Q17 (weekly walk)

1 week =7 days; Total km: $2.75 \times 7$
$275 \times7=1925$; 2 decimal places → $19.25$

Step18: Solve Q18 (electricity use)

Use: $8.4 \times 0.5$
$84 \times5=420$; 2 decimal places → $4.20=4.2$

Answer:

1. 2 decimal places, 0 decimal places, 2 decimal places; Product: $9.75$
2. 1 decimal place, 0 decimal places, 1 decimal place; Product: $25.6$
3. 1 decimal place, 2 decimal places, 3 decimal places; Product: $1.788$
4. 2 decimal places, 2 decimal places, 4 decimal places; Product: $0.0192$
5. Product: $0.15$
6. Product: $0.092$
7. Product: $0.0108$
8. Product: $1.14$
9. Product: $0.0056$
10. Product: $0.0119$
11. Product: $24.5$
12. Product: $1.62$
13. Product: $0.14$
14. Product: $1.953$
15. Product: $1.38$
16. Product: $2.99$
17. $19.25$ kilometers
18. $4.2$ kilowatts