# 6.5 Multiplication of decimals  (Page 2/2)

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## Practice set b

Use a calculator to find each product. If the calculator will not provide the exact product, round the result to four decimal places.

$5\text{.}\text{126}\cdot \text{4}\text{.}\text{08}$

20.91408

$0\text{.}\text{00165}\cdot \text{0}\text{.}\text{04}$

0.000066

$0\text{.}\text{5598}\cdot \text{0}\text{.}\text{4281}$

0.2397

$0\text{.}\text{000002}\cdot \text{0}\text{.}\text{06}$

0.0000

## Multiplying decimals by powers of 10

There is an interesting feature of multiplying decimals by powers of 10. Consider the following multiplications.

 Multiplication Number of Zeros in the Power of 10 Number of Positions the Decimal Point Has Been Moved to the Right $\text{10}\cdot 8\text{.}\text{315274}=\text{83}\text{.}\text{15274}$ 1 1 $\text{100}\cdot 8\text{.}\text{315274}=\text{831}\text{.}\text{5274}$ 2 2 $1,\text{000}\cdot 8\text{.}\text{315274}=8,\text{315}\text{.}\text{274}$ 3 3 $\text{10},\text{000}\cdot 8\text{.}\text{315274}=\text{83},\text{152}\text{.}\text{74}$ 4 4

## Multiplying a decimal by a power of 10

To multiply a decimal by a power of 10, move the decimal place to the right of its current position as many places as there are zeros in the power of 10. Add zeros if necessary.

## Sample set c

Find the following products.

$\text{100}\cdot \text{34}\text{.}\text{876}$ . Since there are 2 zeros in 100, Move the decimal point in 34.876 two places to the right. $1,\text{000}\cdot 4\text{.}\text{8058}$ . Since there are 3 zeros in 1,000, move the decimal point in 4.8058 three places to the right. $\text{10},\text{000}\cdot \text{56}\text{.}\text{82}$ . Since there are 4 zeros in 10,000, move the decimal point in 56.82 four places to the right. We will have to add two zeros in order to obtain the four places. Since there is no fractional part, we can drop the decimal point.  ## Practice set c

Find the following products.

$\text{100}\cdot \text{4}\text{.}\text{27}$

427

$\text{10,000}\cdot \text{16}\text{.}\text{52187}$

165,218.7

$\left(\text{10}\right)\left(0\text{.}\text{0188}\right)$

0.188

$\left(\text{10,000,000,000}\right)\left(\text{52}\text{.}7\right)$

527,000,000,000

## Multiplication in terms of “of”

Recalling that the word "of" translates to the arithmetic operation of multiplica­tion, let's observe the following multiplications.

## Sample set d

Find 4.1 of 3.8.

Translating "of" to "×", we get

Thus, 4.1 of 3.8 is 15.58.

Find 0.95 of the sum of 2.6 and 0.8.

We first find the sum of 2.6 and 0.8.

$\begin{array}{c}\hfill 2.6\\ \hfill \underline{+0.8}\\ \hfill 3.4\end{array}$

Now find 0.95 of 3.4

Thus, 0.95 of $\left(2\text{.}\text{6}+\text{0}\text{.}8\right)$ is 3.230.

## Practice set d

Find 2.8 of 6.4.

17.92

Find 0.1 of 1.3.

0.13

Find 1.01 of 3.6.

3.636

Find 0.004 of 0.0009.

0.0000036

Find 0.83 of 12.

9.96

Find 1.1 of the sum of 8.6 and 4.2.

14.08

## Exercises

For the following 30 problems, find each product and check each result with a calculator.

$3\text{.}4\cdot 9\text{.}2$

31.28

$4\text{.}5\cdot 6\text{.}1$

$8\text{.}0\cdot 5\text{.}9$

47.20

$6\text{.}1\cdot 7$

$\left(0\text{.}1\right)\left(1\text{.}\text{52}\right)$

0.152

$\left(1\text{.}\text{99}\right)\left(0\text{.}\text{05}\right)$

$\left(\text{12}\text{.}\text{52}\right)\left(0\text{.}\text{37}\right)$

4.6324

$\left(5\text{.}\text{116}\right)\left(1\text{.}\text{21}\right)$

$\left(\text{31}\text{.}\text{82}\right)\left(0\text{.}1\right)$

3.182

$\left(\text{16}\text{.}\text{527}\right)\left(9\text{.}\text{16}\right)$

$0\text{.}\text{0021}\cdot 0\text{.}\text{013}$

0.0000273

$1\text{.}\text{0037}\cdot 1\text{.}\text{00037}$

$\left(1\text{.}6\right)\left(1\text{.}6\right)$

2.56

$\left(4\text{.}2\right)\left(4\text{.}2\right)$

$0\text{.}9\cdot 0\text{.}9$

0.81

$1\text{.}\text{11}\cdot 1\text{.}\text{11}$

$6\text{.}\text{815}\cdot 4\text{.}3$

29.3045

$9\text{.}\text{0168}\cdot 1\text{.}2$

$\left(3\text{.}\text{5162}\right)\left(0\text{.}\text{0000003}\right)$

0.00000105486

$\left(0\text{.}\text{000001}\right)\left(0\text{.}\text{01}\right)$

$\left(\text{10}\right)\left(4\text{.}\text{96}\right)$

49.6

$\left(\text{10}\right)\left(\text{36}\text{.}\text{17}\right)$

$\text{10}\cdot \text{421}\text{.}\text{8842}$

4,218.842

$\text{10}\cdot 8\text{.}\text{0107}$

$\text{100}\cdot 0\text{.}\text{19621}$

19.621

$\text{100}\cdot 0\text{.}\text{779}$

$\text{1000}\cdot 3\text{.}\text{596168}$

3,596.168

$\text{1000}\cdot \text{42}\text{.}\text{7125571}$

$\text{1000}\cdot \text{25}\text{.}\text{01}$

25,010

$\text{100},\text{000}\cdot 9\text{.}\text{923}$

$\left(4\text{.}6\right)\left(6\text{.}\text{17}\right)$

 Actual product Tenths Hundreds Thousandths
 Actual product Tenths Hundreds Thousandths 28.382 28.4 28.38 28.382

$\left(8\text{.}\text{09}\right)\left(7\text{.}1\right)$

 Actual product Tenths Hundreds Thousandths

$\left(\text{11}\text{.}\text{1106}\right)\left(\text{12}\text{.}\text{08}\right)$

 Actual product Tenths Hundreds Thousandths
 Actual product Tenths Hundreds Thousandths 134.216048 134.2 134.22 134.216

$0\text{.}\text{0083}\cdot 1\text{.}\text{090901}$

 Actual product Tenths Hundreds Thousandths

$7\cdot \text{26}\text{.}\text{518}$

 Actual product Tenths Hundreds Thousandths
 Actual product Tenths Hundreds Thousandths 185.626 185.6 185.63 185.626

For the following 15 problems, perform the indicated operations

Find 5.2 of 3.7.

Find 12.03 of 10.1

121.503

Find 16 of 1.04

Find 12 of 0.1

1.2

Find 0.09 of 0.003

Find 1.02 of 0.9801

0.999702

Find 0.01 of the sum of 3.6 and 12.18

Find 0.2 of the sum of 0.194 and 1.07

0.2528

Find the difference of 6.1 of 2.7 and 2.7 of 4.03

Find the difference of 0.071 of 42 and 0.003 of 9.2

2.9544

If a person earns $8.55 an hour, how much does he earn in twenty-five hundredths of an hour? A man buys 14 items at$1.16 each. What is the total cost?

$16.24 In the problem above, how much is the total cost if 0.065 sales tax is added? A river rafting trip is supposed to last for 10 days and each day 6 miles is to be rafted. On the third day a person falls out of the raft after only $\frac{2}{5}$ of that day’s mileage. If this person gets discouraged and quits, what fraction of the entire trip did he complete? 0.24 A woman starts the day with$42.28. She buys one item for $8.95 and another for$6.68. She then buys another item for sixty two-hundredths of the remaining amount. How much money does she have left?

## Calculator problems

For the following 10 problems, use a calculator to determine each product. If the calculator will not provide the exact product, round the results to five decimal places.

$0.019\cdot 0.321$

0.006099

$0.261\cdot 1.96$

$4.826\cdot 4.827$

23.295102

${\left(9.46\right)}^{2}$

${\left(0.012\right)}^{2}$

0.000144

$0.00037\cdot 0.0065$

$0.002\cdot 0.0009$

0.0000018

$0.1286\cdot 0.7699$

$0.01\cdot 0.00000471$

0.0000000471

$0.00198709\cdot 0.03$

## Exercises for review

( [link] ) Find the value, if it exists, of $\text{0}÷\text{15}$ .

0

( [link] ) Find the greatest common factor of 210, 231, and 357.

( [link] ) Reduce $\frac{\text{280}}{2,\text{156}}$ to lowest terms.

$\frac{10}{77}$

( [link] ) Write "fourteen and one hundred twenty-one ten-thousandths, using digits."

( [link] ) Subtract 6.882 from 8.661 and round the result to two decimal places.

1.78

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