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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
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 |
$\mathrm{1,}\text{000}\cdot 8\text{.}\text{315274}=\mathrm{8,}\text{315}\text{.}\text{274}$ | 3 | 3 |
$\text{10},\text{000}\cdot 8\text{.}\text{315274}=\text{83},\text{152}\text{.}\text{74}$ | 4 | 4 |
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.
$\mathrm{1,}\text{000}\cdot 4\text{.}\text{8058}$ . 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.
Find the following products.
$\text{10,000}\cdot \text{16}\text{.}\text{52187}$
165,218.7
$(\text{10,000,000,000})(\text{52}\text{.}7)$
527,000,000,000
Recalling that the word "of" translates to the arithmetic operation of multiplication, let's observe the following multiplications.
Find 4.1 of 3.8.
Translating "of" to "×", we get
$\begin{array}{c}\hfill 4.1\\ \hfill \underline{\times 3.8}\\ \hfill 328\\ \hfill \underline{123\text{}}\\ \hfill 15.58\end{array}$
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
$\begin{array}{c}\hfill 3.4\\ \hfill \underline{\times 0.95}\\ \hfill 170\\ \hfill \underline{306\text{}}\\ \hfill 3.230\end{array}$
Thus, 0.95 of $(2\text{.}\text{6}+\text{0}\text{.}8)$ is 3.230.
For the following 30 problems, find each product and check each result with a calculator.
$4\text{.}5\cdot 6\text{.}1$
$6\text{.}1\cdot 7$
$(1\text{.}\text{99})(0\text{.}\text{05})$
$(5\text{.}\text{116})(1\text{.}\text{21})$
$(\text{16}\text{.}\text{527})(9\text{.}\text{16})$
$1\text{.}\text{0037}\cdot 1\text{.}\text{00037}$
$(4\text{.}2)(4\text{.}2)$
$1\text{.}\text{11}\cdot 1\text{.}\text{11}$
$9\text{.}\text{0168}\cdot 1\text{.}2$
$(3\text{.}\text{5162})(0\text{.}\text{0000003})$
0.00000105486
$(0\text{.}\text{000001})(0\text{.}\text{01})$
$(\text{10})(\text{36}\text{.}\text{17})$
$\text{10}\cdot 8\text{.}\text{0107}$
$\text{100}\cdot 0\text{.}\text{779}$
$\text{1000}\cdot \text{42}\text{.}\text{7125571}$
$\text{100},\text{000}\cdot 9\text{.}\text{923}$
$(4\text{.}6)(6\text{.}\text{17})$
Actual product | Tenths | Hundreds | Thousandths |
Actual product | Tenths | Hundreds | Thousandths |
28.382 | 28.4 | 28.38 | 28.382 |
$(8\text{.}\text{09})(7\text{.}1)$
Actual product | Tenths | Hundreds | Thousandths |
$(\text{11}\text{.}\text{1106})(\text{12}\text{.}\text{08})$
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 16 of 1.04
Find 0.09 of 0.003
Find 0.01 of the sum of 3.6 and 12.18
Find the difference of 6.1 of 2.7 and 2.7 of 4.03
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?
$0.261\cdot 1.96$
${\left(9.46\right)}^{2}$
$0.00037\cdot 0.0065$
$0.1286\cdot 0.7699$
$0.00198709\cdot 0.03$
( [link] ) Find the value, if it exists, of $\text{0}\xf7\text{15}$ .
0
( [link] ) Find the greatest common factor of 210, 231, and 357.
( [link] ) Reduce $\frac{\text{280}}{\mathrm{2,}\text{156}}$ 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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