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Estimate the product: $\text{73}\cdot \text{46}$ .
Notice that 73 is near $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{\mathrm{70,}}}}$ and that 46 is near $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{50.}}}$
The product can be estimated by $\text{70}\cdot \text{50}=\text{3,500}$ . (Recall that to multiply numbers ending in zeros, we multiply the nonzero digits and affix to this product the total number of ending zeros in the factors. See [link] for a review of this technique.)
Thus, $\text{73}\cdot \text{46}$ is about 3,500. In fact, $\text{73}\cdot \text{46}=\text{3,358}$ .
Estimate the product: $\text{87}\cdot \text{4,316}$ .
Notice that 87 is close to $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{\mathrm{90,}}}}$ and that 4,316 is close to $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{\mathrm{4,000.}}}}$
The product can be estimated by $\text{90}\cdot \text{4,000}=\text{360,000}$ .
Thus, $\text{87}\cdot \text{4,316}$ is about 360,000. In fact, $\text{87}\cdot \text{4,316}=\text{375,492}$ .
Estimate the product: $\text{31}\cdot \text{87}$ .
$31\cdot 87:30\cdot 90$ . About 2,700. In fact, 2,697.
Estimate the product: $\text{18}\cdot \text{42}$ .
$18\cdot 42:20\cdot 40$ . About 800. In fact, 756.
Estimate the product: $\text{16}\cdot \text{94}$ .
$16\cdot 94:15\cdot 100$ . About 1,500. In fact, 1,504.
Estimate the quotient: $\text{153}\xf7\text{17}$ .
Notice that 153 is close to $\underset{\text{digits}}{\underset{\text{two nonzero}}{\underbrace{\mathrm{150,}}}}$ and that 17 is close to $\underset{\text{digits}}{\underset{\text{two nonzero}}{\underbrace{15.}}}$
The quotient can be estimated by $\text{150}\xf7\text{15}=\text{10}$ .
Thus, $\text{153}\xf7\text{17}$ is about 10. In fact, $\text{153}\xf7\text{17}=\text{9}$ .
Estimate the quotient: $\text{742,000}\xf7\text{2,400}$ .
Notice that 742,000 is close to $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{\mathrm{700,000}}}}$ , and that 2,400 is close to $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{\mathrm{2,000.}}}}$
The quotient can be estimated by $\text{700,000}\xf7\text{2,000}=\text{350}$ .
Thus, $\text{742,000}\xf7\text{2,400}$ is about 350. In fact, $\text{742,000}\xf7\text{2,400}=\text{309}\text{.}1\overline{6}$ .
Estimate the quotient: $\text{221}\xf7\text{18}$ .
$221\xf718:200\xf720$ . About 10. In fact, 12.27.
Estimate the quotient: $\text{4,079}\xf7\text{381}$ .
$\mathrm{4,079}\xf7381:\mathrm{4,000}\xf7400$ . About 10. In fact, 10.70603675...
Estimate the quotient: $\text{609,000}\xf7\text{16,000}$ .
$\mathrm{609,000}\xf7\mathrm{16,000}:\mathrm{600,000}\xf7\mathrm{15,000}$ . About 40. In fact, 38.0625.
Estimate the sum: $\text{53}\text{.}\text{82}+\text{41}\text{.}6$ .
Notice that 53.82 is close to $\underset{\text{digits}}{\underset{\text{two nonzero}}{\underbrace{\mathrm{54,}}}}$ and that 41.6 is close to $\underset{\text{digits}}{\underset{\text{two nonzero}}{\underbrace{42.}}}$
The sum can be estimated by $\text{54}+\text{42}=\text{96}$ .
Thus, $\text{53}\text{.}\text{82}+\text{41}\text{.}6$ is about 96. In fact, $\text{53}\text{.}\text{82}+\text{41}\text{.}\text{6}=\text{95}\text{.}\text{42}$ .
Estimate the sum: $\text{61}\text{.}\text{02}+\text{26}\text{.}8$ .
$61.02+26.8:61+27$ . About 88. In fact, 87.82.
Estimate the sum: $\text{109}\text{.}\text{12}+\text{137}\text{.}\text{88}$ .
$109.12+137.88:110+138$ . About 248. In fact, 247. We could have estimated 137.88 with 140. Then $110+140$ is an easy mental addition. We would conclude then that $109.12+137.88$ is about 250.
Estimate the product: $(\text{31}\text{.}\text{28})(\text{14}\text{.}2)$ .
Notice that 31.28 is close to $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{\mathrm{30,}}}}$ and that 14.2 is close to $\underset{\text{digits}}{\underset{\text{two nonzero}}{\underbrace{15.}}}$
The product can be estimated by $\text{30}\cdot \text{15}=\text{450}$ . ( $\text{3}\cdot \text{15}=\text{45}$ , then affix one zero.)
Thus, $(\text{31}\text{.}\text{28})(\text{14}\text{.}2)$ is about 450. In fact, $(\text{31}\text{.}\text{28})(\text{14}\text{.}2)=\text{444}\text{.}\text{176}$ .
Estimate 21% of 5.42.
Notice that $\text{21\%}=\text{.}\text{21}$ as a decimal, and that .21 is close to $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{\mathrm{.2.}}}}$
Notice also that 5.42 is close to $\underset{\text{digit}}{\underset{\text{one nonzero}}{\underbrace{5.}}}$
Then, 21% of 5.42 can be estimated by $(\text{.}2)(5)=\text{1}$ .
Thus, 21% of 5.42 is about 1. In fact, 21% of 5.42 is 1.1382.
Estimate the product: $(\text{47}\text{.}8)(\text{21}\text{.}1)$ .
$\left(47.8\right)\left(21.1\right):\left(50\right)\left(20\right)$ . About 1,000. In fact, 1,008.58.
Estimate 32% of 14.88.
32% of $14.88:\left(.3\right)\left(15\right)$ . About 4.5. In fact, 4.7616.
Estimate each calculation using the method of rounding. After you have made an estimate, find the exact value and compare this to the estimated result to see if your estimated value is reasonable. Results may vary.
$\mathrm{1,}\text{402}+\mathrm{2,}\text{198}$
about 3,600; in fact 3,600
$\text{3,481}+\text{4,216}$
$\text{611}+\text{806}$
$\mathrm{4,}\text{681}+\mathrm{9,}\text{325}$
about 14,000; in fact 14,006
$\mathrm{6,}\text{476}+\mathrm{7,}\text{814}$
$\mathrm{7,}\text{805}-\mathrm{4,}\text{266}$
about 3,500; in fact 3,539
$\mathrm{8,}\text{427}-\mathrm{5,}\text{342}$
$\text{14},\text{106}-\mathrm{8,}\text{412}$
about 5,700; in fact 5,694
$\text{26},\text{486}-\text{18},\text{931}$
$\text{67}\cdot \text{42}$
$\text{426}\cdot \text{741}$
$\text{18},\text{012}\cdot \text{32},\text{416}$
about 583,200,000; in fact 583,876,992
$\text{22},\text{481}\cdot \text{51},\text{076}$
$\text{884}\xf7\text{33}$
$\mathrm{2,}\text{189}\xf7\text{42}$
$\mathrm{8,}\text{092}\xf7\text{239}$
about 33; in fact 33.86
$\mathrm{2,}\text{688}\xf7\text{48}$
$\text{72}\text{.}\text{14}+\text{21}\text{.}\text{08}$
about 93.2; in fact 93.22
$\text{43}\text{.}\text{016}+\text{47}\text{.}\text{58}$
$\text{96}\text{.}\text{53}-\text{26}\text{.}\text{91}$
about 70; in fact 69.62
$\text{115}\text{.}\text{0012}-\text{25}\text{.}\text{018}$
$\text{206}\text{.}\text{19}+\text{142}\text{.}\text{38}$
about 348.6; in fact 348.57
$\text{592}\text{.}\text{131}+\text{211}\text{.}6$
$\left(\text{32}\text{.}\text{12}\right)\left(\text{48}\text{.}7\right)$
about 1,568.0; in fact 1,564.244
$\left(\text{87}\text{.}\text{013}\right)\left(\text{21}\text{.}\text{07}\right)$
$\left(3\text{.}\text{003}\right)\left(\text{16}\text{.}\text{52}\right)$
about 49.5; in fact 49.60956
$\left(6\text{.}\text{032}\right)\left(\text{14}\text{.}\text{091}\right)$
$\left(\text{114}\text{.}\text{06}\right)\left(\text{384}\text{.}3\right)$
about 43,776; in fact 43,833.258
$\left(\mathrm{5,}\text{137}\text{.}\text{118}\right)\left(\text{263}\text{.}\text{56}\right)$
$\left(6\text{.}\text{92}\right)\left(0\text{.}\text{88}\right)$
about 6.21; in fact 6.0896
$\left(\text{83}\text{.}\text{04}\right)\left(1\text{.}\text{03}\right)$
$\left(\text{17}\text{.}\text{31}\right)\left(\text{.}\text{003}\right)$
about 0.0519; in fact 0.05193
$\left(\text{14}\text{.}\text{016}\right)\left(\text{.}\text{016}\right)$
$\text{93}\text{\% of}7\text{.}\text{01}$
about 6.3; in fact 6.5193
107% of 12.6
74% of 21.93
4% of .863
( [link] ) Find the difference: $\frac{7}{\text{10}}-\frac{5}{\text{16}}\text{.}$
( [link] ) Find the value $\frac{6-\frac{1}{4}}{6+\frac{1}{4}}\text{.}$
$\frac{\text{23}}{\text{25}}$
( [link] ) Convert the complex decimal $1\text{.}\text{11}\frac{1}{4}$ to a decimal.
( [link] ) A woman 5 foot tall casts an 8-foot shadow at a particular time of the day. How tall is a tree that casts a 96-foot shadow at the same time of the day?
60 feet tall
( [link] ) 11.62 is 83% of what number?
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