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\(a)\) \(\left(-4,125\right).0,01=-0,04125\)
\(b)\) \(\left(-28,45\right):\left(-0,01\right)=2845\)
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`MSC: 756`
Có: `5/21=[5.36]/[21.36]=180/756`
`3/28=[3.27]/[28.27]=81/756`
`45/[-108]=[-45.7]/[108.7]=[-315]/756`
Quy đồng \(\dfrac{5}{21};\dfrac{3}{28};\dfrac{45}{-108}\)
Chuyển dấu \(\dfrac{45}{-108}=\dfrac{45
.
\left(-1\right)}{\left(-108\right)
.
\left(-1\right)}=-\dfrac{45}{108}\)
Ta có MSC(21,28,108): 756
\(\dfrac{5}{21}=\dfrac{5
.
36}{21
.
36}=\dfrac{180}{756}\) ; \(\dfrac{3}{28}=\dfrac{3
.
27}{28
.
27}=\dfrac{81}{756}\) ; \(-\dfrac{45}{108}=\dfrac{\left(-45\right)
.
7}{108
.
7}=-\dfrac{315}{756}\)
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Giải:
Vì:
\(\dfrac{1}{2}< \dfrac{2}{3}.\)
\(\dfrac{2}{3}< \dfrac{3}{4}.\)
.............
\(\dfrac{9999}{10000}< \dfrac{10000}{10001}.\)
\(\Rightarrow S^2< \dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{9999}{10000}.\dfrac{10000}{10001}.\)
\(\Rightarrow S^2< \dfrac{1}{10001}< \dfrac{1}{10000}=\left(\dfrac{1}{100}\right)^2.\)
Mà \(\left(\dfrac{1}{100}\right)^2=0,01^2.\)
\(\Rightarrow S^2< 0,01^2\left(=\left(\dfrac{1}{100}\right)^2\right).\)
\(\Rightarrow S< 0,01.\)
Vậy \(S< 0,01.\)
~ Học tốt!!! ~
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\(\frac{\left(\frac{11^2}{200}+0,415\right):0,01}{\frac{1}{12}-37,25+3\frac{1}{6}}=\frac{\left(\frac{121}{200}+\frac{83}{200}\right):\frac{1}{100}}{\frac{1}{12}-\frac{149}{4}+\frac{19}{6}}=\frac{\frac{51}{50}.100}{\frac{1}{12}-\frac{447}{12}+\frac{38}{12}}\)
=\(\frac{102}{-34}=-3\)
2845 nha