Kopertina e librit Matematika 9

Zgjidhja e ushtrimit 5

Zgjidhja e ushtrimit 5 të mësimit 2.5 në librin Matematika 9 nga shtëpia botuese Ideart Botime me autorë Patrick Kivlin, Sue Pemberton, Paul Winters.

Pyetja

Pasi të keni shkruar numrat në trajtë shkencore, kryeni veprimet e mëposhtme.

  1. 50000000×20000000×(0.0003)50000000 \times 20000000 \times (0.0003)
  2. 2500000×0.00004:20000002500000\times0.00004:2000000
  3. 400000:(2000×0.0008)400000:(2000\times0.0008)
  4. (0.1)6×(0.001)2×(0.01)3(−2)2×(0.1)4×(3)−4\dfrac{(0.1)^6\times(0.001)^2\times(0.01)^3}{(-2)^2\times(0.1)^4 \times (3)^{-4}}
  5. 24000×(30000×0.006)20.0008×2×105\dfrac{24000\times(30000\times0.006)^2}{0.0008\times2\times10^5}

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Zgjidhja

  1. 5×107×2×106×3×10−4=5×2×3×107+6+(−4)=30×1013−4=3×10×109=3×10105\times10^7\times2\times10^6\times3\times10^{-4}=5\times2\times3\times10^{7+6+(-4)}=30\times10^{13-4}=3\times10\times10^9=\boxed{3\times10^{10}}
  2. 2.5×106×4×10−5:2×106=2.5×106×4×10−52×106=2.5×106×2×10−5−6=2.5×2×106×10−11=5×106+(−11)=5×106−11=5×10−52.5\times10^6\times4\times10^{-5}:2\times10^6=2.5\times10^6\times\dfrac{4\times10^{-5}}{2\times10^6}=2.5\times10^6\times2\times10^{-5-6}=2.5\times2\times10^6\times10^{-11}=5\times10^{6+(-11)}=5\times10^{6-11}=\boxed{5\times10^{-5}}
  3. 4×105:(2×103×8×10−4)=4×105:(2×8×103+(−4))=4×10516×10−1=1054×10−1=14×105−(−1)=0.25×105+1=0.25×1064\times10^5:(2\times10^3\times8\times10^{-4})=4\times10^5:(2\times8\times10^{3+(-4)})=\dfrac{\cancel4\times10^5}{\cancel{16}\times10^{-1}}=\dfrac{10^5}{4\times10^{-1}}=\dfrac{1}{4}\times10^{5-(-1)}=0.25\times10^{5+1}=\boxed{0.25\times10^6}
  4. (10−1)6×(10−3)2×(10−2)34×(10−1)4×13=10−6×10−6×10−643×10−4=(10−6)343×10−4=34×10−1810−4=0.75×10−18−(−4)=0.75×10−18+4=7.5×10−1×10−14=7.5×10(−1)+(−14)=7.5×10−15\dfrac{(10^{-1})^6\times(10^{-3})^2\times(10^{-2})^3}{4\times(10^{-1})^4\times\frac{1}{3}}=\dfrac{10^{-6}\times10^{-6}\times10^{-6}}{\frac{4}{3}\times10^{-4}}=\dfrac{(10^{-6})^3}{\frac{4}{3}\times10^{-4}}=\dfrac{3}{4}\times\dfrac{10^{-18}}{10^{-4}}=0.75\times10^{-18-(-4)}=0.75\times10^{-18+4}=7.5\times10^{-1}\times10^{-14}=7.5\times10^{(-1)+(-14)}=\boxed{7.5\times10^{-15}}
  5. 2.4×104×(3×104×6×10−3)28×10−4×2×105=2.4×104×(18×104+(−3))216×10−4+5=2.4×104×(1.8×10×10)21.6×10×10=2.4×104×(1.8×102)21.6×102=2.4×104×1.82×102×21.6×102=2.4×3.24×104+41.6×102=1.5×3.24×108102=4.86×108−2=4.86×106\dfrac{2.4\times10^4\times(3\times10^4\times6\times10^{-3})^2}{8\times10^{-4}\times2\times10^5}=\dfrac{2.4\times10^4\times(18\times10^{4+(-3)})^2}{16\times10^{-4+5}}=\dfrac{2.4\times10^4\times(1.8\times10\times10)^2}{1.6\times10\times10}=\dfrac{2.4\times10^4\times(1.8\times10^2)^2}{1.6\times10^2}=\dfrac{2.4\times10^4\times1.8^2\times10^{2\times2}}{1.6\times10^2}=\dfrac{\cancel{2.4}\times 3.24\times10^{4+4}}{\cancel{1.6}\times10^2}=\dfrac{1.5\times3.24\times10^{8}}{10^2}=4.86\times10^{8-2}=\boxed{4.86\times10^6}