Question

20．根據(jù)下列要求的精確度，求2.03⁶的近似值．
（1）精確到0.1；
（2）精確到0.001．

Answer 1

分析 根據(jù)2.03⁶ =（2+0.03）⁶，按照二項(xiàng)式定理展開，結(jié)合精度求得它的值．

解答 解：（1）精確到0.1時(shí)，2.03⁶=（2+0.03）⁶=${C}_{6}^{0}$×2⁶+${C}_{6}^{1}$×2⁵×0.03+…+${C}_{6}^{6}$×0.03⁶
≈${C}_{6}^{0}$•2⁶+${C}_{6}^{1}$•2⁵×0.03+${C}_{6}^{2}$×2⁴×0.03²=64+5.76+0.216≈71.0．
即 2.03⁶≈71.0．
（1）精確到0.01時(shí)，2.03⁶=（2+0.03）⁶=${C}_{6}^{0}$×2⁶+${C}_{6}^{1}$×2⁵×0.03+…+${C}_{6}^{6}$×0.03⁶
≈${C}_{6}^{0}$•2⁶+${C}_{6}^{1}$•2⁵×0.03+${C}_{6}^{2}$×2⁴×0.03²+${C}_{6}^{3}$×2³×0.0³=64+5.76+0.216+0.00432≈70.98．
即 2.03⁶≈70.98．

點(diǎn)評(píng) 本題主要考查二項(xiàng)式定理的應(yīng)用，精確度的定義，屬于基礎(chǔ)題．