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1. 计算$3.8×10^{7}-3.7×10^{7}$的结果用科学记数法表示为 （
A.$0.1×10^{7}$
B.$0.1×10^{6}$
C.$1×10^{7}$
D.$1×10^{6}$
D
）A.$0.1×10^{7}$
B.$0.1×10^{6}$
C.$1×10^{7}$
D.$1×10^{6}$
答案
D 解析:$3.8×10^{7}-3.7×10^{7}=(3.8-3.7)×10^{7}=0.1×10^{7}=1×10^{6}$.故选 D.
2. 若$a = -\dfrac{1235×1235 - 1235}{1234×1234 + 1234}$，$b = -\dfrac{1236×1236 - 1236}{1235×1235 + 1235}$，$c = \dfrac{1237×1237 - 1237}{1236×1236 + 1236}$，则$abc$的值为（
A.-1
B.3
C.-3
D.1
D
）A.-1
B.3
C.-3
D.1
答案
D 解析:由题意得 $a=-\dfrac{1\ 235×(1\ 235-1)}{1\ 234×(1\ 234+1)}=-1$,同理可得$b=-1,c=1$,则 $abc=(-1)×(-1)×1=1$.故选 D.
3. 计算:
(1) $4×(\dfrac{1}{2}-\dfrac{3}{10}+\dfrac{2}{5})×(-25)=$ ______；
(2) $-0.85×\dfrac{8}{17}+14×\dfrac{2}{7}-(14×\dfrac{3}{7}-\dfrac{9}{17}×0.85)=$ ______。
(1) $4×(\dfrac{1}{2}-\dfrac{3}{10}+\dfrac{2}{5})×(-25)=$ ______；
(2) $-0.85×\dfrac{8}{17}+14×\dfrac{2}{7}-(14×\dfrac{3}{7}-\dfrac{9}{17}×0.85)=$ ______。
答案
(1)-60 解析:原式=$4×(-25)×(\dfrac{1}{2}-\dfrac{3}{10}+\dfrac{2}{5})=(-100)×(\dfrac{5}{10}-\dfrac{3}{10}+\dfrac{4}{10})=(-100)×\dfrac{6}{10}=-60$.
(2)-1.95 解析:原式=$-0.85×\dfrac{8}{17}+14×\dfrac{2}{7}-14×\dfrac{3}{7}+\dfrac{9}{17}×0.85=0.85×(-\dfrac{8}{17}+\dfrac{9}{17})+14×(\dfrac{2}{7}-\dfrac{3}{7})=0.85×\dfrac{1}{17}+14×(-\dfrac{1}{7})=0.05-2=-1.95$.
(2)-1.95 解析:原式=$-0.85×\dfrac{8}{17}+14×\dfrac{2}{7}-14×\dfrac{3}{7}+\dfrac{9}{17}×0.85=0.85×(-\dfrac{8}{17}+\dfrac{9}{17})+14×(\dfrac{2}{7}-\dfrac{3}{7})=0.85×\dfrac{1}{17}+14×(-\dfrac{1}{7})=0.05-2=-1.95$.
4. 简便运算：
(1) $(-\dfrac{3}{4})^3 × 0.75 + 0.5^2 × (-\dfrac{3}{4})^3 + \dfrac{25}{37} × (-1\dfrac{12}{25}) × (-\dfrac{3}{4})^3 + 4^3 ÷ (-\dfrac{4}{3})^3$；
(2) $(-1001) × (-0.125)^2 × (-\dfrac{2}{7}) × (-\dfrac{4}{13}) × (-\dfrac{1}{11})$。
(1) $(-\dfrac{3}{4})^3 × 0.75 + 0.5^2 × (-\dfrac{3}{4})^3 + \dfrac{25}{37} × (-1\dfrac{12}{25}) × (-\dfrac{3}{4})^3 + 4^3 ÷ (-\dfrac{4}{3})^3$；
(2) $(-1001) × (-0.125)^2 × (-\dfrac{2}{7}) × (-\dfrac{4}{13}) × (-\dfrac{1}{11})$。
答案
(1)原式$=(-\dfrac{3}{4})^3 ×0.75+0.25×(-\dfrac{3}{4})^3 -1×(-\dfrac{3}{4})^3 +64×(-\dfrac{3}{4})^3 =(-\dfrac{3}{4})^3 ×(0.75+0.25-1+64)=-27$.
(2)原式$=(-1\ 001) × (-\dfrac{2}{7}) × (-\dfrac{4}{13}) × (-\dfrac{1}{11}) × (-0.125)^2=8×(\dfrac{1}{8})^2=\dfrac{1}{8}$.
(2)原式$=(-1\ 001) × (-\dfrac{2}{7}) × (-\dfrac{4}{13}) × (-\dfrac{1}{11}) × (-0.125)^2=8×(\dfrac{1}{8})^2=\dfrac{1}{8}$.
5. 计算:$1023÷ 1023\dfrac{1023}{1024}$
答案
因为 $1\ 023\dfrac{1\ 023}{1\ 024}÷ 1\ 023 =\dfrac{1\ 023×1\ 024+1\ 023}{1\ 024}×\dfrac{1}{1\ 023}=\dfrac{1\ 025}{1\ 024}$,所以$1\ 023÷ 1\ 023\dfrac{1\ 023}{1\ 024} =\dfrac{1\ 024}{1\ 025}$.
6. 计算：$- ( -5 \dfrac{1}{2} ) + 16 \dfrac{2}{7} + (-15.5) - ( -3 \dfrac{5}{7} ) = \_\_\_\_\_\_$
答案
10 解析:原式=$5.5-15.5+(16\ \dfrac{2}{7}+3\ \dfrac{5}{7})=-10+20=10$.
7. 计算：$5\frac{1}{2}+1\frac{3}{5}+3\frac{3}{8}+2\frac{1}{6}+6\frac{2}{5}+4\frac{1}{3}+\frac{5}{8}.$
答案
原式$=(5\ \dfrac{1}{2}+2\ \dfrac{1}{6}+4\ \dfrac{1}{3})+(1\ \dfrac{3}{5}+6\ \dfrac{2}{5})+(3\ \dfrac{3}{8}+\dfrac{5}{8})=(9\ \dfrac{5}{6}+2\ \dfrac{1}{6})+8+4=24$.
