1. 计算$3.8×10^{7}-3.7×10^{7}$的结果用科学记数法表示为 (
D
)
A.$0.1×10^{7}$
B.$0.1×10^{6}$
C.$1×10^{7}$
D.$1×10^{6}$
答案：D
解析：
解：$3.8×10^{7}-3.7×10^{7}$
$=(3.8 - 3.7)×10^{7}$
$=0.1×10^{7}$
$=1×10^{6}$
结论：D
2. 若$a = -\frac{1235×1235 - 1235}{1234×1234 + 1234}$,$b = -\frac{1236×1236 - 1236}{1235×1235 + 1235}$,$c = \frac{1237×1237 - 1237}{1236×1236 + 1236}$,则$abc$的值为 (
D
)
A.$-1$
B.$3$
C.$-3$
D.$1$
答案：D 解析:由题意得 $ a = - \frac { 1 2 3 5 × ( 1 2 3 5 - 1 ) } { 1 2 3 4 × ( 1 2 3 4 + 1 ) } = - 1 $，同理可得 $ b = - 1 $，$ c = 1 $，则 $ a b c = ( - 1 ) × ( - 1 ) × 1 = 1 $。故选 D。
3. 计算:
(1)$4×(\frac{1}{2}-\frac{3}{10}+\frac{2}{5})×(-25)=$
$-60$
;
(2)$-0.85×\frac{8}{17}+14×\frac{2}{7}-(14×\frac{3}{7}-\frac{9}{17}×0.85)=$
$-1\frac{19}{20}$
.
答案：(1)$-60$;(2)$-1\frac{19}{20}$
解析：
(1)解：$4×(\frac{1}{2}-\frac{3}{10}+\frac{2}{5})×(-25)$
$=4×(-25)×(\frac{1}{2}-\frac{3}{10}+\frac{2}{5})$
$=-100×(\frac{5}{10}-\frac{3}{10}+\frac{4}{10})$
$=-100×\frac{6}{10}$
$=-60$
(2)解：$-0.85×\frac{8}{17}+14×\frac{2}{7}-(14×\frac{3}{7}-\frac{9}{17}×0.85)$
$=-0.85×\frac{8}{17}+14×\frac{2}{7}-14×\frac{3}{7}+\frac{9}{17}×0.85$
$=0.85×(-\frac{8}{17}+\frac{9}{17})+14×(\frac{2}{7}-\frac{3}{7})$
$=0.85×\frac{1}{17}+14×(-\frac{1}{7})$
$=0.05 - 2$
$=-1.95$
$=-1\frac{19}{20}$
4. 简便运算:
(1)$(-\frac{3}{4})^{3}×0.75 + 0.5^{2}×(-\frac{3}{4})^{3} + \frac{25}{37}×(-1\frac{12}{25})×(-\frac{3}{4})^{3} + 4^{3}÷(-\frac{4}{3})^{3}$;
(2)$(-1001)×(-0.125)^{2}×(-\frac{2}{7})×(-\frac{4}{13})×(-\frac{1}{11})$.
答案：(1) 原式 $ = \left( - \frac { 3 } { 4 } \right) ^ { 3 } × 0.75 + 0.25 × \left( - \frac { 3 } { 4 } \right) ^ { 3 } - 1 × \left( - \frac { 3 } { 4 } \right) ^ { 3 } + 6 4 × \left( - \frac { 3 } { 4 } \right) ^ { 3 } = \left( - \frac { 3 } { 4 } \right) ^ { 3 } × ( 0.75 + 0.25 - 1 + 6 4 ) = - 2 7 $。(2) 原式 $ = ( - 1 0 0 1 ) × \left( - \frac { 2 } { 7 } \right) × \left( - \frac { 4 } { 1 3 } \right) × \left( - \frac { 1 } { 1 1 } \right) × ( - 0.125 ) ^ { 2 } = 8 × \left( \frac { 1 } { 8 } \right) ^ { 2 } = \frac { 1 } { 8 } $。
解析：
(1) 解：原式$=\left(-\frac{3}{4}\right)^{3}× 0.75+0.5^{2}× \left(-\frac{3}{4}\right)^{3}+\frac{25}{37}× \left(-\frac{37}{25}\right)× \left(-\frac{3}{4}\right)^{3}+4^{3}÷ \left(-\frac{4}{3}\right)^{3}$
$=\left(-\frac{3}{4}\right)^{3}× 0.75+0.25× \left(-\frac{3}{4}\right)^{3}+\left(-1\right)× \left(-\frac{3}{4}\right)^{3}+4^{3}× \left(-\frac{3}{4}\right)^{3}$
$=\left(-\frac{3}{4}\right)^{3}× \left(0.75 + 0.25 - 1 + 64\right)$
$=\left(-\frac{27}{64}\right)× 64$
$=-27$
(2) 解：原式$=(-1001)× \left(-\frac{2}{7}\right)× \left(-\frac{4}{13}\right)× \left(-\frac{1}{11}\right)× \left(-\frac{1}{8}\right)^{2}$
$=(-1001)× \left(-\frac{1}{11}\right)× \left(-\frac{2}{7}\right)× \left(-\frac{4}{13}\right)× \frac{1}{64}$
$=91× \left(-\frac{2}{7}\right)× \left(-\frac{4}{13}\right)× \frac{1}{64}$
$=(-26)× \left(-\frac{4}{13}\right)× \frac{1}{64}$
$=8× \frac{1}{64}$
$=\frac{1}{8}$
5. 计算:$1023÷1023\frac{1023}{1024}$.
答案：因为 $ 1 0 2 3 \frac { 1 0 2 3 } { 1 0 2 4 } ÷ 1 0 2 3 = \frac { 1 0 2 3 × 1 0 2 4 + 1 0 2 3 } { 1 0 2 4 } × \frac { 1 } { 1 0 2 3 } = \frac { 1 0 2 5 } { 1 0 2 4 } $，所以 $ 1 0 2 3 ÷ 1 0 2 3 \frac { 1 0 2 3 } { 1 0 2 4 } = \frac { 1 0 2 4 } { 1 0 2 5 } $。
解析：
解：先计算 $1023\frac{1023}{1024} ÷ 1023$，
$\begin{aligned}1023\frac{1023}{1024} ÷ 1023&=\frac{1023×1024 + 1023}{1024} × \frac{1}{1023}\\&=\frac{1023×(1024 + 1)}{1024} × \frac{1}{1023}\\&=\frac{1025}{1024}\end{aligned}$
所以 $1023÷1023\frac{1023}{1024}=\frac{1024}{1025}$。
答案：$\frac{1024}{1025}$
6. $-(-5\frac{1}{2}) + 16\frac{2}{7} + (-15.5) - (-3\frac{5}{7})= $
10
.
答案：10
解析：
解：原式$=5\frac{1}{2} + 16\frac{2}{7} - 15.5 + 3\frac{5}{7}$
$=5.5 - 15.5 + (16\frac{2}{7} + 3\frac{5}{7})$
$=-10 + 20$
$=10$
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 $ = \left( {5\frac{1}{2} + 2\frac{1}{6} + 4\frac{1}{3}} \right) + \left( {1\frac{3}{5} + 6\frac{2}{5}} \right) + \left( {3\frac{3}{8} + \frac{5}{8}} \right) = \left( {9\frac{5}{6} + 2\frac{1}{6}} \right) + 8 + 4 = 24 $。
解析：
解：原式$=\left(5\frac{1}{2}+2\frac{1}{6}+4\frac{1}{3}\right)+\left(1\frac{3}{5}+6\frac{2}{5}\right)+\left(3\frac{3}{8}+\frac{5}{8}\right)$
$=\left(5+\frac{1}{2}+2+\frac{1}{6}+4+\frac{1}{3}\right)+\left(1+\frac{3}{5}+6+\frac{2}{5}\right)+\left(3+\frac{3}{8}+\frac{5}{8}\right)$
$=\left[(5+2+4)+\left(\frac{3}{6}+\frac{1}{6}+\frac{2}{6}\right)\right]+\left[(1+6)+\left(\frac{3}{5}+\frac{2}{5}\right)\right]+\left[3+\left(\frac{3}{8}+\frac{5}{8}\right)\right]$
$=(11 + 1)+(7 + 1)+(3 + 1)$
$=12 + 8 + 4$
$=24$
