"按有效数字运算规则，算出下列各式之值(写出中间运算步骤).(1)dfrac (100.0times ( {5.6+4.412) )} ( ( {78.00-77.0) )times 10.000}+110.0(2)dfrac (101.0times ( {4.6+4.402) )} ( ( {89.00-88.0) )times 10.000}+210.00(3)dfrac (21.00) (40.00-33.0)(4)dfrac ( ( {26.10-14.1) )times 30.00} ( ( {204-30) )times ( (1.00+0.001) )}"

【答案】

(1)$210.12$；(2)$300.9202$；(3)3；(4)$\dfrac {60000} {29029}$.

【解析】

(1)

$\dfrac {100.0\times \left ( {5.6+4.412} \right )} {\left ( {78.00-77.0} \right )\times 10.000}+110.0$

$=\dfrac {100.0\times 10.012} {1.00\times 10.000}+110.0$

$=\dfrac {1001.2} {10}+110.0$

$=100.12+110.0$

$=210.12$

(2)

$\dfrac {101.0\times \left ( {4.6+4.402} \right )} {\left ( {89.00-88.0} \right )\times 10.000}+210.00$

$=\dfrac {101.0\times 9.002} {1.0\times 10.000}+210.00$

$=\dfrac {909.202} {10}+210.00$

$=90.9202+210.00$

$=300.9202$

(3)

$\dfrac {21.00} {40.00-33.0}$

$=\dfrac {21.00} {7.00}$

$=3$

(4)

$\dfrac {\left ( {26.10-14.1} \right )\times 30.00} {\left ( {204-30} \right )\times \left ( {1.00+0.001} \right )}$

$=\dfrac {12.00\times 30.00} {174\times 1.001}$

$=\dfrac {360.00} {174.174}$

$=\dfrac {60000} {29029}$