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1. $0.4^{\circ}=$____$^{\prime}$
答案
24
解析
$0.4×60=24$，故答案为$24$。
2. $0.4^{\circ}=$____$^{\prime\prime}$
答案
1440
解析
因为$1^{\circ}=60^{\prime}$，$1^{\prime}=60^{\prime\prime}$，所以$0.4^{\circ}=0.4×60^{\prime}=24^{\prime}$，$24^{\prime}=24×60^{\prime\prime}=1440^{\prime\prime}$。
1440
1440
3. $33^{\prime}=$____$^{\circ}$
答案
0.55
解析
因为$1^{\circ}=60'$，所以$33'=\frac{33}{60}^{\circ}=0.55^{\circ}$。
$0.55$
$0.55$
4. $33^{\prime}=$____$^{\prime\prime}$
答案
1980
解析
因为$1^{\prime}=60^{\prime\prime}$，所以$33^{\prime}=33×60^{\prime\prime}=1980^{\prime\prime}$。
1980
1980
5. $23^{\circ}30^{\prime}=$____$^{\circ}$
答案
23.5
解析
因为 $1^{\circ}=60'$，所以 $30'=\left(\frac{30}{60}\right)^{\circ}=0.5^{\circ}$，则 $23^{\circ}30'=23^{\circ}+0.5^{\circ}=23.5^{\circ}$
23.5
23.5
6. $35^{\circ}19^{\prime}=$____$^{\prime}$
答案
2119
解析
因为$1^{\circ}=60^{\prime}$，所以$35^{\circ}=35×60^{\prime}=2100^{\prime}$，则$35^{\circ}19^{\prime}=2100^{\prime}+19^{\prime}=2119^{\prime}$。
2119
2119
7. $43.21^{\circ}=$____$^{\circ}$____$^{\prime}$____$^{\prime\prime}$
答案
43 12 36
8. $48^{\circ}15^{\prime}36^{\prime\prime}=$____$^{\circ}$
答案
48.26
解析
因为$1''=\left(\frac{1}{60}\right)'$，所以$36''=36×\left(\frac{1}{60}\right)'=0.6'$；则$15'+0.6' = 15.6'$。又因为$1'=\left(\frac{1}{60}\right)^{\circ}$，所以$15.6'=15.6×\left(\frac{1}{60}\right)^{\circ}=0.26^{\circ}$。故$48^{\circ}15'36'' = 48^{\circ}+0.26^{\circ}=48.26^{\circ}$。
$48.26$
$48.26$
9. $20^{\circ}15^{\prime}$的余角为____$^{\circ}$.
答案
69.75
解析
$90^{\circ}-20^{\circ}15'=89^{\circ}60'-20^{\circ}15'=69^{\circ}45'$，$45'=\left(\frac{45}{60}\right)^{\circ}=0.75^{\circ}$，所以$69^{\circ}45'=69.75^{\circ}$。
69.75
69.75
10. $23^{\circ}36^{\prime}$的补角为____$^{\circ}$.
答案
156.4
解析
$180^{\circ}-23^{\circ}36'=179^{\circ}60'-23^{\circ}36'=156^{\circ}24'$，$24'=\left(\frac{24}{60}\right)^{\circ}=0.4^{\circ}$，所以补角为$156.4^{\circ}$
11. $56^{\circ}18^{\prime}+72^{\circ}48^{\prime}$
答案
129°6′
解析
$56^{\circ}18^{\prime}+72^{\circ}48^{\prime}$
$=(56^{\circ}+72^{\circ})+(18^{\prime}+48^{\prime})$
$=128^{\circ}+66^{\prime}$
$=128^{\circ}+1^{\circ}6^{\prime}$
$=129^{\circ}6^{\prime}$
$=(56^{\circ}+72^{\circ})+(18^{\prime}+48^{\prime})$
$=128^{\circ}+66^{\prime}$
$=128^{\circ}+1^{\circ}6^{\prime}$
$=129^{\circ}6^{\prime}$
12. $131^{\circ}28^{\prime}-51^{\circ}32^{\prime}15^{\prime\prime}$
答案
79°55′45″
解析
$131^{\circ}28^{\prime}-51^{\circ}32^{\prime}15^{\prime\prime}$
$=130^{\circ}87^{\prime}60^{\prime\prime}-51^{\circ}32^{\prime}15^{\prime\prime}$
$=(130^{\circ}-51^{\circ})+(87^{\prime}-32^{\prime})+(60^{\prime\prime}-15^{\prime\prime})$
$=79^{\circ}+55^{\prime}+45^{\prime\prime}$
$=79^{\circ}55^{\prime}45^{\prime\prime}$
$=130^{\circ}87^{\prime}60^{\prime\prime}-51^{\circ}32^{\prime}15^{\prime\prime}$
$=(130^{\circ}-51^{\circ})+(87^{\prime}-32^{\prime})+(60^{\prime\prime}-15^{\prime\prime})$
$=79^{\circ}+55^{\prime}+45^{\prime\prime}$
$=79^{\circ}55^{\prime}45^{\prime\prime}$
13. $12^{\circ}30^{\prime}20^{\prime\prime}×2$
答案
25°40″
解析
$12^{\circ}30^{\prime}20^{\prime\prime}×2$
$= (12^{\circ}×2) + (30^{\prime}×2) + (20^{\prime\prime}×2)$
$= 24^{\circ} + 60^{\prime} + 40^{\prime\prime}$
$= 24^{\circ} + 1^{\circ} + 40^{\prime\prime}$
$= 25^{\circ}40^{\prime\prime}$
$= (12^{\circ}×2) + (30^{\prime}×2) + (20^{\prime\prime}×2)$
$= 24^{\circ} + 60^{\prime} + 40^{\prime\prime}$
$= 24^{\circ} + 1^{\circ} + 40^{\prime\prime}$
$= 25^{\circ}40^{\prime\prime}$
14. $12^{\circ}31^{\prime}21^{\prime\prime}÷3$
答案
4°10′27″
解析
$12^{\circ}31^{\prime}21^{\prime\prime}÷3$
$=12^{\circ}÷3 + 30^{\prime}÷3 + 71^{\prime\prime}÷3$（此处原解析有误，应为$31^{\prime}=30^{\prime}+1^{\prime}=30^{\prime}+60^{\prime\prime}$，所以$12^{\circ}31^{\prime}21^{\prime\prime}=12^{\circ}30^{\prime}81^{\prime\prime}$）
$=4^{\circ} + 10^{\prime} + 27^{\prime\prime}$
$=4^{\circ}10^{\prime}27^{\prime\prime}$
$=12^{\circ}÷3 + 30^{\prime}÷3 + 71^{\prime\prime}÷3$（此处原解析有误，应为$31^{\prime}=30^{\prime}+1^{\prime}=30^{\prime}+60^{\prime\prime}$，所以$12^{\circ}31^{\prime}21^{\prime\prime}=12^{\circ}30^{\prime}81^{\prime\prime}$）
$=4^{\circ} + 10^{\prime} + 27^{\prime\prime}$
$=4^{\circ}10^{\prime}27^{\prime\prime}$
15. $48^{\circ}39^{\prime}+67^{\circ}31^{\prime}-21^{\circ}17^{\prime}$
答案
94°53′
解析
$48^{\circ}39^{\prime}+67^{\circ}31^{\prime}-21^{\circ}17^{\prime}$
$=(48^{\circ}+67^{\circ}-21^{\circ})+(39^{\prime}+31^{\prime}-17^{\prime})$
$=94^{\circ}+53^{\prime}$
$=94^{\circ}53^{\prime}$
$=(48^{\circ}+67^{\circ}-21^{\circ})+(39^{\prime}+31^{\prime}-17^{\prime})$
$=94^{\circ}+53^{\prime}$
$=94^{\circ}53^{\prime}$
16. $180^{\circ}-45^{\circ}17^{\prime}-52^{\circ}57^{\prime}$
答案
81°46′
解析
$180^{\circ}-45^{\circ}17^{\prime}-52^{\circ}57^{\prime}$
$=179^{\circ}60^{\prime}-45^{\circ}17^{\prime}-52^{\circ}57^{\prime}$
$=(179^{\circ}-45^{\circ}-52^{\circ})+(60^{\prime}-17^{\prime}-57^{\prime})$
$=82^{\circ}-14^{\prime}$
$=81^{\circ}46^{\prime}$
$=179^{\circ}60^{\prime}-45^{\circ}17^{\prime}-52^{\circ}57^{\prime}$
$=(179^{\circ}-45^{\circ}-52^{\circ})+(60^{\prime}-17^{\prime}-57^{\prime})$
$=82^{\circ}-14^{\prime}$
$=81^{\circ}46^{\prime}$
17. $56^{\circ}17^{\prime}+12^{\circ}45^{\prime}-16^{\circ}21^{\prime}×4$
答案
3°38′
解析
$56^{\circ}17'+12^{\circ}45'-16^{\circ}21'×4$
$=68^{\circ}62'-64^{\circ}84'$
$=69^{\circ}2'-65^{\circ}24'$
$=3^{\circ}38'$
$=68^{\circ}62'-64^{\circ}84'$
$=69^{\circ}2'-65^{\circ}24'$
$=3^{\circ}38'$
18. $90^{\circ}-(36^{\circ}31^{\prime}52^{\prime\prime}+12^{\circ}22^{\prime}14^{\prime\prime})$
答案
41°5′54″
解析
$36^{\circ}31^{\prime}52^{\prime\prime}+12^{\circ}22^{\prime}14^{\prime\prime}=48^{\circ}53^{\prime}66^{\prime\prime}=48^{\circ}54^{\prime}6^{\prime\prime}$
$90^{\circ}-48^{\circ}54^{\prime}6^{\prime\prime}=89^{\circ}59^{\prime}60^{\prime\prime}-48^{\circ}54^{\prime}6^{\prime\prime}=41^{\circ}5^{\prime}54^{\prime\prime}$
$90^{\circ}-48^{\circ}54^{\prime}6^{\prime\prime}=89^{\circ}59^{\prime}60^{\prime\prime}-48^{\circ}54^{\prime}6^{\prime\prime}=41^{\circ}5^{\prime}54^{\prime\prime}$
19. $(90^{\circ}-78^{\circ}19^{\prime}34^{\prime\prime})×2$
答案
23°20′52″
解析
$90^{\circ}-78^{\circ}19^{\prime}34^{\prime\prime}=11^{\circ}40^{\prime}26^{\prime\prime}$
$11^{\circ}40^{\prime}26^{\prime\prime}×2=23^{\circ}20^{\prime}52^{\prime\prime}$
$23^{\circ}20^{\prime}52^{\prime\prime}$
$11^{\circ}40^{\prime}26^{\prime\prime}×2=23^{\circ}20^{\prime}52^{\prime\prime}$
$23^{\circ}20^{\prime}52^{\prime\prime}$
20. $23^{\circ}53^{\prime}×3-107^{\circ}43^{\prime}÷5$
答案
50°6′24″
解析
$23^{\circ}53^{\prime}×3 = 69^{\circ}159^{\prime} = 71^{\circ}39^{\prime}$
$107^{\circ}43^{\prime}÷5 = 21^{\circ}32^{\prime}36''$
$71^{\circ}39^{\prime}-21^{\circ}32^{\prime}36'' = 50^{\circ}6^{\prime}24''$
$50^{\circ}6^{\prime}24''$
$107^{\circ}43^{\prime}÷5 = 21^{\circ}32^{\prime}36''$
$71^{\circ}39^{\prime}-21^{\circ}32^{\prime}36'' = 50^{\circ}6^{\prime}24''$
$50^{\circ}6^{\prime}24''$
