Approximations Negative Numbers

[Zelda22]

Enter rational number r satisfying the given conditions.

UA D2 (r)= -5.03 BA D2(r)= -5.02

Answer: Imposible

BA D2(r)=-5.02 = LA D2(r)

-5.03 < -5.02 (Upper approximations >r and Lower approximation <r,

UA > r >LA
so follows UA > LA, and -5.03 is less than -5.02.
Is my reasoning correct? Thanks

 

[topsquark]

Enter rational number r satisfying the given conditions.

UA D2 (r)= -5.03 BA D2(r)= -5.02

Answer: Imposible

BA D2(r)=-5.02 = LA D2(r)

-5.03 < -5.02 (Upper approximations >r and Lower approximation <r,

UA > r >LA
so follows UA > LA, and -5.03 is less than -5.02.
Is my reasoning correct? Thanks

What are UA, D2, BA, LA?

-Dan

 

[Zelda22]

What are UA, D2, BA, LA?

-Dan

UA Upper approximations
LA Lower approximation
BA Best approximation
D2 (rounded to two decimal places, ex 2.36 D means decimal)

 

[BigBeachBanana]

Enter rational number r satisfying the given conditions.

UA D2 (r)= -5.03 BA D2(r)= -5.02

Answer: Imposible

BA D2(r)=-5.02 = LA D2(r)

-5.03 < -5.02 (Upper approximations >r and Lower approximation <r,

UA > r >LA
so follows UA > LA, and -5.03 is less than -5.02.
Is my reasoning correct? Thanks

What is your reason for saying LA=BA?

 

[Zelda22]

What is your reason for saying LA=BA?

You have two approximations, the upper approximation and lower approximation. The best approximation is whichever approximation (lower or upper) is closer to the number you are approximating.
Upper approximation is given, and it’s different than the given best approximation, so it belongs to the lower approximation.

ex r= 2.2
LAD0(r)= 2
UPD0(r)=3

BAD0(r)=LAD0(r)
Since 2.2 is closer to 2 than to 3

r= 3.556
LAD2(r)= 3.55
UPD2(r)=3.56

BAD2(r)=UPD2(r)
Since 3.556 is closer to 3.56 than to 3.55