How to Convert to base 3 the number: (375.54)8 -(base eight)?

Question

6. Convert to base 3:

(375.54)8

Answer 1

I tend to convert to base 10 and then convert the result to the new base

375.54 base 8 = (3*64)+(7*8)+(5*1)+(5*(1/8))+(4*(1/64))

192+56+5+5/8+4/64

253+44/64

253+11/16

253.6875 base 10



now let's think about base 3

its all in powers of 3

(3^5)=243

(3^4)=81

(3^3)=27

(3^2)=9

(3^1)=3

(3^0)=1

with that we can determine what 253 base 10 equals in base 3

(1*243)+(0*81)+(0*27)+(1*9)+(0*3)+(1*1)

100101 base 3=253 base 10



how about .6875 at the end you ask?

(3^(-1))=1/3=0.3333..

(3^(-2))=1/9=0.1111..

(3^(-3))=1/27=0.0366..

(3^(-4))=1/81=0.0123 approx

(2*0.3333)+(0*0.1111)+(0*0.0366)+((2*0.0123)

0.6875 base 10 approximately - 0.2002 base 3



put the two pieces together

100101.2002 base 3 approximately equals 375.54 base eight

Answer 2

in one step? i do no longer comprehend, yet the two steps are not that stressful. case in point, in case you want to transform 211 (base 3) to base 5. Convert the backside-3 selection to base-10: 2*3^2 + a million*3 + a million = 22 (base 10) Then divide the hot selection by potential of 5 lower back and lower back: 22/5 = 4 r 2 4/5 = 0 r 4 answer: 40 two (base 5)

Answer 3

375.54 base 8 to base 3

Convert to base 10

375.54 = (3(8) + 7)(8) + 5 + 5/8 + 4/64

= 253.6875 base 10



To convert to base the integer part by repeated division by 3

253/3 = 84 remainder 1

84/3 = 28 remainder 0

28 / 3 = 9 remainder 1

9 / 3 = 3 remainder 0

3 / 3 = 1 remainder 0

1 / 3 = 0 remainder 1

253 base 10 = 100101 base 3



Work on fraction part by repeated multiplication by 3

0.6875 x 3 = 2.0625 Integer part = 2

0.0625 x 3 = 0.1875 integer part = 0

0.1875 x 3 = 0.5625 integer part = 0

0.5625 x 3 = 1.6875 integer part = 1

Fraction part = .200120012001... base 3



375.54 base 8 = 253.6875 base 10 = 100101.200120012001... base 3

Answer 4

375.54

= (3*8^2)+(7*8^1)+(5*8^0)+(5*8^-1)+(4*8^-2)

=(3*64)+(7*8)+(5*1)+(5/8)+(4/64)

=192+56+5+0.625+0.0625

=253.6875 (base 10)



now,



by division method,



3 | 253.6875 |

3 | 84......

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so on



:P



further i don't remember :P :D