How do you find in decimals the ratio ( binary 1.01)/(octal 2.4)?

2 Answers

Answer:

(Binary 1.01) /(Octal 2.4) = #0.5#

Explanation:

Binary #1.01#

= Decimal #1+0/2+1/2^2#

= Decimal #1+0+1/4#

= Decimal #1.25#

Octal #2.4#

= = Decimal #2+4/8#

= Decimal #2+1/2#

= Decimal #2.5#

(Binary 1.01) /(Octal 2.4) = #1.25/2.5=0.5#

Answer:

Convert to decimal each number...

Explanation:

An floating point expression in a given base can be converted to decimal by following way:

let the base be #b#
right most digit before (at the left of) the point be #n0#
second one be #n1#
third one be #n2#
...and so on #(n3,n4,n5 ...)#

now lets take the right side of the point
first digit after (at the right of) point be #m1#
second one be #m2#
third one be #m3#
and so on #(m4,m5,m6...)#

then number in decimal is:

#n0*b^0 + n1*b^1 + n2*b^2 + n3*b^3 + (n4*b^4 + n5*b^5...)#
#+ m1*1/b^1 + m2*1/b^2 + m3*1/b^3 + m4*1/b^4 + ...#

so the solution is:

#(1.01)b= (?)decimal#

#1.01 = 1*2^0 + 0*2^(-1) + 1*2^(-2)#

#= 1 + 0/2 + 1/4 = (1.25)decimal#

#(2.4)octal = 2*8^0 + 4*8^-1#
#= 2 + 4/8 = (2.5)decimal#

so expression in decimal is:
#1.25/2.5 = 1/2 = 0.5#