Question

I need help understanding this in detail!!!!!! Find the rational number between these two numbers: 3/10 and 0.4555555555555555555555 you get the point.

Answer 1

3/10 = .3

the rational expression of 0.45555555555555555555555555555555 can be found by letting \(x=0.4\bar{5}\) and then \(10x=4.\bar{5}\) so that \(9x=4.1\Rightarrow x = \frac{41}{90}\)

Answer 2

ok so if 0.45555= 41/90 thennnn 3/10= 27/90?

Answer 3

if you want the rational number exactly half way inbetween, simply add the numbers together and divide by 2.

yes, 3/10 = 27/90

Answer 4

so if 27/90+41/90=68/90
then 68/90 divided by 2 then uhmm...?

Answer 5

remember that dividing by 2 is the same as multiplying by the reciprocal, namely 1/2.

Answer 6

in fact, dividing by any number is the same as multiplying by its reciprocal

Answer 7

ok so 68/90 divided by 1/2 = 0.377777

Answer 8

how exactly do i convert that?

Answer 9

no, like this...
\[\frac{68}{90}\cdot \frac{1}{2}=\frac{68\cdot 1}{90\cdot 2}=\frac{\cancel2\cdot \cancel2\cdot 17}{\cancel2\cdot \cancel2\cdot 45}=\frac{17}{45}\]

Answer 10

ok let me do this on paper real quick

Answer 11

where do the crossed out two's come from?

Answer 12

\(68 = 4\cdot 17 = 2\cdot 2\cdot 17\)
\(2\cdot 90 = 2\cdot 2\cdot 45\)

Answer 13

does that make sense?

Answer 14

opps sry didnt men to do that

Answer 15

ya that makes sense thanks!

Answer 16

you're welcome!