Every rational number has a base-2 representation, but only the ones with denominators that are powers of 2 will require a finite number of bits to fully represent it.

For example,

$\dfrac12 = 1\cdot2^{-1} = 0.1_2$

$\dfrac14 = 1\cdot2^{-2} = 0.01_2$

$\dfrac34 = \dfrac12 + \dfrac14 = 0.11_2$

$\dfrac{1023}{1024} = 1 - \dfrac1{2^{10}} = 1_2 - 0.0000000001_2 = 0.1111111111_2$

whereas a number whose denominator contains anything else like 1/3 will need an infinite number of bits to represent it exactly.

$\dfrac13 = \dfrac1{2^2} + \dfrac1{12} = \dfrac1{2^2} + \dfrac1{2^4} + \dfrac1{48} = \dfrac1{2^2} + \dfrac1{2^4} + \dfrac1{2^8} + \dfrac1{192}$

and so on, so that it has a repeating but non-terminating base-2 representation

$\dfrac13 = 0.010101\ldots_2$

5 0

2 years ago

How do you convert 7/6 into a mixed number

Natali [406]

Wel its kinda difficult to say but look on how much times 6 can fit into 7 which is 1 but that will be 6,so in order to become seven you need 1 which is our left over number,so in the end you will get 1 whole and 1/6 and you use the leftover number as your numerator and just leave the 6 as it was.Whoof that was long but its no nearly as long as i explain it.

6 0

3 years ago

Read 2 more answers

SOLVE FOR X. HELP ME NOW PLEASE!

Drupady [299]

Answer:

For number 2, its A. For number 1, its C.

Step-by-step explanation:

For both equations, you just set it equal to to each other because alternate interior angles are equivalent.

2) The equation would be

7x+3=6x+12

Then solve.

1) The equation would be

14x-3=95

Then solve.

I love geometry! If you have questions, just comment.

5 0

3 years ago

Graph -2x+10+5y=0 using intercepts. Add two intercept points on the graph.

mihalych1998 [28]

If you need any steps explained lmk

7 0

3 years ago