$($

b

$)$

$$Express

$1$

$9$

$.$

$2$

$1$

$0$

$$in binary.

$($

c

$)$

$$You$\text{'}$ll notice that in part

$($

b

$)$

$,$

$$the fractional part in decimal

$($

$.$

$2$

$)$

$$does not convert nicely to a binary value. If we seek a particular precision, how do we know when to stop? Let's assume that there is an uncertainty of

$+$

$-$

$1$

$$in the last digit of the original number; i

$.$

e

$.$

$,$

$$the value we want to convert is

$($

$1$

$9$

$.$

$2$

$+$

$-$

$0$

$.$

$1$

$)$

$($

in base

$1$

$0$

$)$

$.$

$$Thus$,$ we want to find out how many digits we need in the fractional part of the converted binary value so that it is at least as precise as the original value. Putting it all together, we need to satisfy the condition:

$($

precision

$/$

$$uncertainty in converted value

$)$

$<=$

$($

precision

$/$

$$uncertainty in original value

$)$

$2$

$-$

$$

$<=$

$1$

$0$

$-$

$$

$$

$=$

$1$

$$since there was one digit in the fractional part of the original number and

$$

$$will be the number of digits needed in the fractional part of the converted binary answer. With all this in mind, solve for the required

$$

$($

which must be an integer

$)$

$$to express

$1$

$9$

$.$

$2$

$$in binary, to an appropriate precision.

$($

d

$)$

$$Express the value

$0$

xE

$3$

FED.

$2$

$$A

$9$

$$in decimal, to appropriate precision.