Answer:
A. 0.545454 - 1/4 = 0.295454 yes this is an irrational number
C. 3.4641016 - 1/4 = 3.2141016 yes this is an irrational number
Explanation:
A. 0.545454 - 1/4 = 0.295454 is an irrational number as the closest fraction is shown below at 3 decimal points only
As this can be converted to a fraction 147727 /500000 ≈ 0.295
B. - 4/9 - 1/4 = -0.694444444 is not an irrational number so answer is no
As this can be converted to a fraction -173611111 / 250000000
To write 0.694444444 as a fraction you have to write 0.694444444 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
0.694444444 = 0.694444444/1 = 6.94444444/10 = 69.4444444/100 = 694.444444/1000 = 6944.44444/10000 = 69444.4444/100000 = 694444.444/1000000 = 6944444.44/10000000 = 69444444.4/100000000 = 694444444/1000000000. Then divide by 470 and we know to use this some as 250000000/531915 = 470
C. 3.4641016 - 1/4 = 3.2141016 yes this is an irrational number
closest fraction is only 4 significant figures
4017627 / 1250000
=3 and 267627 over 12500003
267627 /1250000
≈3.214 so in closer proof it is an irrational number.
D. sq rt 4 - 1/4 = 1.75 is not an irrational number as this fraction is 7/4 = 1 3/4