Question

Find the difference between 3.47777... and 2.85888​

Answer 1

First we need to convert 3.47777...... and 2.858888..... in p/q form.

$let \: x = 3.47777..... \\ 10x = 34.7777..... \\ 10x = 31.3 + 3.47777.... \\ 10x = 31.3 + x \\ 9x = 31.3 \\ x = \frac{31.3}{9} \: or \: x = \frac{313}{90}$

$let \: y = 2.858888..... \\ 100y = 285.8888..... \\ 100y = 283.03 + 2.858888.... \\ 100y = 283.03 + y \\ 99y = 283.03 \\ y = \frac{283.03}{99} \: or \: y = \frac{28303}{9900}$

by doing

$x - y$

we will get

$\frac{313}{90} - \frac{28303}{9900}$

LCM of 90 and 9900 is 9900

$= \frac{313 \times 110}{90 \times 110} - \frac{28303}{9900} \\ = \frac{34430 - 28303}{9900} \\ = \frac{6,127}{9900} = 0.618888......$

Or the simplest way is that

$3.477777778 - 2.858888889 \\ =0.618888889$

since 3.47777..... is approximately 3.477777778 and 2.858888..... is approximately 2.858888889

Therefore the difference is 0.618888889 which is approximation of 0.618888.....

HOPE IT WILL HELP YOU A LOT