Question

Find approximate value of $\frac{1}{4.08}$ upto four places of decimals.

Answer 1

Solution :

1/4.08

= 100/408

408) 1000( 0.24509
********816
_________
**********1840
**********1632
__________
**********2080
**********2040
___________
**************4000
**************3681
______________
*****************319

Therefore ,

1/4.08 = 0.24509...

≈ 0.2451

••••

Answer 2

Answer:

0.2451

Step-by-step explanation:

Hi,

Consider f(x) = 1/x

f'(x) = -1/x²

Δf(x)/Δx = f(x+h)-f(x)/h

As limit h->0, Δf(x)/Δx = f'(x)

Put x = 4 in the above equation and h = 0.08

f(x + h) = f(4.08) = 1/4.08

= f(x) + h*f'(x), where x = 4

But f'(4) = -1/16 =

f(4.08) = f(4) + (0.08)*(-0.0625)

= 0.25 - 0.005

= 0.245 which is approximated to 3 decimal places

But, we need approximation upto 4 decimal places , so we need to

consider the second order term in taylor's series as well

= h²*f''(x)/2!

f''(x) = 2/x³

f"(4) = 2/64 = 1/32

h²f(x)/2! = 0.08²/64 = 0.0001

Hence, f(x+ h) = f(x) + h*f'(x) + h²f"(x)/2! + O(h³)

Hope, it helps !

1/4.08 = 0.245 + 0.0001

= 0.2451 approximate upto 4 decimal places

Hope, it helps!