(Q). Find the first two non-zero digit (FTNZD) of .
(i) 12
(ii) 72
(iii) 96
(iv) 38
Solution:-
FTNZD(555!) =
FTNZD(555!) = Uₜ(12ᴴ) × Uₜ(Q₁×Q₂×Q₃×Q₄)
=Uₜ(12¹³⁷) × Uₜ(11×62×24)
∴ FTNZD(555!) = 56
now to find FTNZD(444!) =
∴ FTNZD(444!) = Uₜ(12ᴴ) × Uₜ(Q₁ × Q₂ × Q₃ × Q₄)
∴ FTNZD(444!) = 48
now to find FTNZD
Let
i.e. 444! × Quotient = 555!
So FTNZD(444!) × FTNZD(Quotient) = FTNZD(555!)
because we know that irrespective of the size of the number & ignoring its all trailing zeros, To find the FTNZD we only need the FTNZD of the numbers & remaining digits of the numbers are useless when finding FTNZD.
∴ 48 × x = 56
now from the given options
(i) 12
(ii) 72 ✔
(iii) 96
(iv) 38
Uₜ(48×72) = 56
Hence option (ii) is correct
∴ FTNZD = 72 (option(ii)) Answer