Number of cyphers after decimal before a significant figure starts in ((5/2))-50 is [Use: log 10 2=0.3010 ]

Question

Number of cyphers after decimal before a significant figure starts in ((5/2))-50 is [Use: log 10 2=0.3010 ] (A) 17 (B) 18 (C) 19 (D) 20

Tardigrade Admin · Accepted Answer

text Let N =((5/2))-50 ⇒ log 10 N =-50 ⋅ log 10((5/2))=-50( log 10((10/2))- log 10 2)=-50(1-2 log 10 2) =-50(1-2 × 0.3010)=-50(1-0.6020)=-50 × 0.3980=-19 ⋅ 9=-20+0.1= overline20 .10 ∴ text Number of zeroes =19

Q. Number of cyphers after decimal before a significant figure starts in (25​)−50 is [Use : log10​2=0.3010 ]

17

18

19

20

Let N=(25​)−50 ⇒log10​N=−50⋅log10​(25​)=−50(log10​(210​)−log10​2)=−50(1−2log10​2) =−50(1−2×0.3010)=−50(1−0.6020)=−50×0.3980=−19⋅9=−20+0.1=20.10 ∴ Number of zeroes =19

Q. Number of cyphers after decimal before a significant figure starts in $(\frac{5}{2})^{- 50}$ is [Use : $lo g_{10} 2 = 0.3010$ ]