You are given that lo g 1 0 5 ≈ 0 . 6 9 9 0 is accurate to 3 decimal places. Find the number of digits in the number 5 0 5 0 .
Note: For accurate results via approximation, you have to verify that you have enough significant figures.
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Simple standard approach.
In the question, for clarity, it should be clearly stated that the value is accurate to 3 sig fig. Otherwise, we could have used a slightly different approximation, and obtained a wrong answer.
Marvelous!
Number of digits in n is
⌊ lo g n ⌋ + 1
Plugging in 5 0 5 0 , length is
= ⌊ lo g 5 0 5 0 ⌋ + 1 = ⌊ 5 0 lo g 5 0 ⌋ + 1
Since 5 0 = 5 ⋅ 1 0 ,
= ⌊ 5 0 ( lo g 5 + lo g 1 0 ) ⌋ + 1 = ⌊ 5 0 ( 0 . 6 9 9 + 1 ) ⌋ + 1 = ⌊ 8 4 . 9 5 ⌋ + 1 = 8 5
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find 50*log50 = 84.95 this implies that no. of digits is 85....i.e.characteristic+1