The position of significant digits and Logarithms relationship..... I am unable to solve the following question as i don't understand what the relationship is between significant figures and Logarithms. Q-If log_(10)(7)= 0.8451 then the position of the first significant figure of 7^(-20)
figoveck38
Answered question
2022-11-06
The position of significant digits and Logarithms relationship..... I am unable to solve the following question as i don't understand what the relationship is between significant figures and Logarithms. Q-If then the position of the first significant figure of . The answer is the position of the first significant figure is 17th. My book solves it in the following method-
so the position is 17. I fail to understand how and why this has happened please explain this solution to me and the relationship between significant figures and Logarithms...
Answer & Explanation
embutiridsl
Beginner2022-11-07Added 26 answers
Take a number like and rewrite it in scientific notation: . Now apply to it and use your log rules:
Now, notice that is between and , and so is between and , and the lower number just happens to be the spot that the first significant digit is sitting. This isn't a coincidence. Whenever you write a number in scientific notation: and apply to that number, you get
Since (this is what it means to write something in scientific notation) I know that So I can get the power from the scientific notation of a number by applying and taking the integer to the left. On the other hand, the power is also the spot where the first significant digit is sitting.