Gauss M.D. said:The true value is ranging between 3526 and 3610. Why is there two significant digits and not one? I can't even find a specific definition of significant digits anywhere, just random examples.
Significant digits, also known as significant figures, are the digits in a number that are known with certainty. They are important because they indicate the precision of a measurement or calculation. The more significant digits, the more precise the value is considered to be.
The rules for determining significant digits are as follows: 1. All non-zero digits are significant 2. Zeros between non-zero digits are significant 3. Leading zeros (zeros to the left of the first non-zero digit) are not significant 4. Trailing zeros (zeros to the right of a non-zero digit and after the decimal point) are significant 5. Trailing zeros that act as placeholders (zeros to the right of a non-zero digit but before the decimal point) are not significant 6. Exact numbers (such as counting numbers or defined constants) have an infinite number of significant digits.
Precision refers to the level of detail or exactness in a measurement or calculation. It is determined by the number of significant digits. Accuracy, on the other hand, refers to how close the measurement or calculation is to the true or accepted value. A measurement can be precise but not accurate if it is consistently off by the same amount. A measurement can also be accurate but not precise if it is close to the true value but lacks detail.
The error in a measurement or calculation is determined by comparing the result to the true or accepted value. The absolute error is the difference between the measured value and the true value. The relative error is the absolute error divided by the true value. Both types of error can be expressed as a percentage.
In calculations, the result should have the same number of significant digits as the value with the fewest significant digits. This is to prevent giving the appearance of having more precision than is actually known. When adding or subtracting, the result should have the same number of decimal places as the value with the fewest decimal places. When multiplying or dividing, the result should have the same number of significant digits as the value with the fewest significant digits. Error can also be propagated through calculations, meaning the error in the final result is affected by the errors in the individual values used in the calculation.