Lesson 3 of 12 · 7 min
Scientific notation, precision and accuracy
NCERT § "Uncertainty in Measurement"
Write the number of molecules in Diya's tumbler in ordinary digits and you need 25 of them: 6 022 000 000 000 000 000 000 000. There has to be a better way.
The lesson in notes
In short
Very large or very small numbers are written in scientific (exponential) notation as N × 10ⁿ, where N lies between 1.000 and 9.999 and n is an integer.
When multiplying numbers in this form, the N parts are multiplied and the exponents are added; when dividing, the exponents are subtracted.
For addition or subtraction, first rewrite the numbers with the same exponent, then combine the N parts.
Precision describes how close repeated measurements of the same quantity are to one another.
Accuracy describes how close a measurement (or the average of several) is to the true value.
A set of readings can be precise without being accurate, for example when an instrument has a constant error.