Significant Figures and Rounding Rules (Video Notes)

Vocabulary flashcards covering significant figures, zeros, and rounding rules as discussed in the video notes.

Significant figures (sig figs)

Digits in a measurement that contribute to its precision; the last reported digit is uncertain.

Leading zeros

Zeros before the first nonzero digit; they are not significant.

Significant figures in 400 (no decimal)

In 400 written without a decimal point, there is 1 significant figure (the 4); trailing zeros are not significant unless specified.

Significant figures in 0.0040

Leading zeros are not significant; the two significant figures are the 4 and the trailing 0 after it.

Rounding

Process of reducing a number to a specified precision by removing digits to the right.

Rounding up when next digit > 5

If the digit immediately to the right of the last kept digit is greater than 5, increase the last kept digit by 1.

Rounding down when next digit < 5

If the next digit is less than 5, keep the last kept digit unchanged.

Round half to even (banker's rounding)

When the digit to be dropped is 5 with no further digits, round to make the last kept digit even (e.g., 7.5 → 8; 6.5 → 6).

Uncertainty of the last significant digit

The last reported digit in a measurement is uncertain by ±1 in its place value.