Oct.26--Significant Figures

Significant figures are measured or meaningful digits. The more significant digits there are in a number, the more precise the number is.

Uncertain Digit: the last digit in a measurement is called the uncertain digit as it could be one digit lower or higher depending on the digit after it.

The significant digits in the measurement include ALL of the certain digits and the first uncertain digit.

Ex. 2.56g : 2 & 5 are certain, 6 is uncertain

   2.56 has three significant digits

Zeros

- Leading zeros are not counted

- Trailing zeros after the decimal point are counted

- Trailing zeros without a decimal point are not counted

Exact Numbers

Some quantities are defined as exactly a certain amount. You do not need to round those numbers.

Ex. a pair of gloves, five people, etc.

Rounding Rules: how to round measurements

1.      Look at the digit after the position of rounding.

2.      If the digit is greater than 5, round up.

3.      If the digit is less than 5, keep the same.

4.      If the digit is equal to 5, look at the digit(s) after it:

- more non-zero digits, round up

- it ends at 5, round to make the last digit even

* When rounding, do not round until the final answer!

Math Rules

Adding or subtracting: round to the fewest number of decimal places

Multiplying or dividing: round to the fewest number of significant digits.

Finally, there is a Youtube Video that can help understand better.