Measurement and Significant Digits

You should already be very familiar with the rules of significant digits and how to express your final mathematical answers to science problems. Below is a brief summary of what you need to know.

Significant digit rules only apply to measured values and calculations involving measured values.

Significant digit rules do not apply to counted values because no measuring device was used.

1. The last digit of any measurement is estimated.

Suppose you measure the length of a pencil and find it to be 28.73 cm long. The 28.7 is certain and the digit 3 is estimated. Someone else making the same measurement must also agree with 28.7 however the last digit might vary by one unit. Thus the maximum possible length of the pencil would be __________ and the minimum length would be___________.

2. All digits in a measurement are significant except zeros to the left of non-zero digits.

Therefore the measurement 0.00054 s has ____ significant digits and should be expressed as in scientific notation as ________________. The measurement of 1500 m has _________ significant digits and if expressed in scientific notation it would be ____________.

3. Rule for addition and subtraction.

The final answer of a calculation involving addition or subtraction must have the same number of decimals as the number in the computation that has the fewest number of decimals.

Example: 4.877 m + 1018.7 m =

** Your answer can only be as good as you worst piece of data!

4. Rule for multiplication and division.

The final answer of a calculation involving multiplication or division must have the same number of significant digits as the number in the computation that has the fewest number of significant digits.

Example: 78.4 mx 2475.3 m =

Min: 78.3 mx 2475.2 m =

Max 78.5 mx 2475.4 m =