Rule 1: All nonzero digits are significant.

• 2.345 m (4 significant digits)
  
• 9.86 g (3 significant digits)

Rule 2: Final zeroes to the right of the decimal point are significant.

• 2.0 km (2 significant digits)
  
• 6.300 cm (4 significant digits)

Rule 3: Zeroes found between two significant digits are significant.

• 5.0019 L (5 significant digits)
  
• 23.0005 moles (6 significant digits)

Rule 4: Zeroes as placeholders are not significant.

• 0.00038 m (2 significant digits)
  
• 17000 miles (2 significant digits)

Ex.   0.080090 grams

• 0.080090 - Rule 1 - (2 sig. digits)
  
• 0.080090 - Rule 3 - (2 sig. digits)
  
• 0.080090 - Rule 2 - (1 sig. digit)
  
• 0.080090 - Rule 4 - Two zeroes are not significant.
  
• 0.080090 -Total number of significant digits = 5.

Significant Digits and Calculations:

When Adding and Subtracting:

The general rule is that you cannot report a value with greater precision than the quantity with the least amount of precision. In other words, since precision is dependent on the amount of certainty in your value and the more decimal places you have in your value the more certainty it has...one can say that the value having the least amount of precision also has the least number of decimal places. Therefore, you can only include as many decimal places as the value having the largest uncertainty or the least number of decimal places.

When Multiplying and Dividing:

Here, the rule states that you can only include as many significant digits in your final answer as contained in the factor with the least number of significant digits. What to do? Count up the number of significant digits in all the factors, and determine which one has the fewest. This will be how many you include in your final answer.

Time to Round:

In most cases, you will end up having to round your answer to facilitate the correct number of significant digits. The basic rules that have been taught for many years are the same. You look at the number directly following the digit to be rounded. If the digit is less than five, you round down. If the digit is greater than five, you round up. What if the digit is five?! In this case, it has been agreed that if the number to be rounded is odd you will make it even. If it is even, then you will leave it even.

• Odd:   Need to round 2.35 m to the tenth of a meter, so it would become 2.4 g.
• Even:   Need to round 514.5 mL to the ones position, so it would become 514 mL.

Two Types of Quantities:
(Important when determining sig. digits after a calculation)

Measured Quantities:

Any quantity that has been measured by either you or someone else is a measured quantity. An example would be when you made measurements of the lab. Here, you used the meter sticks to determine lengths of objects in the classroom for use in volume calculations. Another example of a measured quantity is found in the conversion from centimeters to inches. The accepted value rounded to two decimal places is 2.54 cm/inch (2.54 cm = 1 inch). This is a measured quantity, because someone has measured one inch with a metric ruler. Can you think of any other way to get from centimeters to inches without measuring? Converting between systems (English to Metric or vice versa) requires a measurement to be made. Now, someone else using a ruler with greater precision might find that there are 2.5436 cm equal to one inch. The number of significant digits in the conversion depends on the precision of the measurement then. Again, it is important to realize what quantity is the measured quantity. In this case, the 2.54 centimeters is the measurement while the inch is just an inch (a defined quantity).

Defined Quantities:

When working with conversions, you will often encounter quantities that are not measured. These quantities are known as defined or exact quantities. An example would include converting from centimeters to meters. This involves the conversion 100 cm = 1 m. Someone a long time ago sat down and defined a centimeter as 1/100 of a meter (as opposed to 1/200 of a meter), so the values can have infinite numbers of significant digits since they are not measured. Who cares, right?! You need to care! This means you shouldn't base the number of significant digits needed for your final answer on defined quantities. When multiplying and dividing, you can only base your final answer on the measured quantities involved.