Significant Numbers

Greetings Significant People! 

Happy Independence Day for Turkmenistan from the USSR!
!warning! excessive links ahead

When creating measurements, there is always uncertainty. To minimize the importance or meaning of the error; we write down digits of a measurement that will be meaningful. 

To better understand the meaning of significant digits/figures, we'll look at some examples:

• We'll use 3.29 grams as an example
• 3 and 2 are certain digits
• when measuring we are sure that these digits are correct
• 9 is uncertain
• the last digit of any measurement is always uncertain as it is the last number that is measured

Significant digits in the measurement include all of the certain digits plus the first uncertain digit for a given measurement. To further understand these important figures of significance, let us look at how we figure out significant figures! 

• leading zeros are not counted
• 0.000004
• there is only one sig fig
• trailing zeros are counted
• 50.0540
• there are six sig figs
• trailing zeros without a decimal point are not counted
• 1 000 000 000
• there is only one sig fig

Exact Numbers

Some quantities are defined as a certain amount.

There is no need for rounding and have an infinite amount of significant figures.

Objects that are counted are exact numbers.

Rounding Rules

When writing answers, we must round to the appropriate number

• if the number is > than 5; round up
• if the number is < than 5; round down
• if the number is 5 with non-zero digits following it; round up
• if the number is 5; make the last digit 'even'
• even numbers to be exact (2, 4, 6, 8)

http://www.youtube.com/watch?v=5UjwJ9PIUvE


Adding and Subtracting Significant Digits
When adding or subtracting, we round to the fewest number of decimal places, as well as the first uncertain digit.
http://www.youtube.com/watch?v=U6k7VpdW_rQ
http://www.youtube.com/watch?v=cEMSHsIeKMM&feature=related


Multiplying and Dividing Significant Digits
When multiplying or dividing, we round to the fewest number of significant digits.
http://www.youtube.com/watch?v=qm2bY8tcNQ0
http://www.youtube.com/watch?v=oxqW1LFm7aw&feature=related

and for those who enjoy awkward music videos

http://www.youtube.com/watch?v=ZuVPkBb-z2I

-JY