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Significant DigitsSignificant Digits
…….or “Sig Digs”, if you prefer..or “Sig Digs”, if you prefer.
Sometimes called “Significant figures”
That’s right: “Sig Figs”
Anyway…..
First, some rules:
1. All non-zero digits ARE significant.1, 2, 3, 4, 5, 6, 7, 8, 9.
Example: the number “5691” has…_____ sig digs.4
Next Rule:
2. Zeros between other sig digsARE significant.
Example: the number “204017” has____ sig digs. 6
33rdrd Rule: Rule:
(hold on tight- this is where it gets a little complicated…)(hold on tight- this is where it gets a little complicated…)
3. Zeros to the right of the decimal place
andand…to the right other sig digs
ARE significant.Example: The number “1.000” has
____ sig digs.4
Last Rule:
4. All other zeros are NOT significant.
…they are just “place holders”.
Confused?
Lets do some examples….
Examples:Examples:
.00081 has ____ sig dig(s).2
100 has ____ sig dig(s).(only) 1
100.0 has ___ sig dig(s).4
54900 has ____ sig dig(s).3
Multiplying & Dividing:Multiplying & Dividing:
So what’s the big deal? So what’s the big deal?Remember the old saying: Remember the old saying:
“A chain is only a strong as it’s…..
…weakest link”?
Same kind of idea with sig digs:
A calculated number is only as accurate as ….
…the least accurate measured number that went into that calculation.
In other words:
Your answer should have no more(and no less) sig digs than the least number that went into that calculation.
OK- more examples….
Multiplying & Dividing:Multiplying & Dividing:
12.6 12.6 divided by divided by 5.1 5.1
Your calculator would say….2.470588235
But you should only report the answer as…
2.5
(5.1 has only 2 sig digs)Round up when appropriate.
Multiplying & Dividing:Multiplying & Dividing:
One more example:One more example:
• 6.000 x 634512226.000 x 63451222
Your calculator would say…380707332
But you should only report
380700000 since 6.000 has only 4 sig digs.
Multiplying & Dividing:Multiplying & Dividing:
OK- last one, really….
…how ‘bout:2.00 x 1.500
The answer is just “3”, right…?
Nope- you need to report your answer as3.00
(remember- answers can have no more but no less sig digs than the least number that went into the calculation.)
Multiplying & Dividing:Multiplying & Dividing:
Adding & Subtracting Adding & Subtracting
This rule is a little different.This rule is a little different.
This time, it’s limited to the least sensitive decimal place.
So, with adding & subtracting, you don’t need to count sig digs,You look at decimal places!!!
Example:
3.9 + 12.479 + 3.49
When added gives you 19.869
HOWEVER:
Since 3.9 in the above problem only goes tothe tenths place….
You must only report your answer tothe tenths place: 19.9
Notice: you can have as many sig digs as you need, as longas you keep to the least sensitive decimal place.
So to review:So to review:
For multiplying & dividing:Count sig digs in the equation and
limit the answer to the least number.
For adding & subtracting:
Look for the least number of decimal places
and limit it that way.