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.