Significant Digits or Sig Digs if you prefer

Significant Digits …. 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… _____ 4 sig digs.

Next Rule: 2. Zeros between other sig digs ARE significant. Example: the number “ 204017” has ____ 6 sig digs.

rd 3 Rule: (hold on tight- this is where it gets a little complicated…) 3. Zeros to the right of the decimal place and Example: …to the right other sig digs ARE significant. The number “ 1. 000” has 4 sig digs. ____

Last Rule: All other zeros are NOT significant. …they are just “place holders”. Confused? Lets do some examples….

Examples: 2 sig dig(s). . 00081 has ____ 100 has ____ (only) 1 sig dig(s). 4 sig dig(s). 100. 0 has ___ 3 sig dig(s). 54900 has ____

Multiplying & Dividing: So what’s the big deal? 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….

12. 6 divided by 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.

One more example: • 6. 000 x 63451222 Your calculator would say… 380707332 But you should only report 380700000 since 6. 000 has only 4 sig digs.

OK- last one, really…. …how ‘bout: 2. 00 x 1. 500 The answer is just “ 3”, right…? Nope- you need to report your answer as 3. 00 (remember- answers can have no more but no less sig digs than the least number that went into the calculation. )

Adding & Subtracting 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 18. 869 HOWEVER: Since 3. 9 in the above problem only goes to the tenths place…. You must only report your answer to the tenths place: 18. 9 Notice: you can have as many sig digs as you need, as long as you keep to the least sensitive decimal place.

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.