# Significant Digits - Helm's Realm

Significant Digits .or Sig Digs, if you prefer. Sometimes called Significant figures Thats 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. 3rd 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 whats the big deal? Remember the old saying: A chain is only a strong as its.. 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, its limited to the least sensitive decimal place. So, with adding & subtracting, you dont 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.

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