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Significant Digits

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Significant Digits

In Chemistry, because numbers (i.e. data) are connected with making measurements, they carry a measure of uncertainty based on the accuracy of the measuring instrument and/or the measuring skill of the chemist.

Therefore, we must use the concept of significant digits when doing mathematical processes and when reporting numerical values.

Which numbers are significant?

1) All non-zero digits ARE significant. (ex. 1-9)

2) Zeroes between two significant digits ARE significant.

(ex. 203 or 2.0008)

3) Zeroes beyond the decimal point and at the end of a number ARE significant.

(ex. 0.0007100 The two zeroes at the end ARE significant.)

Which numbers are NOT significant?

1) Zeroes after a non-zero number when there is NO decimal are

NOT significant.

(ex. 1203000 The three zeroes at the end are NOT significant.

They are only place holders because the number can be written

as 1.203 x 106.)

2) Zeroes after the decimal point but before the first non-zero digit are NOT significant.

(ex. 0.0007010 or .0007010 The first three zeroes after the

decimal are NOT significant. They are only place holders because the number can be written as 7.010 x 10-4.)

How can I quickly see how many significant digits are in any number?

Think about the United States.

Yes, that’s the United States

pictured here.

The Pacific Ocean is to your LEFT.

The Atlantic Ocean is to your RIGHT.

SOOOOOO……….

If a decimal is PRESENT (PACIFIC) count from the LEFT until you reach the first non-zero digit. The rest of the digits will be significant.

If a decimal is ABSENT (ATLANTIC)

count from the RIGHT until you reach the first non-zero digit. The rest of the digits will be significant.

So, let’s try that number?technique!

How many significant digits are in each of the following numbers?

160,000,000

Ans. 2

12.00950

Ans. 7

0.009865

Ans. 4

4507

Ans. 4

23.007

Ans. 5

950

Ans. 2

0.0000000000000000000004

Ans. 1

The rule is that the number?right-most significant position in the answer is that which is common to all the numbers being added and/or subtracted.

Ex. 15.994

+1.00170

16.99570

Report as: 16.996

Ex. 5280

18.05

+110.913

5408.963

Report as: 5410

The Rules for Addition and SubtractionThe rule is your answer should be limited to the l number?owest number of significant digits of the values that are used to determine the final answer.

Ex. 123.4

x17

2097.8

Report as: 2100

Ex. 4350.25 / 15.5 =

280.66129

Report as: 281

The Rules for Multiplication and Division