“A man with a watch knows what time it is. A man with two watches is never sure”

(Unknown)

Significant Figures

Physical Science

What is a significant figure?

• There are 2 kinds of numbers:

–Exact: the amount of money in your account. Known with certainty.

What is a significant figure?

–Approximate: weight, height—anything MEASURED. No measurement is perfect.

When to use Significant figures

• When a measurement is recorded only those digits that are dependable are written down.

When to use Significant figures

–If you measured the width of a paper with your ruler you might record 21.7cm.

To a mathematician 21.70, or 21.700 is the same.

But, to a scientist 21.7cm and 21.70cm is NOT the same

• 21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

But, to a scientist 21.7cm and 21.70cm is NOT the same

• If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

How do I know how many Sig Figs?

• Rule: All digits are significant starting with the first non-zero digit on the left.

How do I know how many Sig Figs?

• Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

How many sig figs?

• 7• 40• 0.5• 0.00003• 7 x 105

• 7,000,000

• 1• 1• 1• 1• 1• 1

How do I know how many Sig Figs?

• 2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

How do I know how many Sig Figs?

• 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.

How do I know how many Sig Figs?

• 3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

How many sig figs here?

• 1.2• 2100• 56.76• 4.00• 0.0792• 7,083,000,000

• 2• 2• 4• 3• 3• 4

How many sig figs here?

• 3401• 2100• 2100.0• 5.00• 0.00412• 8,000,050,000

• 4• 2• 5• 3• 3• 6

What about calculations with sig figs?

• Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

Add/Subtract examples• 2.45cm + 1.2cm = 3.65cm,

• Round off to = 3.7cm

• 7.432cm + 2cm = 9.432 round to 9cm

Multiplication and Division

• Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

A couple of examples

• 56.78 cm x 2.45cm = 139.111 cm2

• Round to 139cm2

•75.8cm x 9.6cm = ?

The End

Have Fun Measuring and Happy Calculating!

How wide is our universe?

210,000,000,000,000,000,000,000 miles

(22 zeros)

This number is written in decimal notation. When numbers get this large,

it is easier to write them in scientific notation.

Scientific Notation

A number is expressed in scientific notation when it is in the form

a x 10n

where a is between 1 and 10

and n is an integer

Write the width of the universe in scientific notation.

210,000,000,000,000,000,000,000 miles

Where is the decimal point now?

After the last zero.

Where would you put the decimal to make this number be between 1 and 10?

Between the 2 and the 1

2.10,000,000,000,000,000,000,000.

How many decimal places did you move the decimal?

23When the original number is more than 1,

the exponent is positive.The answer in scientific notation is

2.1 x 1023

1) Express 0.0000000902 in scientific notation.

Where would the decimal go to make the number be between 1 and 10?

9.02The decimal was moved how many places?

8When the original number is less than 1, the

exponent is negative.9.02 x 10-8

Write 28750.9 in scientific notation.1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 2.87509 x 105

2) Express 1.8 x 10-4 in decimal notation.

0.00018

3) Express 4.58 x 106 in decimal notation.

4,580,000

On the graphing calculator, scientific notation is done with the button.

4.58 x 106 is typed 4.58 6