Significant Figures

What is a significant figure?There are 2 kinds of numbers:1. Exact: Known with certainty. Example: the number of students in

this room2. Approximate: anything

MEASURED. Example: Mass, volume, length,

weight, heightNo 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

• 21.700 cm to a scientist means the measurement is accurate to within 1/1000 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 1: All non zero digits are significant.

Example: 1,246 (4 sig figs)

How do I know how many Sig Figs?

• Rule 2: Any zeros between significant digits are also significant.

Example: 1,206 (4 sig figs)

How do I know how many Sig Figs?

• Rule 3: If the number does not contain a decimal point, any zeros to the right of a nonzero number are NOT significant

Example: 1,200 (2 sig figs)

How do I know how many Sig Figs?

• Rule 4: If zeros are at the end of a number that has a decimal, the zeros are significant.

Example: 1,200. (4 sig figs)

How do I know how many Sig Figs?

• Rule 5: If a value has no significant digits to the left of a decimal point, any zeros to the right of the decimal point before the non zero numbers (leading zeros) are not significant.

Example: 0.0012 (2 sig figs)

How do I know how many Sig Figs?

• Rule 6: Zeros that are found after non zero numbers to the right of a decimal point are significant (trailing zeros)

Example: 0.1200 (4 sig figs)

How many sig figs?• 7• 40• 0.5• 0.00003• 7 x 105

• 7,000,000

111111

How many sig figs here?• 1.2• 2100• 56.76• 4.00• 0.0792• 7,083,000,000

224334

How many sig figs here?• 3401• 2100• 2100.0• 5.00• 0.00412• 8,000,050,000

425336

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 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 9.60cm = ? 728 cm2

Have Fun Measuring and Happy Calculating!