Significant figures and rounding

Rounding and significant figures

by Susan Duderstadt

In chemistry we deal with two kinds of numbers:

​Exact numbers

Numbers we know by counting

​

​Measured numbers

​Numbers we get by measuring

​In science, it is important to measure things accurately

We must also report our measurements accurately.

​When we measure, we report all the certain digits plus one uncertain, estimated digit.

​

​These are the digits that have meaning and are significant

​Any digits beyond the estimated digit are not reliable.

​By using significant figures, we present only the numbers that we actually measured

​...and the one number at the end that we estimated.

Multiple Choice

Which of the following is a measured number

• There are 350 cats

• There are 24 hours in a day

• This cat weighs 25 kilograms

• There are 12 inches in a foot

Multiple Choice

Which of the following is an exact number?

• The insect is 250 centimeters

• There are 24 hours in a day

• I have 2 liters of Coca Cola

• I walked 500 miles...and then I walked 500 more

Significant Figures Rules​

​Part 1: No decimal point

Multiple Choice

How many significant figures: 216 m

• 1

• 2

• 3

• 0

Multiple Choice

How many significant figures: 2016 m

• 1

• 2

• 3

• 4

Multiple Choice

How many significant figures: 1000 mL

• 1

• 2

• 3

• 4

Multiple Choice

How many significant figures: 450 m

• 3

• 2

• 1

• 0

Multiple Choice

How many sig figs are there? 100000000

• 1

• 9

• 10

​Exception: If there is a decimal after the number, the zeroes are significant

​100,000,000.

​

​Has 9 significant figures

Significant figures​

When there is a decimal ​

Multiple Choice

How many significant figures: 153.0 mL

• 1

• 2

• 3

• 4

Multiple Choice

How many significant figures: 100.000 cL

• 1

• 3

• 5

• 6

Multiple Choice

How many significant figures: 4.20 cm

• 1

• 2

• 3

• 4

Multiple Choice

How many sig figs are there? 0.000008

• 1

• 2

• 6

• 7

Multiple Choice

How many significant figures: 0.012 km

• 1

• 2

• 3

• 4

Multiple Choice

How many significant figures: 0.010 L

• 1

• 2

• 3

• 4

We are often told to round to a certain number of significant figure​s

​

​

​If the digit to be rounded is greater than or equal to 5, the preceding digit is increased by 1

​

​If the digit to be removed is less than 5, the preceding digit stays the same.  You round down

Multiple Choice

Round 5.793 to two significant digits

• 5.79

• 5.7

• 5.8

• 5.79