writing numbers in scientific notation and using significant figures

Bell Ringer: Oct. 4, 2010: Complete the table below. Place X in the appropriate box to indicate the type of each measurement unit. Reference: Physical Science, page 16

Measurement SI Unit Derived Unit

Gram per centimeter cubed (g/cm3)

Decimeter (dm)

Liter (L)

Meter cubed (m3)

Kilogram (kg)

Glenn C. SoltesIntegrated Science

Biology2010-2011

Objectives: Define Scientific Notation and Significant

Figures.Identify the rules in writing scientific notation

and significant figures.Use scientific notation and significant figures

in problem solving.Identify the significant figures in calculations.

Scientific Notation

A short-hand way of writing large numbers without writing all of the zeros.

A number is expressed in scientific notation when it

is in the forma x 10n

where a is between 1 and 10and n is an integer

The Distance From the Sun to the Earth

93,000,000 miles

Write the width of the universe in scientific notation.210,000,000,000,000,000,000,000

milesWhere 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

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.

0.000183) 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

Practice Problem

1) 98,500,000 =2) 64,100,000,000 =3) 279,000,000 =4) 4,200,000 =5) .000567 =

Write in scientific notation. Decide the power of ten.

A prescribed decimal place that determines the amount of rounding off to be done based

on the precision of the measurement.

There are 2 kinds of numbers:Exact: the amount of money in your account. Known with certainty.

Approximate: weight, height—anything MEASURED.

No measurement is perfect.

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

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 same21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

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

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

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

How many significant figures?7400.50.000037 x 105

7,000,000

111111

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

How many significant figures here?1.2210056.764.000.07927,083,000,000

224334

How many sig figs here?340121002100.05.000.004128,000,050,000

425336

Practice: Count the number of significant figures.1. 800002. 0.00153. 8 002 0004. 1.125. 1.oo5

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 examples2.45cm + 1.2cm = 3.65cm,

Round off to = 3.7cm

7.432cm + 2cm = 9.432 round to 9cm

Multiplication and DivisionRule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

A couple of examples56.78 cm x 2.45cm = 139.111 cm2

Round to 139cm2

75.8cm x 9.6cm = ?

Perform the following calculations, and write the answer with the correct number of significant figures.a. 12.65 cm x 42.1 cmb. 3.02 cm x 6.3 cm x 8.225 cmc. 3.7 g ÷ 1.o83 cm3

Credit:Holt, Physical Science 2006