The table shows the planets and their distances from the SUN. (in km) MERCURY 58,000,000 VENUS EARTH MARS JUPITER SATURN URANUS NEPTUNE 103,000,000 155,000,000 228,000,000 778,000,000 1,430,000,000 2,870,000,000 4,500,000,000

What could be a problem when trying to write out the distances of the planets from the sun?

• • • THINK PAIR SHARE

Sometimes when numbers are very large or very small it can be difficult to keep track of the place value.

• • Therefore, we use SCIENTIFIC NOTATION Let’s practice writing the distances from the planet to the Sun in scientific notation!

I will do the first planet: Mercury The distance is 58,000,000 In scientific notation this would be: 5.8 x 10 7 How did I do that? Can you come up with a rule for writing numbers in scientific notation?

To write a number in scientific notation: • 1. Count the number of spaces to move the decimal so that there is one number in front of it.

58,000,000.

5.

8,000,000 2. DROP ALL OF THE ZEROS!

5.8

3. Multiply by a power of 10. (the exponent is the same number of SPACES you moved the decimal) 5.8 x 10 7

The table shows the planets and their distances from the SUN. (in km) MERCURY 58,000,000 VENUS EARTH MARS JUPITER SATURN URANUS NEPTUNE 103,000,000 155,000,000 228,000,000 778,000,000 1,430,000,000 2,870,000,000 4,500,000,000

The table shows the planets and their distances from the SUN. (in km) MERCURY 5. 8 x 10 7 VENUS EARTH MARS JUPITER SATURN URANUS NEPTUNE 1.03 x 10 8 1.55 x 10 8 2.28 x 10 8 7.78 x 10 8 1.43 x 10 9 2.87 x 10 9 4.5 x 10 9

SOMETIMES NUMBERS ARE VERY SMALL:

Red Blood Cell 0.0065 cm Plant cell Animal cell Proton Neutron Water Molecule Distance between DNA pairs 0.005 cm 0.001 cm 0.000000000000001 m 0.000000000000022

0.0000000003 m 0.00000000034m

SCIENTIFIC NOTATION IS ALSO HELP WITH VERY SMALL NUMBERS: • The diameter of a water molecule is 0.0000000003 m In Scientific Notation this is equivalent to : 3.0 x 10 10

SOMETIMES NUMBERS ARE VERY SMALL:

Red Blood Cell 0.0065 cm Plant cell Animal cell Proton Neutron Water Molecule Distance between DNA pairs 0.005 cm 0.001 cm 0.000000000000001 m 0.000000000000022

0.0000000003 m 0.00000000034m

PRACTICE: • WRITE IN SCIENTIFIC NOTATION: • 2,000,000

PRACTICE: • WRITE IN SCIENTIFIC NOTATION: • 0.000078

PRACTICE: • WRITE IN SCIENTIFIC NOTATION: 50,000,000

PRACTICE: • WRITE IN SCIENTIFIC NOTATION: 0.0125

PRACTICE: • WRITE IN SCIENTIFIC NOTATION: 0.000425

Write in standard form:

4.24 x 10

2

Write in standard form:

3.347 x 10

-1

Write in standard form:

1.5 x 10

-4

Write in standard form:

2.505 x 10

3

Write in standard form:

1.399 x 10

5

• WHY ARE NUMBERS WRITTEN IN SCIENTIFIC NOTATION?