5 3 an application of exponents scientific notation
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5 3 an application of exponents scientific notation

5.3An Application of Exponents: Scientific Notation


Numbers occurring in science are often extremely large (as the distance from Earth to sun, 93,000,000 mi) or extremely small (wavelength of yellow-green light, approx. 0.0000006 m). Due to the difficulty of working with many zeros, scientists often express such numbers with exponents, using a form called scientific notation.

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

where 1 ≤ |a| < 10 and n is an integer.

A number in scientific notation is always written with the decimal point after the first nonzero digit an then multiplied by the appropriate power of 10. For example 56,200 is written 5.62 × 104, since


Writing a Number in Scientific Notation the distance from Earth to sun, 93,000,000 mi) or extremely small (wavelength of yellow-green light, approx. 0.0000006

To write a number in scientific notation, follow these steps.

Step 1:Move the decimal point to the right of the first nonzero digit.

Step 2:Count the number of places you moved the decimal point.

Step 3:The number of places in Step 2 is the exponent on 10.

The exponent is negative if you moved the decimal to the right.(Original Number was a Small Number)

The exponent is positive if you moved the decimal to the left. (Original Number was a Large Number)


Example 1
EXAMPLE 1 the distance from Earth to sun, 93,000,000 mi) or extremely small (wavelength of yellow-green light, approx. 0.0000006

Write in scientific notation.

Solution:

The exponent is positive if the original number is “large”.

Likewise, the exponent will be negative if the original if the original

number is “small”.


Convert numbers in scientific notation to numbers without exponents.

  • To convert a number written scientific notation to a number without exponents, work in reverse. Multiplying a number by a positive power of 10 will make the number greater; multiplying by a negative power of 10 will make the number less.


Example 2
EXAMPLE 2 exponents.

Write without exponents.

Solution:


Example 3

CALC? exponents.

EXAMPLE 3

Perform each calculation. Write answers in scientific notation and also without exponents.

Solution:


Example 4
EXAMPLE 4 exponents.

The speed of light is approximately 3.0 × 105 km per sec. How far does light travel in 6.0 × 101 sec?

Solution:

Light would travel 18,000,000 km in 60 seconds.


Example 5
EXAMPLE 5 exponents.

If the speed of light is approximately 3.0 × 105 km per sec, how many seconds does it take light to travel approximately 1.5 × 108 km from the sun to Earth?

Solution:

It would take 500 seconds for light from the sun to reach Earth.


Homework
Homework exponents.

  • 5.1: 1 – 87 EOO

  • 5.2: 1 – 77 ODD

  • 5.3: 1 – 83 EOO


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