6th Grade Math Textbook, Fundamentals

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4-10

4.4 1 and 4.4 10 1,000,000,000  109

Update your skills. See page 410.

Scientific Notation

Objective To write the scientific notation for numbers given in standard form • To write

the standard form for numbers given in scientific notation • To compare and order numbers

in scientific notation

The world’s smallest bird is the male bee hummingbird.

The weight of this bird, which lives in Cuba, is 0.056 ounce.

How can you express 0.056 ounce using a power of 10?

To express the mass of the bird using a power of 10, write

the number in. A number is written in

scientific notation when it is the product of two factors:

one factor is a number, a, that is greater than or equal to 1

but less than 10; the other factor is a power of 10.

a 10 b, where 1 a10 and bis any integer

To write 0.056 in scientific notation, express it as a product

of two factors.

0.056  Read the decimal, and write it as a fraction.



 Write 100 in exponential form.

5.6    10 ^2

So 0.056 ounce can be written as 5.6 10 ^2 ounce.

Numbers greater than 1 can also be written in scientific notation.

4,400,000,000  44   100,000,000

4.4 1,000,000,000

4.4    109

So 4,400,000,000 in scientific notation is 4.4  109.

Use a shortcut to write numbers in scientific notation.

Move the decimal point to the left or right to write the

first factor as a number greater than or equal to 1 but

less than 10. Count the number of decimal places moved

to write the power of 10 in exponent form.

0.056 5.6  10 ^2

67,800 6.78    104

To divide both terms by 10, move

the decimal point 1 place to the left.

Apply the meaning

of negative exponents.

5.6

102

5.6

100

56

1000

scientific notation

Move the decimal point 4 places

to the left. The exponent of 10 is 4.

Move the decimal point 2 places to

the right. The exponent of 10 is 2.

Rename as a power of

10 in exponential form.

Divide the first factor by 10,

and multiply the second factor

by 10 to adjust the place value.

Remember:

• To multiply by a power of 10,
  move the decimal point 1 place
  to the right for each zero in the
  standard form of the divisor.


• To divide by a power of 10,
  move the decimal point 1 place
  to the left for each zero in the
  standard form of the divisor.

Key Concept

Scientific Notation

• Move the decimal point to write the
  first factor as a number greater than
  or equal to 1 but less than 10. If the
  original number is less than 1, move
  the decimal point to the right. If the
  original number is greater than 10,
  move the decimal point to the left.


• Count the number of places the
  decimal point was moved. This
  number is the exponent for the
  power of 10.


• If the original number is 10 or greater,
  the exponent is positive. If the original
  number is less than 1, the exponent
  is negative.