Note on Scientific Notation

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Scientific Notation is used to handle very large or very small numbers. Scientists have developed a shorter method to express very large numbers. It is written as the product of a number (integer and decimal) and a power of 10.

Here are some examples of scientific notation.

10,000 = 1\(\times\)104 34,567 = 3.4567\(\times\) 104
1000 = 1\(\times\)103 495 = 4.95 \(\times\)102
10 = 1\(\times\)101 98 = 9.8 \(\times\)101(not usually done)
\(\frac{1}{10}\)=1\(\times\)10-1 0.23 = 2.3 \(\times\)10-1(not usually done)
\(\frac{1}{100}\)= 1\(\times\)10-2 0.026 = 2.6\(\times\)10-2
\(\frac{1}{1000}\) = 1\(\times\)10-3 0.0064 =6.4\(\times\)10-3
\(\frac{1}{10,000}\) = 1\(\times\)10-4 0.00088 = 8.8\(\times\)10-4

Example:

0.000457

= \(\frac{0.000457\times 1000000}{1000000}\)

=\(\frac{457}{10^6}\)

=457\(\times\) 10-6

=4.57\(\times\)102\(\times\)10-6

= 4.57\(\times\)10-4

  • Scientific notation is the way that scientists easily handle very large numbers or very small numbers.
  • Scientific notation can be used to turn 0.0000053 into 5.3 x 10-6
  • A power of ten with  a positive exponent, such as 105, means the decimal was moved to the left.
  • A power of ten with a negative exponent, such as 10-5, means decimal was moved to the right.
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Very Short Questions

Solution:

324000000

= 324 × 106

= 3.24 × 102× 106

= 3.24 × 102+6

= 3.24 × 108

Solution:

45000000

= 45×106

= 4.5×101×106

= 4.5×101+6

= 4.5×107

Solution:

45

= 4.5×10

= 4.5×101

Solution:

101000

=1.01×100000

=1.01×105

Solution:

0.00671

= \(\frac{6.71}{100000}\)

= \(\frac{6.71×100}{10^5}\)

= 6.71×102-5

=6.71×10-3

Solution:

0.0000435

= \(\frac{0.0000435×10000000}{10000000}\)

= \(\frac{435}{10^7}\)

Solution:

0.0000435

= \(\frac{0.0000435×10000000}{10000000}\)

= \(\frac{435}{10^7}\)

Solution:

= 2.4×105

= 240000

Solution:

= 3.2×104+2.3×104

= (3.2+2.3)×104

= 5.5×104

Solution:

299792458

= 2.99792458 × 100000000

= 2.99792458 × 108 m/s

Solution:

3.2 × 104 + 2.3 × 104

= ( 3.2 + 2.3 )× 104

= 5.5× 104

0%
  • 3400

    2.5×103 
    3.4×103 
    1.3×103 
    3.4×93 
  • 0.000023

    2.3×10-5
    2.1×10-5
    4.3×10-2
    2.3×10-4
  • 0.010

    1×10-2
    4×10-2
    1×9-2
    2×10-2
  • 7000000

    6×106 
    7×106 
    8×106 
    2×104 
  • 0.000037

    3.7×10-5
    2.7×10-5
    4.7×10-1
    3.3×10-3
  • 2.30×104

    10000
    23000
    22500
    22000
  • 3456.78

    3.44677×103
    3.45677×103
    3.45678×102
    3.45678×103
  • 8.41×10-5-7.00×10-6

    8.72×10-5
    6.71×9-5
    5.11×10-5
    7.71×10-5
  • The mass of the moon is 73,000,000,000,000,000,000,000 kg. What is this written in scientific notation.

    7.2( imes)1018 kg
    7.2( imes)1015kg
    7.2( imes) 1019 kg
    7.2( imes)1017 kg
  • Simplify:

    (4( imes)105) ( imes)(3( imes)106)

    1.2( imes)1011
    1.2( imes)1012
    1.2( imes)1010
    1.2( imes)1015
  • Simplify:

    (7( imes)108)( imes)(2( imes)1010)

     1.4( imes)1010
     1.4( imes)1019
     1.4( imes)1012
     1.4( imes)1015
  • Simplify the following and give your answers in scientific notation:

    108+ 106

    1.01( imes)108
    1.01( imes)1012
    1.01( imes)1015
    1.01( imes)1010
  • Convert the following in general form.

    2.4( imes)105

    24,0000
    2400
    2400000
    24000
  • Write 7.085( imes)10-14 as an ordinary number.

    0.00000000000007085
    0.00000000007085
    0.00000000007085
    0.0000000000000085
  • Simplify:

    4.5( imes)107- 2.2( imes)106

    4.289 imes)1012
    4.28( imes)108
    4.28( imes)107
    4.28( imes)109
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0.000002


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The distance between the sun and the earth is 150000000 Km . Rewrite it in scientific notation.


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