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\(\times\)10^{4} | 34,567 = 3.4567\(\times\) 10^{4} |
1000 = 1\(\times\)10^{3} | 495 = 4.95 \(\times\)10^{2} |
10 = 1\(\times\)10^{1} | 98 = 9.8 \(\times\)10^{1}(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\(\times\)10^{2}\(\times\)10^{-6}
= 4.57\(\times\)10^{-4}
Solution:
324000000
= 324 × 10^{6}
= 3.24 × 10^{2}× 10^{6}
= 3.24 × 10^{2+6}
= 3.24 × 10^{8}
Solution:
45000000
= 45×10^{6}
= 4.5×10^{1}×10^{6}
= 4.5×10^{1+6}
= 4.5×10^{7}
Solution:
45
= 4.5×10
= 4.5×10^{1}
Solution:
101000
=1.01×100000
=1.01×10^{5}
Solution:
0.00671
= \(\frac{6.71}{100000}\)
= \(\frac{6.71×100}{10^5}\)
= 6.71×10^{2-5}
=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:
= 2.4×10^{5}
= 240000
Solution:
= 3.2×10^{4}+2.3×10^{4}
= (3.2+2.3)×10^{4}
= 5.5×10^{4}
Solution:
299792458
= 2.99792458 × 100000000
= 2.99792458 × 10^{8} m/s
Solution:
3.2 × 10^{4} + 2.3 × 10^{4}
= ( 3.2 + 2.3 )× 10^{4}
= 5.5× 10^{4}
3400
0.000023
0.010
7000000
0.000037
2.30×10^{4}
3456.78
8.41×10^{-5}-7.00×10^{-6}
The mass of the moon is 73,000,000,000,000,000,000,000 kg. What is this written in scientific notation.
Simplify:
(4( imes)10^{5}) ( imes)(3( imes)10^{6})
Simplify:
(7( imes)10^{8})( imes)(2( imes)10^{10})
Simplify the following and give your answers in scientific notation:
10^{8}+ 10^{6}
Convert the following in general form.
2.4( imes)10^{5}
Write 7.085( imes)10^{-14} as an ordinary number.
Simplify:
4.5( imes)10^{7}- 2.2( imes)10^{6}
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0.000002
Feb 05, 2017
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The distance between the sun and the earth is 150000000 Km . Rewrite it in scientific notation.
Feb 05, 2017
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