1.4 Scientific Notation
Scientific notation is a short way of representing very large or very small numbers. Writing the values of these quantities in ordinary form takes up much space. They are difficult to read, their relative sizes are difficult to visualize, and they are awkward to use in calculations. Their decimal places are more conveniently expressed as powers of 10.
The numerical part of the quantity is written as a number from 1 to 9 multiplied by whole number powers of 10. To write numbers using scientific notation, move the decimal point until only one non-zero digit remains on the left. Then count the number of places through which the decimal point is moved and use this number as the power or exponent of 10.
The average distance from the Sun to the Earth is 138,000,000 km. In scientific notation, this distance would be written as 1.38 × 10⁸ km. The number of places the decimal moved to the left is expressed as a positive exponent of 10.
The diameter of a hydrogen atom is about 0.000000000052 m. To write this number in scientific notation, the decimal point is moved 11 places to the right. As a result, the diameter is written as 5.2 × 10⁻¹¹ m. The number of places moved by the decimal to the right is expressed as a negative exponent of 10.
lightbulbQuick Quiz: Express the following into scientific notation: (a) 0.00534 m <br> (b) 2574.32 kg <br> (c) 0.45 m <br> (d) 0.004 kg <br> (e) 186000 s