Chapter P.1, Problem 58E

Solution

To write the number $-0.00000000000000000016$ in scientific notation.

  $-1.6\times {10}^{-19}$

Given:

The electric charge, in coulombs, of an electron is about $-0.00000000000000000016$ .

Concept Used:

• A number in scientific notation contains a nonzero integer followed by a decimal and some nonzero integer exponent over 10.
• If the decimal point moved to the left side, raise the exponent of 10 by the positive integer digit by which the decimal moved to left.
• If the decimal point moved to the right side, raise the exponent of 10 by the negative integer digit by which the decimal moved to left.

Calculation:

In order to write the number $-0.00000000000000000016$ into scientific notation, move the decimal point to next to the first non-zero integer.

Note that there are 19 digits before the first nonzero integer, so move the decimal 19 digits right and raise the exponent of 10 by $-19$ , it follows

  $-0.00000000000000000016=-1.6\times {10}^{-19}$

Therefore, the number in scientific notation is $-1.6\times {10}^{-19}$ .