Question

How would 0.00008 be written in scientific notation?

Answer 1

Hint: A decimal number is given whose non-zero digits reside at the end of the number. To express this given number in scientific notation, the last non-zero digit is separated from the second last digit (it can be zero or non-zero) by a decimal point. In other words, the decimal point is shifted backwards to the non-zero digits. The zero digits are then indicated in powers of 10.

Complete answer:
Scientific notation is sometimes referred to as the standard index form. The general representation of scientific notation is: \[a{\text{ }} \times {\text{ }}{10^{b\;\;}}\;\] where \[1{\text{ }} \leqslant {\text{ }}a{\text{ }} < {\text{ }}10\] and \[b\] can be any integer. The number \[b\] is known as the order of magnitude while the number \[a\] is referred to as the mantissa or significant. The number \[a\] is the coefficient of the scientific notation and is normally greater than or equal to 1 and less than 10.
The given number is 0.00008. The non-zero digit is 8. Then according to the condition of significant numbers, these two digits can be separated by a decimal point. Thus we can write it as 8.0 or 8. Thus, \[a = 8.0\]and the remaining zeros can be written as power of 10. Thus, \[0.00008 = \dfrac{{8.0}}{{100000}} = 8.0 \times {10^{ - 5}}\]. The power factor appears to be \[{10^{ - 5}}\]. Therefore, \[b = - 5\]. This is a negative exponent.

Therefore, 0.073 would be written in scientific notation as\[8.0 \times {10^{ - 5}}\].

Note:The number given in the question has the non-zero digits at the end of the number. In this case, the last non-zero digit is separated from the second last digit by a decimal point. Note that the second last digit can be zero or non-zero. But, there are also numbers in which the non-zero digits are at the start of the number. In this case, the first non-zero digit is separated from the second digit (zero or non-zero) by a decimal point.