Chapter CSB, Problem 3.7E

To determine

To express: the given number in scientific form.

Answer to Problem 3.7E

  $0.000078=7.8\times {10}^{-5}$ .

Explanation of Solution

Given:

The given number is $0.000078$ .

Concept used:

Scientific notation is a standard way of writing very large and very small numbers so that they’re easier to both compare and use in computations. To write in scientific notation, follow the form $N\times {10}^a$

where  N  is a number between 1 and 10, but not 10 itself, and  a  is an integer (positive or negative number).

Calculation:

The given number is $0.000078$ .

Move the decimal place to the right to create a new number from 1 up to 10.

As it is a whole number, the decimal point is understood to be at the end of the number: $0.000078$ . So, $N=7.8$

Determine the exponent, which is the number of times you moved the decimal.

Moved the decimal 5 times, because moved the decimal to the right, the exponent is negative. Therefore,  $a =-5$

Put the number in the correct form for scientific notation.

Therefore, $N\times {10}^a=7.8\times {10}^{-5}$

Hence, $0.000078=7.8\times {10}^{-5}$ .