Question 15 on the MAT0020/24C Beginning Algebra State Exam

Scientific Notation (To and From)

Solution:

Convert to scientific notation:  0.000000195

The first step will be to determine where the decimal place should be to convert this number from standard notation to scientific notation.  In scientific notation the decimal should be after the first non zero from the left. 

In this case the decimal should be after the 1 which is 7 movements to the right.

If the decimal moved to the right the exponent is negative, to the left the exponent is positive.

Then place in this form: 

The solution is: 

Note: This can be checked by converting from scientific notation to standard notation.

To convert  to standard notation, start at the decimal point and the -7 means move the decimal point 7 movements to the left (due to the negative).  A positive exponent means move the decimal to the right, a negative means move to the left.

Practice Problems for Question 15

Scientific Notation (To and From)

1.  Convert to standard form:   

a.           b.                c.         d. 

2.  Convert to standard form:   

a.                   b.                   c.                      d. 

3.  Convert to scientific notation:          

a.              b.                          c.             d. 

4.  Convert to scientific notation:          

a.                b.               c.              d. 

Solutions:

1.  b                 2.  d                 3.  a                 4.  a