MATH - SCIENCE INTEGRATION

bullet1 SCIENTIFIC NOTATION

bullet2 Rules for Mathematical Operations Using The Powers of Ten


When using scientific notation in calculations, the rules of algebra for the powers of ten are followed.  
  • When multiplying two measurements in scientific notation, the powers of ten are added.
  • When dividing measurements in scientific notation, the powers of ten are subtracted.
  • Rule for Addition and Subtraction - when adding or subtracting in scientific notation, you must express the numbers as the same power of 10. This will often involve changing the decimal place of the coefficient.

If you need some help with using your calculator with scientific notation, see the link below.



» See also: Using the OGT Calculator for Scientific Notation

bullet3 Example

EXAMPLE:
Add 3.76 x 104 and 5.5 x 102

First, you must move the decimal to change
5.5 x 102 to 0.055 x 104 .

Then, add the coefficients and leave the base and exponent the same:

3.76 + 0.055 = 3.815 x 104


  • Rules for Writing in Scientific Notation
    Let's look at the steps for calculating with scientific notation.  These steps are easier to learn if we work through a problem.  Here is the problem to solve:


    The city of Steubenville has commisioned a company to design a flag for the city.  They want the dimensions of the flag to be 1.26 x 104  cm by 8.40 x 103 cm.  What will the area of this flag be in square centimeters?


    Step 1:   List the given and unknown measurements:
    • Given:  
    length of flag:1.26 x 104cm
    width of flag:8.40 x 103cm   
    • Unknown:  
    area of flag in cm2


    Step 2:   Write the equation for the area of the flag. This is a multiplication problem since area is determined by multiplying length x width.

    A = l x w


    Step 3:   Insert the known values into the equation and solve.
    A =
    (1.26 x 104cm)(8.40 x 103cm)
    • Regroup the values and units as follows:
    A =
    (1.26 x 8.40)(104 x 103 )(cm x cm)
    • Remember to add the powers of 10 when multiplying.
    A = 10.584 x 107 cm2


    Ready for some practice?



     
    • Practice Problems
      Solve the problems below using scientific notation.  Don't forget to label your answers when measurements are involved!
      PROBLEMS:  
      1.  A contractor buys a parcel of land to establish an industrial park.. The tract of land measures 5.36 x 103 meters by 1.38 x 104 meters.  What is the area of this tract in square meters?

      2.  Use the equation speed = distance/time to find the speed of a car that travels 3.7 x 106 meters in 3.10 x 105 seconds.

      3.  (3.95 x 105) + (7.8 x 103)

      4.  (7.83 x 10-2) - (2.20 x 10-3)

      5.   (1.042 x 10-1) x (4.002 x 10-5)

      6.   (1.92 x 10-2) / (2.3 x 106)

      7.   (4.42 x 10-3) x (4 x 10-2)  

      8.   (8.23 x 104) - (3.02 x 105)

      9.  (2 x 10-3) + (8 x 10-4)

      10.   (6.8 x 103) x (4.54 x 106)