Scientific Notation
Scientific Notation
Scientific notation (also called exponential notation or standard form) is a way of writing numbers that are very large or very small in an easy-to-use format. For example, instead of writing 0.001 watt, we can write 1.0 x 10-3 watt, or 1 milliwatt.
How is this accomplished? Think of 1.0 x 10-3 as the product of two numbers: 1.0 (the digit term) and 10-3 (the exponential term). Note that the digit term is expressed as only one digit and the decimal as a standard, making it is easy to keep one’s place when shifting decimal points left or right.
The exponent indicates the number of places the decimal point must be moved to give the number in long form. If the exponent is positive, the decimal point is moved that number of places to the right. When the exponent is negative, the decimal point is moved that number of places to the left.
For example, to write the number 1.0 x 106 Hz in long form, move the decimal point 6 places to the right, or 1,000,000.0 Hertz. (Note that this can also be written as 1 MHz.)
This form of scientific notation is referred to as normalized scientific notation. However, it is not always easy to represent exponents when using calculators. Therefore, you might also see numbers written in a form of scientific notation referred to as E notation. In our example, 1,000,000 Hertz would be written as 1.0E6, where the E replaces the " x 10."
In the following table, scientific notations for both normalized and E notation have been included (adapted from Table 4 – Metric Prefix – TechTip "Metric Conversion and CATV").
Click here to download this table as a PDF.
Practice
- Write the following numbers in scientific notation (normalized form).
a. 750,000,000
Place a decimal point after the 7. There are 8 digits following the 7. Therefore,
750,000,000 = 7.5 x 108
b. 0.0000006
Place a decimal point after the 6. There are 7 digits preceding the 6. Therefore,
0.0000006 = 6.0 x 10-7
- Write the numbers from question 1. in scientific notation (E notation).
a. 750,000,000 = 7.5 x 108
Replace the "x 10" with E
750,000,000 = 7.5 x 108 = 7.5E8
b. 0.0000006 = 6.0 x 10-7
Replace the "x 10" with E
0.0000006 = 6.0 x 10-7 = 6.0E-7
- Write the following numbers long form.
a. 8.75 x 108
The exponent is +8, therefore, move the decimal point eight digits to the right.
8.75 x 108 = 875,000,000.0
b. 9.87E5
The exponent is +5, therefore, move the decimal point five digits to the right.
9.87E5 = 987,000.0
To assess your understanding of scientific notation, take this short Scientific Notation Quiz.
Understanding this foundational information promotes SCTE certification candidates’ understanding of the mathematical concepts, and therefore, helps candidates prepare for the following certification exams.
For more information on SCTE certification, select "Certifications" from the menu on the left.
For additional information on this topic, here is a good website to explore: http://ts.nist.gov/WeightsAndMeasures/Metric/mpo_home.cfm.
Click here to download this entire TechTip as a PDF file.