• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar

Flight Mechanic

Aircraft Mechanic School Study Supplement for Future Aviation Maintenance Technicians




  • Home
  • AMT Training
    • Basic Aviation Maintenance
    • Airframes
    • Powerplants
  • AMT Schools
  • AMT Books
  • Tip Jar
You are here: Home / Basic Aviation Maintenance / Aviation Mathematics / Scientific Notation
Regretfully, Flight-Mechanic will be turning out the lights after fifteen years. Google, in its infinite wisdom, has chosen to remove Flight-Mechanic from its search results (the claim is that the content on this site is spam). We appealed their decision to shut us down, to no avail.

Unfortunately, since Google has a monopoly over internet search, this means that traffic levels on the site will drop to a level that makes maintaining it uneconomic. As time progresses, we will no longer be able to maintain the server space and will remove the site from the internet. Thanks to all who have supported us over the years.

To fight back against the monopolistic practices of companies like Google, we recommend using a competing search engine such as Brave (you get the added benefit of not being spied on by Big Tech) and advocating for anti-trust legislation from your representatives.

Scientific Notation

Filed Under: Aviation Mathematics

Scientific notation is used as a type of shorthand to express very large or very small numbers. It is a way to write numbers so that they do not take up as much space on the page. The format of a number written in scientific notation has two parts. The first part is a number greater than or equal to 1 and less than 10 (for example, 2.35). The second part is a power of 10 (for example, 10^6). The number 2,350,000 is expressed in scientific notation as 2.35 × 10^6. It is important that the decimal point is always placed to the right of the first digit. Notice that very large numbers always have a positive power of 10 and very small numbers always have a negative power of 10.

Example: The velocity of the speed of light is over 186,000,000 mph. This can be expressed as 1.86 × 10^8 mph in scientific notation. The mass of an electron is approximately 0.000,000,000,000,000,000,000,000,000,911 grams. This can be expressed in scientific notation as 9.11 × 10^-28 grams.

Converting Numbers from Standard Notation to Scientific Notation

Example: Convert 1,244,000,000,000 to scientific notation as follows. First, note that the decimal point is to the right of the last zero. (Even though it is not usually written, it is assumed to be there.)

1,244,000,000,000 = 1,244,000,000,000

To change to the format of scientific notation, the decimal point must be moved to the position between the first and second digits, which in this case is between the 1 and the 2. Since the decimal point must be moved 12 places to the left to get there, the power of 10 will be 12. Remember that large numbers always have a positive exponent. Therefore, 1,244,000,000,000 = 1.244 × 10^12 when written in scientific notation.

Example: Convert 0.000000457 from standard notation to scientific notation. To change to the format of scientific notation, the decimal point must be moved to the position between the first and second numbers, which in this case is between the 4 and the 5. Since the decimal point must be moved 7 places to the right to get there, the power of 10 will be −7. Remember that small numbers (those less than one) will have a negative exponent. Therefore, 0.000000457 = 4.57 × 10^-7 when written in scientific notation.

Converting Numbers from Scientific Notation to Standard Notation

Example: Convert 3.68 × 10^7 from scientific notation to standard notation, as follows. To convert from scientific notation to standard notation, move the decimal place 7 places to the right. 3.68 × 10^7 = 36800000 = 36,800,000. Another way to think about the conversion is 3.68 × 10^7 = 3.68 × 10,000,000 = 36,800,000.

Example: Convert 7.1543 × 10^-10 from scientific notation to standard notation. Move the decimal place 10 places to the left: 7.1543 × 10^-10 =.00000000071543. Another way to think about the conversion is 7.1543 × 10^-10 = 7.1543 × .0000000001 = .00000000071543

When converting, remember that large numbers always have positive powers of ten and small numbers always have negative powers of ten. Refer to Figure 1-11 to determine which direction to move the decimal point.

Figure 1-11. Converting between scientific and standard notation.
Figure 1-11. Converting between scientific and standard notation.

Addition, Subtraction, Multiplication, and Division of Scientific Numbers

To add, subtract, multiply, or divide numbers in scientific notation, change the scientific notation number back to standard notation. Then add, subtract, multiply or divide the standard notation numbers. After the computation, change the final standard notation number back to scientific notation.

Flight Mechanic Recommends

Rod Machado's Private Pilot Handbook -Flight Literacy recommends Rod Machado's products because he takes what is normally dry and tedious and transforms it with his characteristic humor, helping to keep you engaged and to retain the information longer. (see all of Rod Machado's Products).
   
-->

Primary Sidebar

SEARCH FLIGHT MECHANIC

SEARCH FLIGHT MECHANIC

Aircraft Mechanic Training

Basic Aviation Maintenance

Powerplants

Airframes

Popular Posts

Aircraft Mechanic Salary

Aircraft Mechanic Schools

Aircraft Mechanic Requirements

Aircraft Flight Training

Contact Us | Terms of Use | Privacy Policy
Easy Campfire Recipes | Recipe Workbook



Copyright © 2023 Flight-Mechanic.com