Concepts of Standard Form

Introduction
math2ever
Standard form is a simple way to write very large (e.g 230,000,00) or and very small (e.g. 0.000,000,006) numbers.


It is commonly used in scientific calculator when the number to be displayed is too large to be shown on the screen.



General form of standard form
A number written with one digit to the left of the decimal point and multiplied by 10 raised to some power is said to be written in standard form.
±A× 10 n MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8XjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaeyySaeRaamyqaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacaWGUbaaaaaa@3FFA@

Noted, 1A10 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8XjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaaccaGae8xmaeJaeyizImQaamyqaiablQNiWjaaigdacaaIWaaaaa@3F19@ and n is a power in positive or negative whole number.

Example of Number in Standard Form
  1. 5 8370 4decimal places toleft MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGynamaayaaabaGaaGioaiaaiodacaaI3aGaaGimaaWceaGabeaacaaI0aGaaGPaVlaaykW7caWGKbGaamyzaiaadogacaWGPbGaamyBaiaadggacaWGSbaabaGaamiCaiaadYgacaWGHbGaam4yaiaadwgacaWGZbaabaGaaGPaVlaadshacaWGVbGaaGPaVlaadYgacaWGLbGaamOzaiaadshaaaGccaGL44paaaa@57F8@ in standard form is 5.837× 10 4 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGynaiaac6cacaaI4aGaaG4maiaaiEdacqGHxdaTcaaIXaGaaGimamaaCaaaleqabaGaaGinaaaaaaa@41C0@
  2. 0 .004 3decimal places toright 15 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaaGimamaayaaabaGaaiOlaiaaicdacaaIWaGaaGinaaWceaGabeaacaaIZaGaaGPaVlaaykW7caWGKbGaamyzaiaadogacaWGPbGaamyBaiaadggacaWGSbaabaGaamiCaiaadYgacaWGHbGaam4yaiaadwgacaWGZbGaaGPaVdqaaiaadshacaWGVbGaaGPaVlaadkhacaWGPbGaam4zaiaadIgacaWG0baaaOGaayjo+dGaaGymaiaaiwdaaaa@5961@ in standard form is 4.15× 10 3 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaaGinaiaac6cacaaIXaGaaGynaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaIZaaaaaaa@40F8@

As shown above for 58370 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGynaiaaiIdacaaIZaGaaG4naiaaicdaaaa@3D51@ , it is because the decimal point has been moved 4 places to the left side to get the number to be 5.837 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaeyOeI0IaaGynaiaac6cacaaI4aGaaG4maiaaiEdaaaa@3D49@ .

Note using the scientific calculator
Your calculator will have a key 10 x MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbdfwBIjxAHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGabiGaaiaabeqaamaaeaqbaaGcbaGaaGymaiaaicdadaahaaWcbeqaaiaadIhaaaaaaa@3B4A@ and EXP  for entering numbers in standard form.