How to write numbers The 4 different ways

How to write numbers The 4 different ways to represent numbers: Numerical, Word, Scientific, Engineering

Intro • Numbers are used everyday to represent many different things. • In science numbers are mainly used to measure and to count. We call this process “quantification. ” • Quantification is “the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method. ” Reference: http: //en. wikipedia. org/wiki/Quantification • There a variety of ways in which a number can be represented. – Standard form – Word form – Scientific Notation – Modified Scientific Notation

Standard form • This form is written with numbers, commas, and decimals. • No words are used to write the number places. § 123, 456, 789 § 123, 456. 789

Word form • • • This form is written with numbers and decimals. Words are used to define the number place of the number being written. Examples § § § • 35, 000, 000 is written as 35 billion 123, 000, 000 is written as trillion 0. 0000065 is written as 6. 5 millionth Used when you want to express numbers, especially large numbers, that have been rounded out. § § 123, 456, 789 12, 345, 678, 901, 234 123 million or 123. 4 million 12 trillion or 12. 3 trillion

Scientific Notation • • This form is used to represent extremely large or small numbers. The number is expressed using powers of 10. Has the form of A x 10 B where 0<A<10 and B represents the number of places used to move the decimal behind the first non-zero digit. B is positive if the decimal is moved left. B is negative if the decimal is moved right. Examples: . § § • Sometimes a number is rounded when it is placed in scientific notation. § § • 123, 456, 789 is written as 1. 23456789 x 108 0. 00000123456 is written as 1. 23456 x 10 -11 29, 984, 583, 748 is written as 3. 00 x 1010 0. 00000080093421 is written as 8. 00 x 10 -7 The speed of light is 299, 792, 458 m/s can be written as 3. 00 × 108 m/s Avogadro’s number is 6022141500000000 can be written as 6. 022 x 1023 This is done to show it in a simpler form that keeps the magnitude of the number.

Engineering Notation • • • This form is similar to the Word form and Scientific Notation. Has the form of A x 10 B It is normally used with large or small numbers. The difference being 0<A<1000 and A comes from the digits representing the initial number place of the number. 10 B represents the number place and B is a multiple of 3. Examples: . § § • 98, 000 is written as 98 x 106 or 98 million 123, 000, 000 is written as 123 x 1015 or 123 quadrillion This can also be used to write approximated numbers § 789, 432, 863, 202, 100 is written as 789. 4 x 1012 or 789. 4 trillion

Table of SI Units Prefix yotta zetta exa Symbol Y Z E Numerical Form 1000000000000 100000000000 1000000000 Sci. Not. 1. 00 x 1024 1. 00 x 1021 1. 00 x 1018 Number Place Septillion Sextillion Quintillion peta tera giga mega kilo hecto deca P T G M k h da deci centi d c 100000000 1000000 1000000 100 10 1 0. 01 1. 00 x 1015 1. 00 x 1012 1. 00 x 109 1. 00 x 106 1. 00 x 103 1. 00 x 102 1. 00 x 101 1. 00 x 100 1. 00 x 10 -1 1. 00 x 10 -2 Quadrillion Trillion Billion Million Thousand Hundred Ten One Tenth Hundredth milli micro nano pico m μ n p 0. 001 0. 000000001 0. 0000001 1. 00 x 10 -3 1. 00 x 10 -6 1. 00 x 10 -9 1. 00 x 10 -12 Thousandth Millionth Billionth Trillionth femto f 0. 00000001 1. 00 x 10 -15 Quadrillionth atto a 0. 0000000001 1. 00 x 10 -18 Quintillionth zepto z 0. 00000000001 1. 00 x 10 -21 Sextillionth yocto y 0. 0000000000001 1. 00 x 10 -24 Septillionth