Analía Bellizzi – Chemistry Classes

Ronald Reagan High School

Scientific Notation Notes

Scientific notation, or exponential notation, is a convenient way to write down a very large or a very small number.
In scientific notation each number is written as a product of two numbers:

Coefficient x 10 Exponent

Coefficients are usually expressed with one digit to the left of the decimal point.
An exponent gives the position of the decimal point in the number and is either:

    • positive (generally for numbers greater than or equal to 10)
    • zero (generally for numbers between 0 and 10)
    • negative (generally for numbers less than 0)

Converting a Number to Scientific (exponential) Notation – worked examples

 
  • Write 0.015 in scientific (exponential) notation.
    1. write the coefficient: 1.5
    2. count the places between the current decimal place and its position in the coefficient: 2
    3. determine the sign of the exponent. Moving to the right gives a negative sign (the number is less than 0): –
    4. write the number in scientific notation: 1.5 x 10-2
  • Write 256.35 in scientific (exponential) notation.
    1. write the coefficient : 2.5635
    2. count the places between the current decimal place and its position in the coefficient: 2
    3. determine the sign of the exponent. Moving to the left gives a positive sign (the number is greater than 10): +
    4. write the number in scientific notation: 2.5635 x 10+2 which is usually written as 2.5635 x 102
  • Write 42.76 in scientific (exponential) notation.
    1. write the coefficient : 4.276
    2. count the places between the current decimal place and its position in the coefficient: 1
    3. determine the sign of the exponent. Moving to the left gives a positive sign (the number is greater than 10): +
    4. write the number in scientific notation: 4.276 x 101
  • Write the number 3.56 in scientific (exponential) notation.
    1. write the coefficient : 3.56
    2. count the places between the current decimal place and its position in the coefficient: 0
    3. Zero is neither positive nor negative in sign.
    4. Finally write the number in scientific notation: 3.56 x 100

Converting Scientific (Exponential) Notation to a Decimal System Number – worked examples

  • Write 1.23 x 103 as a decimal system number.
    1. decide which way the decimal point will move based on whether the exponent is positive (move to right) or negative (move to left) : + therefore moves to right (number is greater than 10)
    2. decide how many places the decimal point will move based on the size of the exponent: 3 places
    3. write the number using zeroes to fill in the places between the decimal point in the coefficient and in the new number: 1230
  • Write 4.76 x 10-7 as a decimal system number.
    1. decide which way the decimal point will move based on whether the exponent is positive (move to right) or negative (move to left) : therefore moves to left (number is less than 0)
    2. Second, decide how many places the decimal point will move based on the size of the exponent: 7 places
    3. Finally write the number using zeroes to fill in the places between the decimal point in the coefficient and in the new number : 0.000000467
  • Write 5.22 x 100 as a decimal system number.
    1. decide which way the decimal point will move based on whether the exponent is positive (move to right) or negative (move to left) : none
    2. decide how many places the decimal point will move based on the size of the exponent: 0 places
    3. write the number using zeroes to fill in the places between the decimal point in the coefficient and in the new number if necessary: 5.22