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Scientific (exponential) Notation

Key Concepts

  • 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:

    a coefficient x 10an 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

  1. Write 0.015 in scientific (exponential) notation.

    First, write the coefficient : 1.5

    Second, count the places between the current decimal place and its position in the coefficient: 2

    Third, determine the sign of the exponent. Moving to the right gives a negative sign (the number is less than 0): -

    Finally write the number in scientific notation: 1.5 x 10-2

  2. Write 256.35 in scientific (exponential) notation.

    First, write the coefficient : 2.5635

    Second, count the places between the current decimal place and its position in the coefficient: 2

    Third, determine the sign of the exponent. Moving to the left gives a positive sign (the number is greater than 10): +

    Finally write the number in scientific notation: 2.5635 x 10+2 which is usually written as 2.5635 x 102

  3. Write 42.76 in scientific (exponential) notation.

    First, write the coefficient : 4.276

    Second, count the places between the current decimal place and its position in the coefficient: 1

    Third, determine the sign of the exponent. Moving to the left gives a positive sign (the number is greater than 10): +

    Finally write the number in scientific notation: 4.276 x 101

  4. Write the number 3.56 in scientific (exponential) notation.

    First, write the coefficient : 3.56

    Second, count the places between the current decimal place and its position in the coefficient: 0

    Zero is neither positive nor negative in sign.

    Finally write the number in scientific notation: 3.56 x 100

Converting Scientific (exponential) Notation to a Decimal System Number

  1. Write 1.23 x 103 as a decimal system number.

    First, 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)

    Second, decide how many places the decimal point will move based on the size of the exponent: 3 places

    Finally write the number using zeroes to fill in the places between the decimal point in the coefficient and in the new number: 1230

  2. Write 4.76 x 10-2 as a decimal system number.

    First, 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)

    Second, decide how many places the decimal point will move based on the size of the exponent: 2 places

    Finally write the number using zeroes to fill in the places between the decimal point in the coefficient and in the new number : 0.0467

  3. Write 5.22 x 101 as a decimal system number.

    First, 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)

    Second, decide how many places the decimal point will move based on the size of the exponent: 1 place

    Finally write the number using zeroes to fill in the places between the decimal point in the coefficient and in the new number if necessary: 52.2


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