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 10^{an 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

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}

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 10^{2}

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 10^{1}

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 10^{0}

Converting Scientific (exponential) Notation to a Decimal System Number

Write 1.23 x 10^{3} 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

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

Write 5.22 x 10^{1} 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