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 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)

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 10²
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
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

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
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 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