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.
- write the coefficient: 1.5
- count the places between the current decimal place and its position in the coefficient: 2
- determine the sign of the exponent. Moving to the right gives a negative sign (the number is less than 0): –
- write the number in scientific notation: 1.5 x 10-2
- Write 256.35 in scientific (exponential) notation.
- write the coefficient : 2.5635
- count the places between the current decimal place and its position in the coefficient: 2
- determine the sign of the exponent. Moving to the left gives a positive sign (the number is greater than 10): +
- 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.
- write the coefficient : 4.276
- count the places between the current decimal place and its position in the coefficient: 1
- determine the sign of the exponent. Moving to the left gives a positive sign (the number is greater than 10): +
- write the number in scientific notation: 4.276 x 101
- Write the number 3.56 in scientific (exponential) notation.
- write the coefficient : 3.56
- 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 – worked examples
- Write 1.23 x 103 as a decimal system number.
- 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)
- decide how many places the decimal point will move based on the size of the exponent: 3 places
- 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.
- 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: 7 places
- Finally write the number using zeroes to fill in the places between the decimal point in the coefficient and in the new number : 0.000000467
- Write 5.22 x 100 as a decimal system number.
- decide which way the decimal point will move based on whether the exponent is positive (move to right) or negative (move to left) : none
- decide how many places the decimal point will move based on the size of the exponent: 0 places
- 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