Analía Bellizzi – Chemistry Classes

Ronald Reagan Senior 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:

## Coefficientx 10Exponent

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