How to Calculate Orders of Magnitude in Exponents

Scientific notation is a strategy for writing numbers that are too large or too small to conveniently write in the normal notation. For example, the number 123,000,000,000 converts to 1.23 x 10^11 in scientific notation. The first number of a scientific notation must be between 1 and 10. This number is referred to as the coefficient. The second number, referred to as the base, must always be 10. The base is then raised to a positive or negative exponent. In 1.23 x 10^11, 1.23 is the coefficient and 11 is the exponent.

Instructions

Converting a Number to Scientific Notation

1. Place a decimal after the first digit of your number. For example, if your number is 50,000, put the decimal after 5 and write the number as 5.0000. The coefficient is 5.00.

2. Count the number of digits from the decimal to the end. In 5.0000, there are four digits. The exponent is 4.

3. Write the number in scientific notation: coefficient x 10^exponent. In our example, 50,000 translates to 5.00 x 10^4.

Converting Scientific Notation to a Number

1. Determine whether you have a positive or negative exponent. For example, 10^-3 is a negative exponent.

2. Move the decimal the number of places equal to the value of the exponent, adding zeros if necessary. If the exponent is positive, move the decimal place right. A negative exponent shifts the decimal place to the left.

3. Move the decimal place three steps to the left if you have 7.8 x 10^-3, forming .0078.

References

• New York University
• Texas A&M