Scientific Notation
Concept
Convert a number in standard form to scientific notation.
Rules
Rules of writing a number in scientific notation:
-If the number is greater than or equal to 1, the power of ten is positive.
-If the number is between 0 and 1, the power of ten is negative.
Steps to writing a number in scientific notation:
1. Determine, using rules above, if the exponent is going to be positive or negative.
2. If the exponent is going to be positive, move the decimal to the left until one number is to the left of the decimal.
3. If the exponent is going to be negative, move the decimal to the right until one non-zero number is to the left of the decimal.
4. Count the number of spaces moved, as it will be your new exponent.
Example
Write in scientific notation.
250,000
Solution
Scientific notation is where numbers are written as a product of a number between 1 and 10 times a power of 10. To make the number in this format, move the decimal point 5 places to the left. The original number is more than ten. Thus the power of 10 is 5
250,000 = 2.5 x 105
Practice Scientific Notation
Practice Problem 1
Write in scientific notation.
0.0000037
Practice Problem 2
Aaron runs 100 km every day. His friend Alison runs 5 × 10-1 km every day. Who runs less?
Practice Problem 3
Evaluate and give the answer in scientific notation.
1.2 × 10-6 ∙ 6.25 × 10-2
Practice Problem 4
Evaluate and give the answer in scientific notation.
Practice Problem 5
Robert has 3.5 × 10-2 kg of gummy bears. He eats 0.005 kg. How much gummy bears he had left?
Write the answer in scientific notation.
Scientific notation: When a number is written as the product of a factor and an integer power of 10. The factor must be greater than or equal to 1 and less than 10.
Standard notation is the normal way of writing numbers.
Pre-requisite Skills
Write Exponents
Powers and Exponents
Powers of Monomials
Negative Exponents