Operations with Small Numbers in Scientific Notation
Operations with Small Numbers in Scientific Notation is a Grade 8 math skill in Saxon Math Course 3, Chapter 6, where students multiply and divide numbers expressed in scientific notation with negative exponents representing very small values. Students apply exponent rules to the powers of ten and simplify results, bridging number operations with algebra for science and engineering applications.
Key Concepts
New Concept To multiply or divide numbers in scientific notation, handle the coefficients first, then apply the Laws of Exponents to the powers of 10. $$10^{ 5} \cdot 10^{ 3} = 10^{ 8}$$ $$\frac{10^{ 5}}{10^{ 3}} = 10^{ 2}$$ What’s next Now that you know the rules, we'll dive into worked examples. You'll see how to solve them step by step, even when the answers need a little adjustment to be in proper form.
Common Questions
How do you multiply numbers in scientific notation?
Multiply the decimal coefficients together and add the exponents of the powers of ten. Then adjust the result so the coefficient is between 1 and 10 if necessary.
How do you divide numbers in scientific notation?
Divide the decimal coefficients and subtract the exponents of the powers of ten. Adjust the coefficient back into proper scientific notation form if needed.
What does a negative exponent mean in scientific notation?
A negative exponent indicates a very small number. For example, 3 x 10 to the power of negative 4 equals 0.0003.
How do you convert a small number to scientific notation?
Move the decimal point to the right until you have a number between 1 and 10, then multiply by 10 raised to the negative power equal to how many places you moved.
Where are operations with small numbers in scientific notation taught?
This skill is covered in Saxon Math Course 3, Chapter 6: Number and Operations and Data Analysis and Probability.