Multiplying in scientific notation (example) | Pre-Algebra | Khan Academy

TL;DR

Multiplying numbers in scientific notation involves multiplying the non-decimal parts, adding the exponents, and then converting the result to scientific notation.

Transcript

Multiply, expressing the product in scientific notation. So let's multiply first, and then let's try to get what we have in scientific notation. Actually, before we do that, let's just even remember what it means to be in scientific notation. To be in scientific notation-- and actually, each of these numbers right here are in scientific notation. I... Read More

Key Insights

• 😑 Scientific notation is a useful way to express very large or very small numbers.
• ✖️ Multiplying numbers in scientific notation involves multiplying the non-decimal parts and adding the exponents.
• ✊ The final answer should be in scientific notation, with a number between 1 and 10 multiplied by a power of 10.

Questions & Answers

Q: What is scientific notation?

Scientific notation is a way of representing numbers by expressing them as a product of a number between 1 and 10 and a power of 10.

Q: How do you multiply numbers in scientific notation?

To multiply numbers in scientific notation, multiply the non-decimal parts of the numbers, add the exponents, and then convert the result to scientific notation.

Q: What is the rule for adding exponents in multiplication?

In multiplication, when the bases are the same, you can add the exponents. In scientific notation, this allows us to add the exponents of 10.

Q: Can you provide an example of multiplying numbers in scientific notation?

Sure, let's say we want to multiply 9.1 x 10^6 and 3.2 x 10^-5. First, multiply the non-decimal parts (9.1 x 3.2 = 29.12). Then, add the exponents (6 + -5 = 1). Finally, convert the result to scientific notation (2.912 x 10^1).

Summary & Key Takeaways

• Scientific notation is a way of writing numbers in the form a times 10 to some power, where a is between 1 and 10.

• To multiply numbers in scientific notation, multiply the non-decimal parts, add the exponents, and then convert the result to scientific notation.

• The final answer should be in scientific notation, with a number between 1 and 10 multiplied by a power of 10.