## anonymous one year ago Will give medal, Help with Scientific notation,

1. anonymous

2. anonymous

@kiamousekia

3. anonymous

@imqwerty

4. anonymous

idk

5. anonymous

ok, do you know anyone who would?

6. anonymous

@Falling_In_Katt

7. anonymous

you still on that first question?

8. anonymous

yep

9. Jhannybean

It is simply $(4.5 \cdot 6)(10^{-8-4})$

10. anonymous

I seriously dont get it, how do I get the answer?

11. mathstudent55

@sadie112 A number written in scientific notation consists of a number from 1 to less than 10 (called the mantissa) multiplied by a power of 10. To multiply two numbers written in scientific notation, multiply the mantissas together, and multiply the powers of 10 together. If the product of the mantissas is a number from 1 to less than 10, then you are done because your product is also in scientific notation. If the product of the mantissas is greater than 10, then you need to adjust the number to make it a number in scientific notation.

12. mathstudent55

Example: Multiply the two numbers below: $$(2 \times 10^4) \times (3 \times 10^6)$$ Solution: $$=2 \times 3 \times 10^4 \times 10^6$$ $$= 6 \times 10^{4 + 6}$$ $$= 6 \times 10^{10}$$ Since 6 is from 1 to less than 10, the product is in scientific notation, and we're done. Do you understand it so far?

13. mathstudent55

Here is a second example that is similar to your problem. Multiply $$(5 \times 10^4) \times (6 \times 10^3)$$ Solution: $$=5 \times 6 \times 10^4 \times 10^3$$ $$= 30 \times 10^7$$ We have the product of the two numbers but, because 30 is not less than 10, this product is not in scientific notation, so we need to adjust it. $$= 3 \times 10 \times 10^7$$ $$= 3 \times 10^8$$ Now we have the correct answer in scientific notation.