Scientific Notation - Dividing

[Acewing]

I'm currently going through exponents, and came across a sort of "wall" so-to-speak. Multiplying is straight-forward, but the example used for expressing and simplifying a problem that uses division has me scratching my head; wondering how they reach each step:

(1.247 × 10^–3) ÷ (2.9 × 10^–2) <-- Simplify and Express in Scientific Notation.

It works through the problem step by step, but I just don't comprehend what it's doing at each stage:

Step 1 -

(1.247 ÷ 2.9)(10^-3 ÷ 10^-2)

^ How in the world did it get to that as step 1? I understand the rearranging, well, no, I don't understand. They're in parenthesis, can you even rearrange it like that, then put the parenthesis back in place? Next, does it matter whether it's (10^-3 ÷ 10^-2) or (10^-2 ÷ 10^-3)?

Step 2 -

(1.247 ÷ 2.9) (10^–3 × 10²)

^ What exactly happened to the division sign? Why is the 10^-2 suddenly positive?

The rest of the example clicks for me, but those initial two steps are raising blanks. I'm most likely (again) missing some basic groundwork, just not sure which concepts they are that are required to give me a better comprehension of what is happening in front of me.

 

[Quaid]

Hello acewing:

Some topics involved here are

• Commutative Property of Multiplication
• Order of Operations
• Simplifying Ratios
• Properties of Exponents

You can relearn these topics, by googling for free online lessons, followed by practice until the concepts become second-nature. (For example sites, try purplemath.com or khanacademy.com)

Cheers :cool:

 

[Acewing]

Glad to see you haven't given up, Ace...

(a*b) / (c*d) = (a/c) * (b/d) = (a/d) * (b/c) ... a bit like 3 * 5 = 5 * 3
Try it by assigning values, like a=100, b=8, c=4, d=2


On negative exponents:
Rule: a^(-p) = 1 / a^p or 1 / a^(-p) = a^p

a^(-p) / b^(-q) = b^q / a^p

Rules, ah, I see now. Right, I believe I now see what was rather rudimentary if you think about the basics. I shall elaborate when answering Quaid's post!

Hello acewing:

Some topics involved here are

• Commutative Property of Multiplication
• Order of Operations
• Simplifying Ratios
• Properties of Exponents

You can relearn these topics, by googling for free online lessons, followed by practice until the concepts become second-nature. (For example sites, try purplemath.com or khanacademy.com)

Cheers :cool:

Zero Exponent Property​	a0 = 1, (a ≠ 0)​
Negative Exponent Property​
Product of Powers Property​
Quotient of Powers Property​	​
Power of a Product Property​	​
Power of a Quotient Property​
Power of a Power Property​	(ab)c = abc​
Rational Exponent Property​	​

^ Found this after you mentioned those concepts, and I recall PurpleMath mentioning something "similar", but not as obvious as another site, which gave me that chart to go by. ALL of it I recognize, but because of the 3 year math hiatus, I "derped", when the steps were plain as day to follow. I was able to go through the notation again, and ultimately came to the same solution as the example did!

_____________________________________________________________________________

Thanks again for the help; Denis and Quaid. I feel rather silly for not recalling the basic formula's. The other three topics, besides Properties of Exponents, I have already gone through, but the 4th bullet point is what I was missing. Everything now fits into place snugly! Thanks you two very much for bearing with me on my voyage to math competency!

I'll be finishing up Exponent/Roots today, and start on Factoring. This scientific notation problem/concept was bothering me all night, but it looks like I just missed what was in plain sight!

 

[Acewing]

I will actually be in the care of Khan Academy for a while. After reading through Quaid's reply, I realized that I missed some very crucial properties in how to deal with exponents.

I was able to find a very helpful table, when re-researching the property of exponents. The equation became painfully obvious in terms of what was being done after I reviewed the laws of exponent/radicals again, and it was equally obvious that I need to review a lot of the most fundamental basis of Math before I continue my review.

So, I thank you two again for helping me along, and I will be building up my math basics starting from...4th grade+ (Wish me luck!).

 

[Acewing]

You're too modest: 5th will do

Conditional Statements are a QUACK. But I feel like I should start at 4th, to at least get a quick "up-to-speed" review.