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May 17th, 2015, 10:29 AM  #1 
Member Joined: Mar 2015 From: earth Posts: 52 Thanks: 0  Confused about dividing and multiplying scientific notations.
(3.3×10^−2)×(4.0×10^−2)= ? 1.32^3 why it's negative three? please explain Last edited by decimate; May 17th, 2015 at 10:38 AM. 
May 17th, 2015, 11:12 AM  #2 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  $\displaystyle \color{blue}3.3\cdot10^{2}\cdot4\cdot10^{2}=(3.3\cdot4)\cdot(10^{2}\cdot10^{2})=13.2\cdot10^{4}=13.2\cdot10^{1}\cdot10^{3}=1.32\cdot10^{3}$ 
May 17th, 2015, 11:27 AM  #3 
Member Joined: Mar 2015 From: earth Posts: 52 Thanks: 0  
May 17th, 2015, 12:30 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988 
RULE: x^(p) = 1 / x^p : TATTOO that on your wrist! 10^(2) = 1/10^2 = 1/100 3.3(1/100) * 4(1/100) = 13.2 / 10000 = .00132 
May 18th, 2015, 05:04 AM  #5 
Member Joined: Mar 2015 From: earth Posts: 52 Thanks: 0  
May 18th, 2015, 05:16 AM  #6 
Senior Member Joined: Jul 2014 From: भारत Posts: 1,178 Thanks: 230  It is just an exponential rule. If a number has a negative power, it is equivalent to its multiplicative inverse (reciprocal) with the same power in positive. $\displaystyle x^{m}=\frac{1}{x^{m}} \\ \text{Example: }3^{3}=\frac{1}{3^{3}}=\frac{1}{9}$ 
May 18th, 2015, 06:51 AM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,040 Thanks: 815 Math Focus: Wibbly wobbly timeywimey stuff. 
For those who are unaware of what discalculia is, see here. I have met a person with this problem, but it is extremely rare. Most people that claim to have it simply have a hard time with Math. Have you been diagnosed? Dan 
May 19th, 2015, 02:28 AM  #8  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,134 Thanks: 720 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
Decimate, let's take a look at each part of Aurel's working stepbystep Quote:
At this part, Aurel multiplied the two "first bits " together (called significands) to get 13.2 and then multiplied the "second parts together" (called powers of ten. The number on each 10 is called an exponent or a power.) to get $\displaystyle 10^{4}$ $\displaystyle 13.2 \times 10^{4}$ is basically the answer. However, it is not in standard form. For a number to be in standard form, its significand must be between 1 and 10, but not exactly equal to 10 (i.e. 9.999999999 is allowed, but not 10). At the moment the significant is 13.2, which is greater than 10. This is where we move the to the next part of Aurel's calculation. Quote:
When doing these, I like to think of it as like a "sliding scale"... if you reduce one thing by a factor of 10, then you must increase the other thing by a factor of 10 to balance it out and vice versa. For example, consider all of the numbers below. They are all the same: $\displaystyle 132 \times 10^{5}$ $\displaystyle 13.2 \times 10^{4}$ $\displaystyle 1.32 \times 10^{3}$ $\displaystyle 0.132 \times 10^{2}$ $\displaystyle 0.0132 \times 10^{1}$ $\displaystyle 0.00132 \times 10^{0} = 0.00132$ So by moving the decimal place by 1 digit to the left as we move down the list (which makes the significant smaller), the exponent increases by 1 (which makes the second part bigger).  
May 19th, 2015, 02:33 AM  #9  
Member Joined: Mar 2015 From: earth Posts: 52 Thanks: 0  Quote:
Not yet  
May 19th, 2015, 06:11 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,955 Thanks: 988 
See if you can follow this: Code: xaxis <........3...........2..........1.........0.........1..........2..........3.....> 10^n 10^3 10^2 10^1 10^0 10^1 10^2 10^3 result 1/1000 1/100 1/10 1 10 100 1000 same as 1/10^3 1/10^2 1/10^1 

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