My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
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.
decimate is offline  
 
May 17th, 2015, 11:12 AM   #2
Senior Member
 
aurel5's Avatar
 
Joined: Apr 2014
From: Europa

Posts: 575
Thanks: 176

$\displaystyle \color{blue}3.3\cdot10^{-2}\cdot4\cdot10^{-2}=(3.3\cdot4)\cdot(10^{-2}\cdot10^{-2})=13.2\cdot10^{-4}=13.2\cdot10^{-1}\cdot10^{-3}=1.32\cdot10^{-3}$
aurel5 is offline  
May 17th, 2015, 11:27 AM   #3
Member
 
Joined: Mar 2015
From: earth

Posts: 52
Thanks: 0

Quote:
Originally Posted by aurel5 View Post
$\displaystyle \color{blue}3.3\cdot10^{-2}\cdot4\cdot10^{-2}=(3.3\cdot4)\cdot(10^{-2}\cdot10^{-2})=13.2\cdot10^{-4}=13.2\cdot10^{-1}\cdot10^{-3}=1.32\cdot10^{-3}$
I can't comprehend the thing greater than 10 something?
decimate is offline  
May 17th, 2015, 12:30 PM   #4
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,590
Thanks: 953

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
Denis is offline  
May 18th, 2015, 05:04 AM   #5
Member
 
Joined: Mar 2015
From: earth

Posts: 52
Thanks: 0

Quote:
Originally Posted by Denis View Post
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
I can't still understand I think I have dyscalculia.
decimate is offline  
May 18th, 2015, 05:16 AM   #6
Senior Member
 
Joined: Jul 2014
From: भारत

Posts: 1,178
Thanks: 230

Quote:
Originally Posted by decimate View Post
I can't still understand I think I have dyscalculia.
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.

$\displaystyle x^{-m}=\frac{1}{x^{m}} \\
\text{Example: }3^{-3}=\frac{1}{3^{3}}=\frac{1}{9}$
Prakhar is offline  
May 18th, 2015, 06:51 AM   #7
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 1,914
Thanks: 774

Math Focus: Wibbly wobbly timey-wimey 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
topsquark is offline  
May 19th, 2015, 02:28 AM   #8
Senior Member
 
Joined: Apr 2014
From: Glasgow

Posts: 2,132
Thanks: 717

Math Focus: Physics, mathematical modelling, numerical and computational solutions
Decimate, let's take a look at each part of Aurel's working step-by-step

Quote:
Originally Posted by aurel5 View Post
$\displaystyle \color{blue}3.3\cdot10^{-2}\cdot4\cdot10^{-2}=(3.3\cdot4)\cdot(10^{-2}\cdot10^{-2})=13.2\cdot10^{-4}$
Firstly, some people use a $\displaystyle \cdot$ symbol to mean "multiply". It's actually really common practise when you do higher level mathematics. Just to avoid confusion, I'm going to use the multiplication symbol $\displaystyle \times$ instead.

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:
Originally Posted by aurel5 View Post
$\displaystyle 13.2\cdot10^{-4}=13.2\cdot10^{-1}\cdot10^{-3}=1.32\cdot10^{-3}$
Aurel has converted the number to standard form. He did this by factorising out a factor of 0.1 (the same as $\displaystyle 10^{-1}$) from the $\displaystyle 10^{-4}$ and then multiply this by 13.2 to get 1.32, which now follows the rule for standard form.

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).
Benit13 is offline  
May 19th, 2015, 02:33 AM   #9
Member
 
Joined: Mar 2015
From: earth

Posts: 52
Thanks: 0

Quote:
Originally Posted by topsquark View Post
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


Not yet
decimate is offline  
May 19th, 2015, 06:11 AM   #10
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 13,590
Thanks: 953

See if you can follow this:
Code:
x-axis <........-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
Take the "-3" column: can you kinda see why 10^-3 = 1/10^3 ?
Denis is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
confused, dividing, multiplying, notations, scientific



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Notations for tetration mathbalarka New Users 10 May 15th, 2013 09:22 AM
Set notations sallyyy Algebra 4 June 30th, 2011 06:34 PM
Multiplying/dividing both sides of the equation.. badrush Algebra 3 January 31st, 2010 04:51 PM
Big Oh Notations Help gear2d Applied Math 5 September 21st, 2008 08:06 AM
Sigma Notations johnny Algebra 1 August 18th, 2007 03:37 AM





Copyright © 2018 My Math Forum. All rights reserved.