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decimals squared, cubed etc. & compound interest

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n2739178
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decimals squared, cubed etc. & compound interest [#permalink] New post   04 Jul 2010, 11:05
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Hi all,

Does anyone know of a shortcut for squaring, or cubing, a decimal greater than 1 such as 1.04, rather than manually multiplying 1.04 * 1.04. This would be specifically handy for quick Compound Interest calculations.

I tried doing something like (1.04) squared = 104*104 then put the decimal point back in 4 places but I'm wondering if there is another, faster way to do this. I tried doing 1squared + .04squared as (1.04)squared which when distributed out is 1squared + .04squared but it returned the wrong result (i.e. 1 + 0.0016 = 1.0016) instead of 1.0816 which is the correct answer of 1.04squared.

There may be no quicker way than actually doing the math but if there is, would love to know it!

thanks
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YourDreamTheater
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Re: decimals squared, cubed etc. & compound interest [#permalink] New post   04 Jul 2010, 16:37
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n2739178 wrote:
Hi all,

Does anyone know of a shortcut for squaring, or cubing, a decimal greater than 1 such as 1.04, rather than manually multiplying 1.04 * 1.04. This would be specifically handy for quick Compound Interest calculations.

I tried doing something like (1.04) squared = 104*104 then put the decimal point back in 4 places but I'm wondering if there is another, faster way to do this. I tried doing 1squared + .04squared as (1.04)squared which when distributed out is 1squared + .04squared but it returned the wrong result (i.e. 1 + 0.0016 = 1.0016) instead of 1.0816 which is the correct answer of 1.04squared.

There may be no quicker way than actually doing the math but if there is, would love to know it!

thanks


Ah! Finally! Something I'm actually good at!!! (pattern recognition) I have a psychological condition that lets me find patterns really quickly, but I have a hard time explaining them. Let me take a shot at this...

I'm doing this on the fly, so feel free to correct any wrong figures I come up with:


\(1.01 ^2 = 1 . (01*2) (01^2) = 1.0201\)
\(1.02^2 = 1 . (02*2) (02^2) = 1.0404\)
\(1.03^2 = 1 . (03*2) (03^2) = 1 . 06 09\)
\(1.04^2 = 1 . (04*2) (04^2) = 1 . 08 16\)

Things get a bit more interesting when you get into higher numbers...
If you get a three digit number as your square (like 10^2 = 100), then shift the ENTIRE number into the HUNDREDTHS place (2nd digit after decimal point). It's like you're shifting the entire three digit number ONE SPOT to the left, and adding any values that overlap.

\(1.10^2 = 1 . (10*2) (10^2) = 1 . 20 + 100\) (shift 100 one space left)\(= 1 . 2 (0+1) 00 = 1.2100\)
\(1.11^2 = 1 . (11*2) (11^2) = 1 . 22 + 121\) (shift 121 one space left)\(= 1 . 2 (2+1) 21 = 1.2321\)
\(1.12^2 = 1 . (12*2) (12^2) = 1 . 24 + 144\) (shift 144 one space left)\(= 1 . 2 (4+1) 44 = 1.2544\)


Does this make sense?
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decimals squared, cubed etc. & compound interest [#permalink] New post   23 Nov 2017, 11:52
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sanram2205 wrote:
Could you help me solve 1.50^2?
= 1.(50*2) 50^2
=1.35
:(

Can u tell me where I am going wrong here.


Super late, but I hope this helps someone.

Like you mention the first part you have is good [= 1.(50*2) 50^2], but you just need a little extra decimal movement to get the right answer.

If we multiply that part out, you'll get 1.(100)(2500). As YourDreamTheater mentioned above, when you have a three-digit number as the answer to the (x*2) or the (x^2) part, you need to move the whole number one decimal place LEFT before you add it. The same goes for a number with 4 digits (e.g., 2500), but it will have to move TWO digits to the left before you add it.

Thus, the answer to 1.5^2 will look more like this:

= 1.(50*2)(50^2)
= 1.(100)(2500)
= (added vertically showing how the numbers moved to the left)
1.00
1.00 (.100 moved left ONE decimal)
0.2500 (.002500 moved left TWO decimals)
---------
= 2.2500 = 2.25 = 1.5^2
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Re: decimals squared, cubed etc. & compound interest [#permalink] New post   05 Jul 2010, 00:48
Wow that's awesome -thanks! Definitely will be a time saver on compound interest problems!
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Re: decimals squared, cubed etc. & compound interest [#permalink] New post   05 Jul 2010, 12:17
No problem! Glad you were able to understand my ramblings.
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Re: decimals squared, cubed etc. & compound interest [#permalink] New post   05 Jul 2010, 13:06
Wow, really useful, thanks for the tip! :)
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Re: decimals squared, cubed etc. & compound interest [#permalink] New post   16 Jul 2010, 00:06
Could you help me solve 1.50^2?
= 1.(50*2) 50^2
=1.35
:(

Can u tell me where I am going wrong here.
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nazmulhasandu
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Re: decimals squared, cubed etc. & compound interest [#permalink] New post   14 Nov 2020, 12:10
vancypants wrote:
sanram2205 wrote:
Could you help me solve 1.50^2?
= 1.(50*2) 50^2
=1.35
:(

Can u tell me where I am going wrong here.


Super late, but I hope this helps someone.

Like you mention the first part you have is good [= 1.(50*2) 50^2], but you just need a little extra decimal movement to get the right answer.

If we multiply that part out, you'll get 1.(100)(2500). As YourDreamTheater mentioned above, when you have a three-digit number as the answer to the (x*2) or the (x^2) part, you need to move the whole number one decimal place LEFT before you add it. The same goes for a number with 4 digits (e.g., 2500), but it will have to move TWO digits to the left before you add it.

Thus, the answer to 1.5^2 will look more like this:

= 1.(50*2)(50^2)
= 1.(100)(2500)
= (added vertically showing how the numbers moved to the left)
1.00
1.00 (.100 moved left ONE decimal)
0.2500 (.002500 moved left TWO decimals)
---------
= 2.2500 = 2.25 = 1.5^2




Hi, It helps me. But could you please show how it works for 5.5
It does not give me correct result :(
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Re: decimals squared, cubed etc. & compound interest [#permalink]
14 Nov 2020, 12:10

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