How do you convert 4/25 into a decimal and percent?

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Tony B Share
Mar 22, 2018

Answer:

Quite a bit of teaching about principles. The calculation should only take a few lines once you are used to these.

Percentage#->16%#
Decimal #" "->0.16#

Explanation:

#color(blue)("Teaching about percentage")#

Percentage is basically a fraction. However it is a special fraction in that the bottom number is fixed at 100.

Using an example of thirty percent.
There are two ways that a percentage can and may be written.

For our example we have #30% and 30/100#. These mean EXACTLY the same thing. If that is the case then we have:

#30/100 = 30xx1/100#

#30% = 30xx%#

If they mean exactly the same thing then #%# is another way of writing #1/100#

When using the shortcut what do they mean by: "multiply by 100 and put a #%# on the end" ?

Basically they are multiplying by 1 but in the form of #100/100#

#"something"xx1 color(white)("dddddddd")->color(white)("dddd")"something"xx100/100 #

#"The multiply by 100 bit"color(white)("d")->color(white)("dddd")"something"xx100xx1/100#

#color(white)("dddddddddddddddddd.d")->color(white)("dddd")"something"xx100xx%#

#color(white)("dddddddddddddddddd.d")->color(white)("dddd")"something"xx100%#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the percent part of the question")#

#color(green)(4/25color(red)(xx1)color(white)("dddd")->color(white)("dddd")4/25color(red)(xx4/4)) #

#color(green)(color(white)("dddddddddd")->color(white)("dddd") (4xx4)/(25xx4)#

#color(green)(color(white)("dddddddddd")->color(white)("ddddd")16/100)#

But this is the same as #16xx1/100# and #1/100# is the same as %. So we have:

#color(white)("dddddddddddddddd")color(green)(4/25=16%)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The decimal part of the question")#

#color(brown)("The teaching bit")#

A decimal construct is such that we have:

units + tenths + hundredths + .....

Using an example: suppose we had the number 23.26

Units #->23 " "larr" Units is counting in 1's" #

Tenths #->2/10#

Hundredths#->6/100#

#23/1+2/10+6/100" "->" "23.26#
....................................................................................
#color(brown)("Back to our question")#

We have #16%->16/100#

So we have: #0/1+1/10+6/100" "->" "0.16#

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