Converting Decimals to Percentages and Vice Versa Video Lecture | Mathematics (Maths) Class 7 (Old NCERT)

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now let us see how do we convert decimal
numbers into percentage so by now you
all know what a decimal numbers right so
these numbers they have a fractional
part and they also have an integer part
and these two parts are separated by the
decimal point so what we do is first of
all we write the decimal numbers in the
form of fractions so let us take any so
let us consider for point five this is a
decimal number this is the integer part
and this is the fractional part so what
we do we write it in the form of
fractions how do we write 45 divided by
10 so we have learnt all of these in our
previous lessons right so point after
decimal how many digits you have that
many zeros you will put in the
denominator so here it is just one digit
after decimal point so just one zero so
45 by 10 so now you have a fraction so
how do you convert a fraction into
percentage you multiply the numerator
and the denominator by 100 so consider
this entire part together so what
happens so you obtain a number which is
divided by 100 so 4500 by 10 divided by
hundred so this divided by hundred can
be written as percentage so this is
equal to 450 percent so basically here
what we are doing is we first convert
the decimal number into fraction and
then we convert the fraction into
percentages the in a similar way we did
earlier so let us look at another
example let us say 0.2 0.2 first we
write it as fraction so 2/10 but here
again we multiply the
and denominator by hundred so this
becomes 2 in 200 divided by 10 percent
so it's 10 into 10 is 100 so this is
equal to 20 percent let's look at
example 3 its 0.05 so this is equal to 5
divided by after decimal point you have
two digits so here you will have two
zeros in the denominator so here also
you will multiply the numerator and
denominator by 100 so you get five in
two hundred divided by hundred percent
so this hundred and one hundred will
cancel out so this is five percent you
see why am I giving so many examples is
for more examples you see the better the
understanding is so for two point one
this can be written as 21 by ten so here
also numerator and denominator
multiplied by 100 so you get back 100 by
n percent so this is equal to two
hundred and ten percent so now here the
interesting observation that we find is
for decimals which are less than one
which are the decimals which are less
than one this is a decimal less than one
this is a decimal which is less than one
so for decimals which are less than one
the percentages are less than 100 you
see here 20 percent 5 percent whereas
for decimals which are greater than one
the percentages are more than 100
percent right like 4.5 it is 44 50
percent 2.1 it is 210 percent so
basically what we conclude is that for
decimals less than one percentage is
less than 100 percent for decimals
greater than one the percentage is
greater than 100 percent
so this is our observation
so now again the vice versa that how do
we convert percentage into decimals so
that's going to be pretty simple so
let's take an example let's say
12-person so how do you convert it into
decimal 12% is nothing but 12 out of 100
so you reduce it to the simplest
possible fraction that is 3 by 25 so
this is in the fractional form now you
convert this fraction into decimal so
this is how we converted right so this
is fine so here you have a decimal point
so you put a 0 to 25 to use a 15 and
therefore 3 by 25 is equal to 0.12 so
you could convert 12 percent into a
decimal number 0.12 similarly if let's
take another example let's say 150
percentage so this is greater than 100
percent that means the decimal number
must be greater than 1 so 150 % is
nothing but 150 by 100 so 5/3 is a 15 5
to 10 10 3 to 30 10 to the 20 so 3 by 2
so when you can go to do to decimal form
this is what you get so 2 5 is a 10
therefore 3 by 2 is equal to 1.5 so you
see 1.5 is greater than 1 and that is
why the percentage is greater than 100
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