Examples: Expansions and Standard Form Video Lecture - Class 7

hello friends this video on exponents
and powers part 10 is brought to you by
exam fear calm no more fear from exam so
let us quickly look at some of the
questions question number 1
write in the expanded form 12700 19 so
let us quickly number 0 1 2 3 4 5 so we
will write it as 1 into 10 to the power
5 plus 2 into 10 to the power 4 plus 0
into 10 to the power 3 plus 7 into 10 to
the power 2 plus 1 into 10 to the power
1 plus 9 into 10 to the power 0 so this
is how we will expand it question number
2 find the number from each of the
following expanded forms
so here the expanded form is given and
you will have to find the number so
whenever you are given the expanded form
first you quickly write down the the
digits now this is not the place value
of the digits this basically shows the
exponent so 0 1 2 3 4 so 4 is the
maximum that you have here right so 4
for the digit is 8 that means here the
digit would be 8 4 3 the digit is 6 so
it would be 6 4 2 the digit is 0 so here
it would be 0 for 1 the digit is 4 & 4 0
the digit is fine therefore the number
would be 8 6 0 4 5 so in a similar way
let us do the second one so here you
have 3 into 10 to the power 4 so 4 is
the maximum so here also 0 1 2 3 4 so 4
X 4 and for the digit is 3 for exponent
3 what is the digit the digit is not at
all given that means the digit is 0
because 0 multiplied by anything will be
0 for 2 the digit is 7 for 1 again it is
not given that means it is 0 and for 0
it is 5 therefore the number would be 3
0 7 0 5 question number 3 express the
following numbers instead
so let's apply the tip here so let us
look at the first one it is 70 lakhs so
how many zeros we have one two three
four five six total six zeros right so
where is the decimal point the decimal
point is here right now so we will make
these jumps so if we reach here what
would be the number the number would be
seven which very clearly lies between 1
and x that's fine so how many jumps we
have taken one two three four five six
and what was the existing exponent X
this thing it's gonna do is 0 because 10
to the power 0 so now here with the
existing exponent you be like 6
therefore it would be 7 into 10 to the
power 6 let us look at the second one it
is 3 1 8 6 5 0 0 0 0 0 this is quite a
big number so here where is the decimal
point located it is here so let's make
jams so that we are able to reach the
extreme left side such that we can get a
number between 0 between 1 and 10 so if
we place the decimal point here what is
the number that you will get thirty one
point eight six five so 31.8 doesn't lie
between 1 and 10 so let us take one more
jump and place it here so what is the
number that we get three point one eight
six five and this lies between 1 and 10
so what would be the power of 10 so the
existing power per 0 so we will add how
much to it 1 2 3 4 5 6 7 8 9 9 job so
you need add 9 to it therefore the
standard form would be 3 point 1 8 6 5
into 10 to the power 9 question number 4
express the number appearing in the
following statements in standard form in
a galaxy there are on average these many
stars so how many stars are there so
let's first count the number
Zero's so even before that let's see how
many jumps do we need to make so this is
the decimal point one two three four
five six seven eight nine ten and eleven
so we have to make eleven jumps to reach
here therefore the standard form would
be 1 into 10 to the power 11 starts next
one the universe is estimated to be
about these many years old so here also
the decimal point was here so how many
jumps we need to make 1 2 3 4 5 6 7 8 9
so if we put the decimal point here the
number would be 12 but we need a number
between 1 and 10 so one more jump so
that makes it 1 point 2 so this would be
one point to multiply it by how many
jumps 1 2 3 4 5 6 7 8 9 10 so this would
be 10 to the power 10 the distance of
the Sun from the center of the Milky Way
galaxy is estimated to be look at the
length tall where this huge size of this
number so now you must be realizing the
importance of having this entire concept
of exponents so here we had the decimal
point here let's make jumps 1 2 3 4 5 6
7 8 9 10 11 12 13 14 15 16 17 18 19 and
20 so you actually need to place the
decimal point here so that the number is
3 so 3 into 10 to the power 20 meters
and the last one the population of India
was about this much in March 2001 so
here the decimal point needs to be
shifted by 1 2 3 4 5 6 7 8 9 so that
makes it 1 point 0 through 7
tend to the power none so you see using
the very simple tip we can actually
represent any large number in its
standard form so I hope that this lesson
on exponents and powers would give I
would have given you an insight on why
do we learn about exponents and also the
laws of exponents and how do we simplify
complicated expressions using the laws
of exponents so I hope this lesson would
have helped you see you all in the next
thank you please visit examview dot-com
for free quality education you can learn
with a simple four-step learning process
wherein you can watch video lessons you
can ask your questions you can refer
notes and you can take a free online
test we have content for class 6 to 12
on physics chemistry mathematics and
biology along with practical videos so
please subscribe to our channel for
daily updates thank you