EmSAT Achieve Exam > EmSAT Achieve Videos > Mathematics for EmSAT Achieve > Expanding Decimal Numbers
Expanding Decimal Numbers Video Lecture | Mathematics for EmSAT Achieve
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FAQs on Expanding Decimal Numbers Video Lecture - Mathematics for EmSAT Achieve
| 1. What are decimal numbers? |  |
Ans. Decimal numbers are a way of representing numbers that have a fractional part. They are based on the base-10 number system, which means they use the digits 0-9. Decimal numbers are commonly used in everyday life for measurements, money, and calculations.
| 2. How do you expand a decimal number? | |
Ans. To expand a decimal number, you need to write it as a sum of its place values. Each digit in a decimal number represents a specific place value, such as units, tenths, hundredths, and so on. By multiplying each digit by its corresponding place value, you can expand the decimal number.
| 3. Why is expanding decimal numbers useful? | |
Ans. Expanding decimal numbers can help us understand the value of each digit in a number and how they contribute to the overall value. It allows us to see the relationship between the digits and their significance in the decimal system. Additionally, expanding decimal numbers can help in performing calculations and solving mathematical problems.
| 4. Can you give an example of expanding a decimal number? | |
Ans. Sure! Let's expand the decimal number 3.75.
The digit 3 is in the units place, so its value is 3 x 1 = 3.
The digit 7 is in the tenths place, so its value is 7 x 0.1 = 0.7.
The digit 5 is in the hundredths place, so its value is 5 x 0.01 = 0.05.
Therefore, the expanded form of 3.75 is 3 + 0.7 + 0.05.
| 5. How can expanding decimal numbers help in comparing and ordering them? | |
Ans. When decimal numbers are expanded, it becomes easier to compare and order them. By looking at the place value of each digit, we can determine which number is greater or smaller. For example, if two decimal numbers have different digits in the units place, we can directly compare them. Similarly, we can compare the digits in the tenths, hundredths, and other places to determine their relative values. Expanding decimal numbers provides a clear understanding of their magnitudes, making comparison and ordering simpler.
Text Transcript from Video
he'll open this video on powers part 4
is brought to you by a fancier calm no
more fear from example now let's see
that how these negative exponents can
help us to the present smaller numbers
now before I do that let's have a quick
recap of expansion of large numbers so
we have learned that the exponents
decrease as we move towards the digits
on the right hand side so let us take
examples of some numbers so here we have
twelve thousand six hundred seventy
eight ages at the unities sessions at
the tens place six advances please - two
at the thousands please and one at the
10,000 split right so this can be
written as 1 into 10 to the power 4 plus
2 into 10 to the power 3 plus 6 into 10
to the power 2 plus 7 into 10 to the
power 1 plus 8 into 10 to the power 0 so
what do we see as we move towards the
digits on the right hand side the value
of the exponent
gradually degrees similarly if you take
another example solutions are yet bigger
numbers so in this case how can you
write this so you see this is unit ten
hundred thousand ten thousand then you
have last ten last and so on so in this
case you can write it as 9 into 10 to
the power 7 plus 2 into 10 to the power
6 plus 5 into 10 to the power 5 plus 3
into 10 to the power 4 plus you have all
zeros after it
so here also you see the same thing as
you move towards right the value of the
exponent gradually decreases now let's
see what happens with smaller numbers or
with decimal numbers because when you
talk about very small numbers or you are
talk about decimal numbers there's the
make use of the negative exponent so
here also the concept remains the same
so let's take an example so here you
have 1025
point six three so in this case the
digit the decimal part of the digit that
is point six three six three is the
fractional part or the decimal part and
this is the whole number part one zero
two five is the whole number part so we
will deal with the whole number but as
usual like how however we have get it
for five so this would be 1 into 10 to
the power 3 because 5 is at the unit's
place 2 is at the tens place 0 is at 100
place and one is at a thousand space so
this would be 1 into 10 to the power 3
plus 0 into 10 to the power 2 plus 2
into 10 to the power 1 plus 5 into 10 to
the power 0 so this is how we have dealt
with a whole number part now what about
the decimal part so in the decimal
partner and we are further moving
towards the right hand side to the value
of the exponent will further reduce so
this becomes 6 into 10 to the power
minus 1 so after 0 you have minus 1 then
you have 3 into 10 to the power minus 2
so gradually as you keep rooting on the
right side what happens is after the
decimal point the fractional part
tabular for that you will use off the
decimal often beautiful exponents so
this is where negative exponents are
beautiful now if you want you can verify
that this value comes out to be the same
but example this would be 1000 plus
hundred plus 20 plus 5 so this will give
you 1025 and what about this but 6 into
10 to the power minus 1 this is
basically 6 into 1 by 10 and this is
basically P into 1 by 10 into 10 30
countries so this gives you point 6 and
this gives you point 0 3 so when you add
1 0 to 5 plus 5
six plus point zero 3 you get 1 0 since
5 point 6 3 right with that also we have
proved that yes this is how we should
expand the decimal numbers like type
number decimal number is one two five
six point two four times so this is unit
10 hundreds and thousands so this can be
expanded as 1 into 10 to the power 3
plus 2 into 10 to the power 2 plus 5
into 10 to the power 1 plus 6 into 10 to
the power 0 plus 2 into 10 to the power
minus 1 plus 4 into 10 to the power
minus 2 plus 9 into 10 to the power
minus 3 30 medical exponents represent a
fractional part and a positive exponent
represent the whole number 5 thank you
please visit example.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
is brought to you by a fancier calm no
more fear from example now let's see
that how these negative exponents can
help us to the present smaller numbers
now before I do that let's have a quick
recap of expansion of large numbers so
we have learned that the exponents
decrease as we move towards the digits
on the right hand side so let us take
examples of some numbers so here we have
twelve thousand six hundred seventy
eight ages at the unities sessions at
the tens place six advances please - two
at the thousands please and one at the
10,000 split right so this can be
written as 1 into 10 to the power 4 plus
2 into 10 to the power 3 plus 6 into 10
to the power 2 plus 7 into 10 to the
power 1 plus 8 into 10 to the power 0 so
what do we see as we move towards the
digits on the right hand side the value
of the exponent
gradually degrees similarly if you take
another example solutions are yet bigger
numbers so in this case how can you
write this so you see this is unit ten
hundred thousand ten thousand then you
have last ten last and so on so in this
case you can write it as 9 into 10 to
the power 7 plus 2 into 10 to the power
6 plus 5 into 10 to the power 5 plus 3
into 10 to the power 4 plus you have all
zeros after it
so here also you see the same thing as
you move towards right the value of the
exponent gradually decreases now let's
see what happens with smaller numbers or
with decimal numbers because when you
talk about very small numbers or you are
talk about decimal numbers there's the
make use of the negative exponent so
here also the concept remains the same
so let's take an example so here you
have 1025
point six three so in this case the
digit the decimal part of the digit that
is point six three six three is the
fractional part or the decimal part and
this is the whole number part one zero
two five is the whole number part so we
will deal with the whole number but as
usual like how however we have get it
for five so this would be 1 into 10 to
the power 3 because 5 is at the unit's
place 2 is at the tens place 0 is at 100
place and one is at a thousand space so
this would be 1 into 10 to the power 3
plus 0 into 10 to the power 2 plus 2
into 10 to the power 1 plus 5 into 10 to
the power 0 so this is how we have dealt
with a whole number part now what about
the decimal part so in the decimal
partner and we are further moving
towards the right hand side to the value
of the exponent will further reduce so
this becomes 6 into 10 to the power
minus 1 so after 0 you have minus 1 then
you have 3 into 10 to the power minus 2
so gradually as you keep rooting on the
right side what happens is after the
decimal point the fractional part
tabular for that you will use off the
decimal often beautiful exponents so
this is where negative exponents are
beautiful now if you want you can verify
that this value comes out to be the same
but example this would be 1000 plus
hundred plus 20 plus 5 so this will give
you 1025 and what about this but 6 into
10 to the power minus 1 this is
basically 6 into 1 by 10 and this is
basically P into 1 by 10 into 10 30
countries so this gives you point 6 and
this gives you point 0 3 so when you add
1 0 to 5 plus 5
six plus point zero 3 you get 1 0 since
5 point 6 3 right with that also we have
proved that yes this is how we should
expand the decimal numbers like type
number decimal number is one two five
six point two four times so this is unit
10 hundreds and thousands so this can be
expanded as 1 into 10 to the power 3
plus 2 into 10 to the power 2 plus 5
into 10 to the power 1 plus 6 into 10 to
the power 0 plus 2 into 10 to the power
minus 1 plus 4 into 10 to the power
minus 2 plus 9 into 10 to the power
minus 3 30 medical exponents represent a
fractional part and a positive exponent
represent the whole number 5 thank you
please visit example.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
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Dec 24, 2024 Last updated |
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