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Convert Terminating Decimal into Rational number - Number Systems Video Lecture - Class 9
FAQs on Convert Terminating Decimal into Rational number - Number Systems Video Lecture - Class 9
| 1. How can I convert a terminating decimal into a rational number? |  |
Ans. To convert a terminating decimal into a rational number, we need to express it as a fraction of two integers. To do this, we can follow these steps:
1. Identify the decimal as a terminating decimal, meaning it has a finite number of digits after the decimal point.
2. Count the number of digits after the decimal point.
3. Write the decimal without the decimal point as the numerator of the fraction.
4. Write the denominator as a power of 10, where the power is equal to the number of digits after the decimal point.
5. Simplify the fraction, if possible, by dividing both the numerator and denominator by their greatest common divisor.
| 2. Can all terminating decimals be converted into rational numbers? | |
Ans. Yes, all terminating decimals can be converted into rational numbers. This is because terminating decimals are finite and can be expressed as fractions of two integers. By following the steps mentioned in the previous answer, any terminating decimal can be represented as a rational number.
| 3. Can a non-terminating decimal be converted into a rational number? | |
Ans. No, a non-terminating decimal cannot be converted into a rational number. Non-terminating decimals are infinite and do not have a finite number of digits after the decimal point. Rational numbers, on the other hand, can be expressed as fractions with a finite number of digits. Therefore, it is not possible to convert a non-terminating decimal into a rational number.
| 4. Are all rational numbers in decimal form terminating decimals? | |
Ans. No, not all rational numbers in decimal form are terminating decimals. Rational numbers can be expressed as fractions, and when these fractions are converted into decimal form, they can be either terminating or non-terminating. For example, the rational number 1/2 can be expressed as the terminating decimal 0.5, while the rational number 1/3 is a non-terminating decimal (0.333...).
| 5. Is every rational number equivalent to a terminating decimal? | |
Ans. No, not every rational number is equivalent to a terminating decimal. While some rational numbers can be expressed as terminating decimals, others can only be represented as non-terminating decimals. For example, the rational number 2/5 can be expressed as the terminating decimal 0.4, but the rational number 1/7 is a non-terminating decimal (0.142857...).
Text Transcript from Video
welcome friends in this video we shall
learn the topic how to convert a
terminating decimal into a rational
number of the form P over Q and we shall
learn this topic by an example an
example is as follows Express each of
the following in P by Q form and this
example has three parts part 1 Cross 2nd
and 3rd and we shall start converting
this decimal number into a P by Q form
big part 1 of this example and part 1 is
0.15 and to convert this decimal number
into a P by Q form first of all we shall
write this decimal number in numerator
and 1 here in denominator now we shall
put as many zeros on the right side of
this one as number of digits in decimal
part of this number so we can count the
digits in decimal part you can count of
1 and 2 so we shall write 2 zeros with
this one as we move this decimal part so
it will be 15 over 100 and here we can
write this 50 like this 3 into 5 and 120
into 5 5 can be cancelled by 5 we get 3
over 20 and he here is 0.15 so this is
the P by Q form of the number 0.15 now
we shall move to the second part and
second part is zero point zero zero two
seven and we shall write this decimal
number here in numerator and one here in
denominator now we shall write as many
zeros as the digits here are in the
decimal part of the number and you can
found
these are four one two three four so we
shall bright whose eros with this one
finally we get and now we shall remove
the decimal point and we get a number 27
over 10,000 so this is P by Q form of
this number now we shall move to the
third part and third part is seventy
point one six and we shall convert this
number into P by Q form then first we
shall write this 70 point one six year
in numerator and one here in denominator
now we shall put as many zeros in the
right side of this one as the number of
digits in decimal part of this number
then you can tell them one and two so
there are two digits in decimal part of
this number so we shall write 2 zeros
here and they both this decimal so the
number will be seven thousand and
sixteen and here in denominator is
hundred now we can cancel out this
hundred by two to get 50 and this seven
thousand sixteen hundred by two to get
3,500 and it we can also cancel out this
50 by two to get 25 and this 3518 eight
by 2 to get 1754 finally the number is
1754 over 25 so this is P by Q form of
this decimal number so this is all about
how we can convert terminating decimal
expansion into P by Q form
thank you
learn the topic how to convert a
terminating decimal into a rational
number of the form P over Q and we shall
learn this topic by an example an
example is as follows Express each of
the following in P by Q form and this
example has three parts part 1 Cross 2nd
and 3rd and we shall start converting
this decimal number into a P by Q form
big part 1 of this example and part 1 is
0.15 and to convert this decimal number
into a P by Q form first of all we shall
write this decimal number in numerator
and 1 here in denominator now we shall
put as many zeros on the right side of
this one as number of digits in decimal
part of this number so we can count the
digits in decimal part you can count of
1 and 2 so we shall write 2 zeros with
this one as we move this decimal part so
it will be 15 over 100 and here we can
write this 50 like this 3 into 5 and 120
into 5 5 can be cancelled by 5 we get 3
over 20 and he here is 0.15 so this is
the P by Q form of the number 0.15 now
we shall move to the second part and
second part is zero point zero zero two
seven and we shall write this decimal
number here in numerator and one here in
denominator now we shall write as many
zeros as the digits here are in the
decimal part of the number and you can
found
these are four one two three four so we
shall bright whose eros with this one
finally we get and now we shall remove
the decimal point and we get a number 27
over 10,000 so this is P by Q form of
this number now we shall move to the
third part and third part is seventy
point one six and we shall convert this
number into P by Q form then first we
shall write this 70 point one six year
in numerator and one here in denominator
now we shall put as many zeros in the
right side of this one as the number of
digits in decimal part of this number
then you can tell them one and two so
there are two digits in decimal part of
this number so we shall write 2 zeros
here and they both this decimal so the
number will be seven thousand and
sixteen and here in denominator is
hundred now we can cancel out this
hundred by two to get 50 and this seven
thousand sixteen hundred by two to get
3,500 and it we can also cancel out this
50 by two to get 25 and this 3518 eight
by 2 to get 1754 finally the number is
1754 over 25 so this is P by Q form of
this decimal number so this is all about
how we can convert terminating decimal
expansion into P by Q form
thank you
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Nov 15, 2024 Last updated |
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