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Find the value of $0.4\div 2.$
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Hint: Transform 0.4 into fraction by multiplying and dividing by 10. Then divide the result by 2, or you can even multiply by $\dfrac{1}{2}$. This is a very easy and simple question to solve.
We have to find the value of,
$0.4\div 2$
We can write the above equation as,
$\dfrac{0.4}{2}...........(1)$
Now, consider the numerator part, that is, 0.4.
First we will convert it into fractions.
To make it into a fraction, let us divide and multiply the numerator of the given expression by 10, so we get
$0.4=\left( \dfrac{0.4\times 10}{10} \right)............\left( 2 \right)$
What is $0.4\times 10$ now?
Remember, multiplying by 10 just shifts decimal place to right.
$\therefore 0.4\times 10=4.0...........\left( 3 \right)$
Now substituting value from equation (3) into equation (2), we get
$0.4=\dfrac{4}{10}$
This is the fraction form of 0.4.
Now, consider the expression (1), an substituting the fraction form of 0.4 in it,, we get
$\dfrac{0.4}{2}=\dfrac{\dfrac{4}{10}}{2}$
We know that dividing by any number is nothing but multiplying by its inverse, so the above expression can be written as,
$\dfrac{0.4}{2}=\dfrac{4}{10}\times \dfrac{1}{2}$
Now we know, $4=2\times 2$, so the above expression can be written as,
$\dfrac{0.4}{2}=\dfrac{2\times 2}{10\times 2}$
Cancelling the like terms, we get
$\dfrac{0.4}{2}=\dfrac{2}{10}$
Now we know dividing any number by 10, then the decimal shift one point to the left, so the above expression can be written as,
$\dfrac{0.4}{2}=0.2$
Hence this is the required answer.
Note: Another method is to count the decimal places, for 0.4 that is one. Ignore decimal and divide 4 by 2, we get 2. Now, apply the one decimal place we get 0.2
We have to find the value of,
$0.4\div 2$
We can write the above equation as,
$\dfrac{0.4}{2}...........(1)$
Now, consider the numerator part, that is, 0.4.
First we will convert it into fractions.
To make it into a fraction, let us divide and multiply the numerator of the given expression by 10, so we get
$0.4=\left( \dfrac{0.4\times 10}{10} \right)............\left( 2 \right)$
What is $0.4\times 10$ now?
Remember, multiplying by 10 just shifts decimal place to right.
$\therefore 0.4\times 10=4.0...........\left( 3 \right)$
Now substituting value from equation (3) into equation (2), we get
$0.4=\dfrac{4}{10}$
This is the fraction form of 0.4.
Now, consider the expression (1), an substituting the fraction form of 0.4 in it,, we get
$\dfrac{0.4}{2}=\dfrac{\dfrac{4}{10}}{2}$
We know that dividing by any number is nothing but multiplying by its inverse, so the above expression can be written as,
$\dfrac{0.4}{2}=\dfrac{4}{10}\times \dfrac{1}{2}$
Now we know, $4=2\times 2$, so the above expression can be written as,
$\dfrac{0.4}{2}=\dfrac{2\times 2}{10\times 2}$
Cancelling the like terms, we get
$\dfrac{0.4}{2}=\dfrac{2}{10}$
Now we know dividing any number by 10, then the decimal shift one point to the left, so the above expression can be written as,
$\dfrac{0.4}{2}=0.2$
Hence this is the required answer.
Note: Another method is to count the decimal places, for 0.4 that is one. Ignore decimal and divide 4 by 2, we get 2. Now, apply the one decimal place we get 0.2
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