Question

Find the values of
i. $7.9\div 1000$
ii. $26.3\div 1000$
iii. $38.53\div 1000$
iv. $128.9\div 1000$
v. $0.5\div 1000$

Answer 1

Hint: We solve this question by using the concept of division by 10 or multiples of 10 like 10, 100, 1000, 10000, etc. We need to use the concept that division by 10 shifts the decimal point by one place to the left. This means that the value is reduced to one-tenth of its original value. For 100, it moves by two places and 1000 it moves by three places. If there are not sufficient digits before the decimal point, we add zeroes.

Complete step-by-step solution:
In order to solve this question, let us consider the question part by part and divide by 1000. Dividing by 1000 means that we are making the value one-thousandth of its original value and this is done just by shifting its decimal point to the left by 3 places. This can also be remembered as moving the decimal point as many times as the number of zeroes. For 1000, there are three zeroes, therefore we move the point 3 times to the left.
i. Let us take the first part and solve now,
$\Rightarrow \dfrac{7.9}{1000}$
We need to move the decimal point by 3 units to the left but we do not have that many digits. In order to do so, we add 3 zeros in front of 7. By doing so, the value of the number does not change.
$\Rightarrow \dfrac{0007.9}{1000}$
Now we move the decimal point 3 times to the left and obtain,
$\Rightarrow 0.0079$
Similarly, let us solve the other parts.
ii. Let us take the second part and solve now,
$\Rightarrow \dfrac{26.3}{1000}$
We need to move the decimal point by 3 units to the left but we do not have that many digits. In order to do so, we add 2 zeros in front of 26. By doing so, the value of the number does not change.
$\Rightarrow \dfrac{0026.3}{1000}$
Now we move the decimal point 3 times to the left and obtain,
$\Rightarrow 0.0263$
iii. Let us now solve the third part in the same way,
$\Rightarrow \dfrac{38.53}{1000}$
We need to move the decimal point by 3 units to the left but we do not have that many digits. In order to do so, we add 2 zeros in front of 38. By doing so, the value of the number does not change.
$\Rightarrow \dfrac{0038.53}{1000}$
Now we move the decimal point 3 times to the left and obtain,
$\Rightarrow 0.03853$
iv. Let us now solve the fourth part in a similar way,
$\Rightarrow \dfrac{128.9}{1000}$
We need to move the decimal point by 3 units to the left but we shall add one more 0 in front so that when we move the decimal point, 0 remains in the whole number part. By doing so, the value of the number does not change.
$\Rightarrow \dfrac{0128.9}{1000}$
Now we move the decimal point 3 times to the left and obtain,
$\Rightarrow 0.1289$
v. Let us now solve the last part in a similar way,
$\Rightarrow \dfrac{0.5}{1000}$
We need to move the decimal point by 3 units to the left but we do not have that many digits. In order to do so, we add 3 zeros in front of it. By doing so, the value of the number does not change.
$\Rightarrow \dfrac{0000.5}{1000}$
Now we move the decimal point 3 times to the left and obtain,
$\Rightarrow 0.0005$
Hence, by dividing any number by 1000, we just need to move the decimal point three places to the left.

Note: We need to note that multiplication by 10 or a multiple of 10 moves the decimal point to the right as its value is increasing and when dividing by 10 or a multiple of 10, the decimal point moves to the left as its value decreases. The number of places to move to the left or right is equal to the number of zeroes in the multiple of 10.