Question

Find \[7.8 = 7 + \dfrac{8}{?}\]
A. 1
B.8
C.10
D.100

Answer 1

Hint: Here in the given question can be solved by using decimal shifting on the left hand side. On the right hand side, by choosing the appropriate denominator the fraction can be converted to decimal number and then it is added to 7. Then we can compare both the left hand side and right hand side.

Complete step by step solution:
For solving the given question, we need to know about the decimal point shifting. When we move the decimal place to the left side then the exponent will be a positive number and when we move the decimal place to the right side then the exponent will be a negative number.
Now we will first consider the left hand side that is 7.8, now using the decimal place shifting we will shift the decimal to the right side the we get
\[ \Rightarrow \]\[78 \times {10^{ - 1}}\] --------(1)
We can express the exponent as follows
\[ \Rightarrow \]\[{10^{ - 1}} = \dfrac{1}{{10}}\] ---------(2)
 now rewriting equation (1) we have
\[ \Rightarrow \] \[\dfrac{{78}}{{10}}\] ---------(3)
Considering the right hand side we have
\[ \Rightarrow \]\[7 + \dfrac{8}{?}\] ---------(4)
 Here the denominator is unknown but by referring the left hand side we can assume the value of
the denominator value as 10.
 Then the fraction will be \[\dfrac{8}{{10}}\], substituting this in equation (4) we get
\[ \Rightarrow \] \[7 + \dfrac{8}{{10}}\] ---------(5)
On simplifying the equation (5)
\[ \Rightarrow \]\[\dfrac{{70}}{{10}} + \dfrac{8}{{10}} = \dfrac{{70 + 8}}{{10}} = \dfrac{{78}}{{10}}\] ---------(6)
On comparing the equation (3) and equation (6) we can see that the left hand side is equal to the right hand side.
Therefore the value 10 assumed for the denominator is the correct option for the given question
So, the correct answer is “Option C”.

Note: Here the question is related to decimal fraction addition. Remember while there are unlike fractions we take LCM and simplify whereas in like fractions we can simplify directly. Similarly when multiplication of decimals is asked we need to multiply the numbers as usual and then count the numbers after the decimal from both the numbers and place the decimal point in the answer after those many numbers towards the left.