Question

Subtract the following numbers : \[6.5 \times {10^{23}}\& 3.2 \times {10^{23}}\]
A) \[3.3 \times {10^{23}}\]
B) \[3.3 \times {10^{22}}\]
C) \[3.2 \times {10^{23}}\]
D) \[3.1 \times {10^{23}}\]

Answer 1

Hint: The two numbers given above are in standard form. When we subtract this type of example we should observe the power of 10 carefully. That should be the same and if it is not then do make it the same first. And then perform the operation.

Complete step by step solution:
Given the numbers are \[6.5 \times {10^{23}}\& 3.2 \times {10^{23}}\]
Now we have checked the power of 10 and both the numbers have the same power so we will go for subtraction.
\[6.5 \times {10^{23}} - 3.2 \times {10^{23}} = 3.3 \times {10^{23}}\]
We should simply subtract the numbers and the power should be the same because we have not used any of the power of 10.
Therefore, option (A) is correct.

Note:
Students note that, here there is no such restriction on the decimal number. We can subtract the number but if the power of 10 is different that makes it difficult to perform the operation. So in these cases the power of the base should be the same. Also note that we can write the answer as \[33 \times {10^{22}}\]. This is also correct but the power of 10 is reduced by 1 since we used one 10 to remove the decimal.
Other options having power of 10 as 23 have the wrong decimal answer.