Question

The order of magnitude of 49 and the order of magnitude of 51
A. Is same
B. Differs by 1
C. Is 1
D. Is 2

Answer 1

Hint: An order of magnitude is an estimate of a value's logarithm with respect to a certain contextually known reference value, typically ten, defined as the source of the logarithm and the magnitude one value's representative. The magnitude order is usually written as 10 to the nth power. The n reflects the magnitude order.

Complete answer:
Now, to solve the given question, let us go step by step
First, let us solve for 49
In this case, we can write 49 as $4.9\times {{10}^{1}}$
Now, as we can see in this case
4.9 < 5, so it is more closer to 1 than 10
So, we can say that the order of magnitude will be 1 for 49
Now, if we similarly solve for 51
We can write 51 as $5.1\times {{10}^{1}}$
Now as we can see,
5.1 > 5, so it is more closer to 10 than 1
Therefore, the order for 51 will be 2
From the above solutions we can see that the order of magnitude of 49 and order of magnitude of 51 differ by 1.

So, the correct answer is “Option B”.

Note:
If two numbers X and Y vary by one order of magnitude, then X is approximately ten times different in quantity than Y. When values differ by two orders of magnitude, they vary by a factor of about 100. Which means you are multiplying the number by 10 while you raise the order by 1 and simply multiplying the number by 0.1 while you reduce a number by one order of magnitude.