Question

The numbers 3.845 and 3.835 on rounding off to three significant figures will be:
A) 3.85 and 3.84.
B) 3.84 and 3.83.
C) 3.85 and 3.83.
D) 3.84 and 3.84.

Answer 1

The concept of rounding off has some rules. You can surely see that the last digit of 3.84 is even and the last digit of 3.83 is odd. Also, three significant figures means there should be just three digits from the left.

Complete solution:
What is a significant figure?
The significant figures (also known as the significant digits or precision) of a number written in positional notation are digits that carry meaningful contributions to its measurement resolution.

They include all but there are exceptions. These exceptions are:
1. Leading zeros.
2. Trailing zeros.
3. Spurious values.

The significant figure in simple words is the meaningful digits in a number.
For example, in the number 67 there are two significant numbers and they are 6 and 7 but in 123.54 there are five significant figures and they are 1,2,3,4 and 5.

What is rounding off?
Rounding off is a kind of estimation done to simplify the value. It is done to have a better but approximate knowledge about measurements. Now for rounding off a given number we have to follow a certain rule. These rules are:

-The leftmost digit is the most significant of all.
-If you are rounding off to ‘n’ significant figures then the least significant digit (the right most) digit is at ${n^{th}}$ position from the most significant (left most) digit.
-The first non-significant figure is the digit at ${(n + 1)^{th}}$ position from the leftmost digit.
-For rounding a number with the first non-significant digit less than 5 the least significant digit is left unchanged.
-For rounding off a number with the first non-significant digit greater than 5, the least significant digit is increased by 1.
-If the first non-significant number is equal to five the there are two cases:
-Case 1: least significant digit is even: then leave it unchanged
-Case 2: least significant digit is odd: then increase it by 1.

So, here we are given that we have to round off 3.845 to three significant figures;

So the first non-significant figure is the digit at fourth position from left;

Thus the first non-significant digit is 5, so we have to see the two cases;

Now the least significant digit here is 4 which is even so we will let it remain unchanged;

Therefore rounding off 3.845 to three significant digits will be 3.84.

Similarly for 3.835 the first non-significant figure is 5;

Thus, the two cases must be checked;

The least significant figure in this case will be 3 which is odd so we will increase it by 1;

Thus rounding off 3.835 to three significant digits will give 3.84

Therefore the correct answer will be option D.

Note:
-The least significant number is the second number from the right.
-The first non-significant number is the first number from right.
-The most significant number is the first number from left.