Question

How do you round $ 105 $ to the nearest hundred?

Answer 1

Hint: Look at the digit which is at the adjacent right position to the digit’s place which we are asked to round off. Then if that digit is smaller than $ 5 $ then the number is rounded down to the nearest number of that digit’s place and if that digit is equal to or greater than $ 5 $ then the number is rounded up to the nearest number of that digit’s place.

Complete step by step answer:
First, let us understand what are basic rulings are taken care of during the rounding off of a number. First, we have to consider the digit’s place to which we are asked to round up to. So this digit’s place becomes our marking point.
Now the key is to look at the digit which is at the next right position to our marking point. If that digit is smaller than $ 5 $ then the number is rounded down to the nearest number of that digit’s place. If that digit is equal to or greater than $ 5 $ then the number is rounded up to the nearest number of that digit’s place.
Let us understand these rules better with an example, we will be rounding up two-digit numbers starting from $ 12 $ to $ 16 $ to the nearest tenth place. Now we have rounded the number to the nearest tenth place so we will be looking at the digit which is at the immediate right position of tenth place in the number which is the one place. First, let us take $ 12 $, we see that the digit which is at the immediate right position of tenth place is $ 2 $ and $ 2 $ is less than $ 5 $, so the number $ 12 $ will be rounded down to the nearest tenth number which is $ 10 $. Now let us round off all the numbers from $ 12 $ to $ 16 $ in the same fashion.
 $
  12 \to 10 \\
  13 \to 10 \\
  14 \to 10 \\
  15 \to 20 \\
  16 \to 20 \\
  $
We see that $ 15 $ and $ 16 $ are rounded up to $ 20 $ because the digit in their place is equal to or greater than $ 5 $.
Now we have to round off $ 105 $ to the nearest hundred. So we will look at the tens position. The digit at the tens position is $ 0 $ which is less than $ 5 $ so $ 105 $ will be rounded down to the nearest hundred which is $ 100 $.
 $ 105 \to 100 $
So, the answer is $ 100 $.

Note:
Rounding is basically replacing a number with a simpler value to make it easy and convenient to use when talking about big numbers. When dealing with precise quantities and numbers, rounding off is not useful as it deviates from the original number. When numbers with decimal digits are rounded off, the number of significant digits decreases thus reduces the accuracy.