# Rounding Off and Estimation

When rounding off, we write a number simpler as it is, but we keep it close to the original value. To do so, we need to understand place value.

In the number 2 398 643,0699 (two million, three hundred and ninety-eight thousand, six hundred and forty-three, comma zero six nine nine) the 3 next to the decimal number is in the place of the units (U), the 4 is in the place of the tens (T) if we move to the left-hand side, the 6 is in the place of the hundreds (H), the 8 is in the place of the thousands (Th), and so on.

On the right-hand side of the comma, the 0 is in the place of the tenths (t), the 6 in the place of the hundredths (h), the first 9 in the place of the thousandths (th), and so on. When we have to round a number off to the nearest hundred, for example, look at the digit on the right-hand side of the rounding position (the hundreds is the rounding position in this example). Now, the 4 is on the right-hand side of the rounding position. Apply the rule: when the digit on the right-hand side of the rounding position is either a 0; 1; 2; 3; or 4, the value of the rounding position will not change. But what happens to the digits on the right-hand side of the rounding position? They will all become zeros. In the case where the digit on the right-hand side of the rounding position is either a 5; 6; 7; 8 or 9, the digit in the rounding position will increase by one when rounding off. And again, what happens to the digits on the right-hand side of the rounding position? They will all become zeros. Be careful when rounding off to a certain decimal place, then you will not change the digits on the right-hand side of the rounding position to zeros – you will not even write them.

When estimating, the first digit should be non-zero while all the other digits in the different place values should become zeros.