Question

How do you find $0.468$ to the nearest hundredth?

Answer 1

Hint: In the given question, we are basically asked to round off the given number $0.468$ to the nearest hundredth. The hundredth means the place after the decimal corresponding to one hundredth. One hundredth is written mathematically as $\dfrac{1}{100}$ which is equal to $0.01$. So the hundredth position corresponds to the digit after the two decimal places. After two decimal places in the number $0.468$, the digit placed is equal to $6$, which is to be rounded off. For this we have to consider the digit at the next place, that is, at the thousandth position. If that digit is less than $5$, then the rounded number is obtained after dropping off the thousandth digit. But if that digit is equal to or greater than $5$, then we have to drop the thousandth digit and increment the hundredth digit by one.

Complete step by step answer:
Let us write the given number as
$n=0.468$
As stated in the question, we have to round the given number to the nearest hundredth. One hundredth is equal to $\dfrac{1}{100}$ which is equal to $0.01$. So this means that we have to round off the given number up to two decimal places. For that, we have to compare the digit at the thousandth place, or at the third decimal position, with $5$. If it is less than $5$, then simply the thousandth digit will be dropped and the number will be written up to two decimal places. But if it is greater than or equal to $5$, then along with dropping the thousandth digit we have to increment the hundredth digit by one.
In this case, the digit at the thousandth place is equal to $8$, which is greater than $5$. So the digit at the hundredth place, which is $6$, is incremented by $1$ to make it equal to $7$, and the digit at the thousandth place is dropped off.

Hence, the number $0.468$ to the nearest hundredth is equal to $0.47$.

Note: We need to be careful regarding the rounding rules for solving this question. For rounding off a particular digit, the next digit is compared with $5$, and not the previous digit. Also, the term “hundredth” used in this question for the second decimal place may not be clear to many students. The explanation for the same is given in the above solution, which can be extended for any decimal place. For example, the term “thousandth” refers to the third decimal place.