Question

How do you round 2,372 to the nearest hundred? \[\]

Answer 1

Hint: We identify the digit at the hundred’s place of the given number. We then identify the digit at the ten’s place . If the digit at ten’s place is less than 5 then we keep the digit at the hundred’s place uncharged and convert the digits after that at ten’s place and unit place to be zero. If digit at ten’s place is greater than or equal to 5 then we add 1 to the digit at hundred’s place and convert the digits after that at ten’s place and unit place to be zero.\[\]

Complete step by step answer:
We can solve it by rounding off digits one by one from the right hand side. We are given the number 2372 which has 2 in its unit place and 7 in its ten’s place. \[\]
\[\begin{matrix}
   2 & 3 & 7 & 2 \\
   Th & H & T & O \\
\end{matrix}\]
We can start by rounding off to nearest 10. We have 2 at one’s place and 7 at ten’s place. Since we have $ 2 < 5$ we round down and keep the digit at ten’s place that is 7 unchanged. We convert the digit at one's place to zero.
\[\begin{matrix}
   2 & 3 & 7 & 0 \\
   Th & H & T & O \\
\end{matrix}\]
Now we see the digit at ten’s place 7 and hundred’s place that is 3. Since we have $7 > 5$ we round up and add 1 to the digit at hundred’s place to get $3+1=4$. We convert the digits at ten’s place to 7 to zero. So we have the number as $2400$.
\[\begin{matrix}
   2 & 4 & 0 & 0 \\
   Th & H & T & O \\
\end{matrix}\]

Note: We know that we round a number to use estimation where calculation involving large numbers is done. If want to round of a particular place value say at ${{\left( {{10}^{n}} \right)}^{\text{th}}},n\ge 0$ place in the number we look at the digit right next to it at ${{\left( {{10}^{n-1}} \right)}^{\text{th}}}$ place. If that digit is less than 5 we round down by keeping the digit at ${{\left( {{10}^{n}} \right)}^{\text{th}}}$ unchanged and converting the digits after it to zeros. If the digit at ${{\left( {{10}^{n-1}} \right)}^{\text{th}}}$ is greater than equal to 5 then we round up by adding to the digit at ${{\left( {{10}^{n}} \right)}^{\text{th}}}$ place and converting the digits after it to zeros.