Question

Give a rough estimation(by rounding off to nearest hundreds) and also a close estimate(by rounding off to nearest tens):
 \[{\text{1,08,734 - 47,599}}\]

Answer 1

Hint: For rounding off of any number to hundreds, we check the last two digit if it greater than or equal to 50 then the hundredth place digit exceeds by 1 and if is lesser, hundredth place digit remains the same but in both cases, the last two-digit will become zero(0).
Similarly, for rounding off to the nearest ten, we check the last digit if it greater than or equal to 5 then the tenth place digit exceeds by 1 and if is lesser, the tenth place digit remains the same but in both cases, the last digit will become zero(0).

Complete step by step solution: Given data: \[{\text{1,08,734 - 47,599}}\]
Now,
\[ \Rightarrow {\text{1,08,734 - 47,599 = 61,135}}\]
For rounding off to hundreds for the number \[{\text{61,135}}\], the last two digits i.e. \[{\text{35 < 50}}\],
Therefore, after rounding off to hundreds, we get our answer as \[{\text{61,100}}{\text{.}}\]
For rounding off to tens for the number \[{\text{61,135}}\], the last digits i.e. \[{\text{5 = 5}}\],

Therefore, after rounding off to tens, we get our answer as \[{\text{61,140}}{\text{.}}\]

Note: We can simply compare the whole number by interchanging the last two digits by 50(for rounding off to hundreds) and the last digit by 5(for rounding off to tens) as shown below;
For rounding off to hundreds,
\[ \Rightarrow {\text{61,135 < 61,150,}}\]
 Therefore, after rounding off to hundreds, we get our answer as \[{\text{61,100}}{\text{.}}\]
For rounding off to tens,
\[ \Rightarrow {\text{61,135 = 61,135,}}\]
Therefore, after rounding off to tens, we get our answer as \[{\text{61,140}}{\text{.}}\]