Rounding Numbers
Rounding involves replacing one number with another number that’s easier to work with. Rounded numbers can be easier to use.
Suppose you want to find 18 × 43, but had lost the calculator. You could find an answer close to 18 × 43 by rounding to the nearest ten.
“Rounding to the nearest ten” means replacing a number with the nearest multiple of 10.
Replacing a number with a higher number is called rounding up.
Replacing a number with a lower number is called rounding down.
Sometimes we use word ‘nearest’ in place of rounding. Ex. Nearest 10 is same as round at tens.
Procedure to round to different place values
You can round numbers to place values other than tens.
Write the number. Underline the digit in the position you want to round to.
If the digit to the right of the underlined digit is 5 or more, round up.
If the digit to the right of the underlined digit is 4 or less, round down.
Note:
When we round a number to nearest place, all other digits to the right of the place becomes zero. Ex round 24912 to nearest hundred, we will get 24900 . Digits to the right of 9 become zero.
1.0Rounding A Number to The Nearest 1000
To round off a number to the nearest thousand, we get the nearest multiples of 1000 for that number.
Rule
Look at the digit in the hundreds place. If it is 5 or more, then round up, i.e., replace the digits at ones, tens and hundreds place by 0 and add 1 to the digit at thousands place.
If it is less than 5, then round down, i.e., replace the digits at ones, tens and hundreds place by zeros and leave the digit at thousands place unchanged.
Using rounded numbers
Now, you will learn more about using rounded numbers. You’ll think about how much certain numbers should be rounded. You’ll also see how rounded numbers are useful for checking your work. People round numbers to different place values depending on what the numbers are being used for.
The amount of rounding affects the accuracy
If you use rounding to estimate a sum, be careful how much you round.
Rounding to higher place values usually gives an estimate farther from the actual answer than rounding to lower place values.
2.0Estimation
Estimation means “making a good guess.” We can use it if we don’t need to know an exact answer, or if a question has no exact right answer.
You can estimate when there's no exact answer
Sometimes in math there is no exact right answer.
You can use the information you do have to make an estimate.
So you can estimate that the small bookshelf will hold about 40 books.
You can estimate if you don't need an exact answer
You don’t always need to use an exact figure. Sometimes an estimate is enough.
Using estimation
Estimation is really useful in a lot of real-life situations, where you might not be able, or don’t need, to do an exact calculation.
There are other times when it’s better to figure out the exact answer.
Estimates aren't always a good idea
There are some situations where you definitely shouldn’t use an estimate.
Use of Numbers in everyday life
Small lengths are measured in millimeter (mm) and centimeter (cm) while bigger lengths are measured in meter (m) and kilometer (km).
3.0Solved Examples
1.Carla has a tall bookshelf and a short bookshelf. When full, the tall bookshelf can hold about 60 books. Estimate from the picture how many books the small bookshelf will hold.
Solution
There is no exact number of books you can fit on a bookshelf, because not all books are the same size.
To estimate the answer, compare the bookshelves. The tall one has 3 shelves, and the small one only 2. All the shelves has the same size, so the small bookshelf will hold around two-thirds the number of books.
2.Round 8691 to the nearest thousand.
Solution
3. Round 4392 to the nearest thousand.
Solution
4. Round off :
(i) 7848
(ii) 5164 to the nearest tens, hundreds, thousands.
Solution
5. Calculate 2343 + 5077. Then check your work by rounding to the nearest hundred.
Solution
The answer to the rounded sum is close to the answer to the actual sum, so the answer to the rounded sum is reasonable.