# Rounding

Rounding is the process of making numbers smoother, simpler; it's about getting rid of the fragments. This allows you to perform operations / calculations more easily, but of course, your result will not be exact, it will be more or less an approximation.

How can we make numbers easier to handle? For example, if we accept 105 as 100, it becomes smoother.

### Example;

How much money should we have if we want to buy 2 pants priced at 395 zed each? ( Zed is the currency of the imaginary country Zed )

395 zed is very close to 400 zed. If we say / consider 400 zed, then we should have about 4

00 + 400 = 800 zed. This is where we've done rounding with that "if". We simplified. Of course, our result is not exactly 800 zed.

What if we had accepted the price of the 395-zed pants as 300 zed ? Wouldn't we have been too wrong?

To prevent excessive deviation from the actual result, rounding should be done to the "nearest ten, hundred, and thousand".

But what if our number is right in the middle? Mathematicians have adopted a rule to round up to the next ten, hundred, thousand. For example, if our price had been 350, we would still round it up to 400.

## Before We Begin

Your teachers, YouTube videos, or other websites might talk about rounding rules. I definitely do not recommend learning and memorizing these rules. Instead, you can manage to round without rules by thinking a bit about the number to be rounded.

## Steps:

* Determine between which two tens the number falls if we're asked to round to the nearest ten, between which two hundreds if we're asked to round to the nearest hundred, and between which two thousands if we're asked to round to the nearest thousand exct..

* Determine which ten, hundred, or thousand the number is closer to.

My point is closer to A, it will be rounded to A.

My point is closer to B, it will be rounded to B.

My point is neither closer to A nor B, it's exactly in the middle. In this case, by rule, we round up to the next number, which is B.

# Rounding to the nearest whole number

Rounding to the nearest unit cannot be done with integers, because there is no place value smaller than the units place in integers. Rounding to the nearest unit can only be done with decimal numbers.

# Rounding to the nearest ten ( 10 )

Our goal is to eliminate the digits less than 10 ( ones and sometimes even decimals ) to simplify the number.

* Determine between which two tens the number is.

The pronunciation of numbers gives you a clue, pay attention to how many tens you say, for example, 73 is pronounced as 'seventy-three'. You already have 'seventy' given, so what's the next ten? It's 'eighty'! So, our number is between 'seventy' and 'eighty', which is between 70 and 80.

** Determine which ten the number is closer to.

To determine which ten a number is closer to, you need to know the midpoint between the numbers. The midpoint between each ten is 5. For example, the midpoint between sixty (60) and seventy (70) is 65.

***Your numbers in tens are going like this 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120...990, 1000, 1010, 1020, 1030.....9990, 10 000...
All these numbers are made up of tens. We will straighten the parts that are smaller than tens, and we will accept the ten that it is closest to.

**** 10, 100, 1000, 10 000, 100 000, 1 000 000 exct.. All these numbers are again made up of tens.
10 is made up of one ten, 100 is made up of ten tens, 1000 is made up of one hundred tens, etc.

## Round 34 to the nearest ten

* Determine between which two tens the number is.

If we want to determine between which two tens a number lies, of course, our number sequence is progressing by tens, and the number in question is between any two of these and closer to one of them.

The number 34 is pronounced as 'thirty-four'. It consists of three tens (or 'thirty') and four units. The next ten after thirty is 'forty', so the number 34 is between thirty and forty.

** Determine which ten the number is closer to.

Between 30 and 40, but which one is it closer to? We need to find the midpoint between 30 and 40, don't we?

35 is the midpoint, but 34 is closer to 30.

# Examples

## 3 >>> 0

The tens place less than 3 is 0, and the tens place greater than 3 is 10. So 3 is a number between 0 and 10, and it's closer to 0, so it's rounded to 0

## 5 >>> 10

The tens place less than 5 is 0, and the tens place greater than 5 is 10. So 5 is a number between 0 and 10, and it's closer to 10, so it's rounded to 10.

## 93 >>> 90

Your numbers in tens are going like this 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 exct...  The tens place less than 93 is 90 (9 tens), and the tens place greater than 93 is 100 (10 tens make 100 ). 93 is a number between 90 and 100, and it's closer to 90, so it's rounded to 90.

## 98 >>> 100

The tens place less than 98 is 90 (9 tens), and the tens place greater than 98 is 100 (10 tens make 100). 98 is a number between 90 and 100, and it's closer to 100, so it's rounded to 100.

## 103 >>> 100

The tens place less than 103 is 100 (10 tens), and the tens place greater than 103 is 110 (11 tens make 110). 103 is a number between 100 and 110, and it's closer to 100, so it's rounded to 100.

## 889 >>> 890

889 is a number closer to 890 than it is to 880.

## 996 >>> 1000

990 is made up of 99 tens, 1000 is made up of 100 tens. 996 is a number between 990 and 1000, and it is closer to 1000.

1003>> 1000
1005 >>1010
1593 >> 1590
1991>>1990
1995 >>2000
2002 >>2000
7 456 >> 7 500
10 045 >> 10 050
89 996 >> 90 000
99 996 >>100 000

# Rounding to the nearest Hundred ( 100 )

Our goal is to eliminate the digits less than 100 (the tens and ones) to simplify the number even further.

* Determine between which two hundred the number is.

The pronunciation of numbers gives you a clue, pay attention to how many hundreds you say, for example, 473 is pronounced as 'four hundred and seventy-three. You already have 'four hundred' given, so what's the next hundred? It's 'five hundred'! So, our number is between 'four hundred' and 'five hundred', which is between 400 and 500.

** Determine which hundred the number is closer to.

To determine which hundred a number is closer to, you need to know the midpoint between the numbers. The midpoint between each hundred is 50. For example, the midpoint between six hundred (600) and seven hundred (700) is 650.

***Your numbers in hundreds are going like this 100, 200, 300, 400, 500...900, 1000, 1100, ..9800, 9900, 10 000, 10 100, 10 200...99 900, 100 000, 100 100, 100 200..... 999 900, 1 000 000 and 1 100 000 exct.. All these numbers are made up of hundreds. We will straighten the parts that are smaller than hundreds, and we will accept the hundred that it is closest to.

**** 0, 100, 1 000, 10 000, 100 000, 1 000 000 exct.. All these numbers are again made up of hundreds. 100 is made up of one hundred, 1000 is made up of ten hundreds, 10000 is made up of one hundred hundreds, etc.

# Round 46 to the nearest hundred

* Determine between which two hundred the number is.

46 is a number between 0 (equivalent to zero hundred) and 100 (equivalent to one hundred)

* Determine which hundred the number is closer to.

To determine whether 46 is closer to 0 (equivalent to zero hundred) or 100 (equivalent to one hundred), you should find the midpoint.

50 is the midpoint between 0 and 100

46 is a number between 0 (equivalent to zero hundred) and 100 (equivalent to one hundred), and it is closer to 0.

## Round 473 to the nearest hundred

* Determine between which two hundred the number is.

Your numbers in hundreds are going like this 100, 200, 300, 400, 500...900, 1000 exct.. Between which two numbers does it fall?

473 is a number between 400 (equivalent to four hundred) and 500 (equivalent to five hundred).

473 is rounded to 500.

## Round 954 to the nearest hundred

* Determine between which two hundred the number is.

954 is a number between 900 (equivalent to nine hundred) and 1000 (equivalent to ten hundred).

954 is closer to 1000 (10 * 100), therefore it rounds to 1000.

## Round 4536 to the nearest hundred

* Determine between which two hundred the number is.

The pronunciation of the number will give you a clue. 4536 "four thousand five hundred thirty-six".

You already have five hundreds, the next hundred is six hundred, so the number must be between 4500 and 4600.

4536 is a number between 4500 and 4600 and it is closer to 4500. Therefore, it rounds to 4500

## Round 4 036 to the nearest hundred

* Determine between which two hundred the number is.

The pronunciation of the number will give you a clue. four thousand thirty-six.  As you see, you didn't mention any hundreds, so the next hundred after zero hundred is one hundred. Therefore, the number must be between 4000 and 4100.

4036 is a number between 4000 and 4100, and when rounded to the nearest hundred, it is 4000.4000 is equivalent to 40 hundreds, and 4100 is equivalent to 41 hundreds.

# Rounding to the nearest Thousand( 1000 )

Our goal is to eliminate the digits less than 1000 (the hundreds, tens, and ones) to simplify the number even further.

*Determine between which two thousands the number is.

The pronunciation of numbers gives you a clue, pay attention to how many thousands you say, for example, 3473 is pronounced as 'three thousand four hundred and seventy-three'. You already have 'three thousand' given, so what's the next thousand? It's 'four thousand'! So, our number is between 'three thousand' and 'four thousand', which is between 3000 and 4000.

** Determine which thousand the number is closer to.

To determine which thousand a number is closer to, you need to know the midpoint between the numbers. The midpoint between each thousand is 500. For example, the midpoint between three thousand (3000) and four thousand (4000) is 3500.

***Your numbers in thousands are going like this 1000, 2000, 3000, 4000, 5000...9000, 10 000, 11 000, ..98 000, 99 000, 100 000, 101 000, 102 000...999 000, 1 000 000, 1 001 000, 1 002 000..... 9 999 000, 10 000 000 and so on.. All these numbers are made up of thousands. We will straighten the parts that are smaller than thousands, and we will accept the thousand that it is closest to.

**** 0, 1000, 10 000, 100 000, 1 000 000 exct.. All these numbers are again made up of thousands. 1000 is made up of one thousand, 10 000 is made up of ten thousands, 100 000 is made up of one hundred thousands, etc.

## Round 136 to the nearest Thousand

* Determine between which two hundred the number is.

Your numbers in thousands are going like this 0, 1000, 2000, 3000, 4000, 5000...9000, 10000 exct.. Between which two numbers does it fall?
The pronunciation of the number will give you a clue.The number 136 is pronounced as "one hundred and thirty-six"
As you see, you didn't mention any thousands, so the next hundred after zero thousand is one thousand. Therefore, the number must be between 0 and 1000.

*Determine which thousand the number is closer to.
To determine whether 136 is closer to 0 (equivalent to zero thousand) or 1000 (equivalent to one thousand), you should find the midpoint.

500 is the midpoint between 0 and 1000.

136 is a number between 0 and 1000 and it is closer to 0, therefore it rounds to 0.

## Round 1520 to the nearest Thousand

*Determine between which two thousands the number is.

The pronunciation of the number will give you a clue. The number 1520 is pronounced as "one thousand five hundred and twenty". You already have 'one thousand' given, so what's the next thousand? It's 'two thousand'! So, our number must be between 1000 and 2000.

*Determine which thousand the number is closer to.
To determine whether 1520 is closer to 1000 (equivalent to one thousand) or 2000 (equivalent to two thousand), you should find the midpoint.

1500 is the midpoint between 1000 and 2000.

1520 is a number between 1000 and 2000 and it is closer to 2000, therefore it rounds to 2000.

# Round 65485 to the nearest Thousand

*Determine between which two thousands the number is.
Your numbers in thousands are going like this: 0, 1000, 2000, 3000, 4000, 5000...9000, 10000, 11000, 12000 etc. Between which two numbers does it fall? The pronunciation of the number will give you a clue. The number 65485 is pronounced as "sixty-five thousand four hundred and eighty-five". You already have 'sixty-five thousand' given, so what's the next thousand? It's 'sixty-six thousand'! So, our number must be between 65000 and 66000.

*Determine which thousand the number is closer to.
To determine whether 65485 is closer to 65000 (equivalent to sixty-five thousand) or 66000 (equivalent to sixty-six thousand), you should find the midpoint.

65500 is the midpoint between 65000 and 66000.

65485 is a number between 65000 and 66000 and it is closer to 66000, therefore it rounds to 65000.