21 Thousandths As A Decimal
Rounding Numbers
Rounding Numbers means adjusting the digits of a number in such a way that it gives an approximate value. This value is an easier representation of the given number. For example, the population of a town could be hands expressed every bit 700,000 rather than 698,869. Rounding numbers makes calculations simpler, resulting in a effigy that is easy to remember. Even so, rounding of numbers is done only for those numbers where the exact value does not hold that much importance.
Let us acquire more about rounding numbers, to get a ameliorate idea of how to circular off a number to the nearest x, hundred, thousand, and and so on.
| i. | What is Rounding Numbers? |
| 2. | Rules for Rounding Numbers |
| 3. | How to Round Off Whole Numbers? |
| 4. | How to Round Off Fractions? |
| 5. | How to Round Off Decimal Numbers? |
| 6. | FAQs on Rounding Numbers |
What is Rounding Numbers?
Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained later on rounding off a number is less authentic, but easier to use. While rounding a number, we consider the place value of digits in a number.
Let usa understand the concept of rounding through an example. Susan covered a distance of 2.05 miles, which she noted as approximately 2 miles. How did she estimate the approximate value of the distance she covered? Why didn't she record her altitude as 3 miles? Noting an approximate and simpler value for a given number helps to make the analysis and calculations easier while using that number. Here, Susan noted an easier value to go along a record of the distance travelled past her.
Numbers can be rounded to different digits, similar, they can be rounded to the nearest ten, hundred, g, and and so on. For example, 541 rounded to the nearest hundred is 500 because 541 is much closer to 500 than 600. While rounding a number, nosotros need to know the answer to the question,' What are we rounding the number to?' Suppose we need to round the number 7456. When 7456 is rounded to the nearest ten, it becomes 7460, but when 7456 is rounded to the nearest thousand, so information technology becomes 7000. A few examples like these are given below.
Rounding Numbers to the Nearest 10
Rounding numbers to the nearest ten means we demand to check the digit to the correct of the tens place, that is the ones identify. For example, when we round the number 7486 to the nearest ten, information technology becomes 7490.
Rounding Numbers to the Nearest Hundred
Rounding numbers to the nearest hundred means we need to check the digit to the right of the hundreds place, that is, the tens identify. For example, when 7456 is rounded to the nearest hundred, it becomes 7500.
Round-Upwards and Round-Down
While rounding is a generic term, we usually use the terms, 'round up' or 'circular down' to specify if the number has increased or decreased after rounding. When the rounded number is increased, and then the given number is said to be rounded upward, whereas, if the rounded number is decreased, so it is said to be rounded down.
Rules for Rounding Numbers
How do we decide which value is more than appropriate betwixt different approximated values of a number? Should we choose a number greater than the given number or go with the smaller one?
At that place are some basic rules that need to be followed for rounding numbers.
- We first need to know what our rounding digit is. This digit is the 1 that volition ultimately be affected.
- After this, we need to check the digit to the right of this identify which volition decide the fate of the rounding digit.
- If the digit to the right is less than v, we do not modify the rounding digit. However, all the digits to the correct of the rounding digit are changed to 0.
- If the digit to the right is 5 or more than than five, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.
Example:
a.) If the nib at a furniture shop comes to $3257, what is the rounded value of the amount to the nearest ten?
b.) If the bill comes to $3284, what would exist the rounded value of this corporeality to the nearest ten?
Solution:
a.) $3257 needs to be rounded to the nearest ten. Then, let us mark the digit in the tens place, which is 5. Now, allow usa check the number to the right, which is 7 in this example. Since seven is more than 5, nosotros will replace 5 with 6, and all the digits to the right volition become 0. So, $3257 is rounded to $3260.
b.) Here, $3284 needs to exist rounded to the nearest 10. And so, let us mark the digit in the tens place, which is 8. At present, allow us check the number to the right, which is 4 in this case. Since 4 is less than 5, 8 will remain unchanged and the remaining digits to the correct will modify to 0. So, $3284 is rounded to $3280.
How to Round Off Whole Numbers?
Whole numbers are rounded off past following the same rules mentioned higher up. Let us apply the rules with the help of an case.
Instance: Round 7234 to the nearest hundred.
- Step i: Mark the place value upwardly to which the number needs to be rounded. Here, 7234 needs to be rounded to the nearest hundred. And then, we mark ii which is in the hundreds identify.
- Stride 2: Observe and underline the digit to the right of 2, that is the tens place. Here, it is 3, and so nosotros will mark it as: sevenii 3iv
- Stride 3: Compare the underlined digit with 5.
- Step 4: If it is less than 5, all the digits towards its correct including it will exist replaced past 0 while the digit in the hundreds place (2) will remain unchanged. Therefore, 7234 will be rounded to 7200.
Note: If the number to the right of 2 was 5 or greater than five, and so all the digits to the right of two would get 0, and 2 would be increased past 1 irresolute it to 3. For example, if the given number was 7268, so information technology would be rounded up to 7300 (to the nearest hundred).
How to Round Off Fractions?
Fractions are numerical values that represent a part of a whole. They are written in the form of (p/q), where q is not equal to nothing. A simple dominion to round fractions to the nearest whole number is to compare proper fractions to i/2. In example if it is an improper fraction, nosotros need to change it to a mixed fraction and so compare the partial part with 1/two. We circular up the fraction if information technology is equal to or greater than 1/2, and we circular down if it is less than ane/2. Let us sympathize rounding off fractions to the nearest whole number using the following case.
Example: Round the given fractions to the nearest whole number:
a.) 3/4
b.) \(6 \dfrac{ii}{5}\)
c.) 21/5
Solution:
a.) Nosotros tin can round off a proper fraction to the nearest whole number by following the simple rule of comparison it with 1/2. Since 3/4 is greater than 1/2, it will be rounded off to 1.
b.) \(6 \dfrac{ii}{five}\) is a mixed fraction. Here, nosotros volition keep the whole number role bated and compare the partial role with i/ii. So, keeping half dozen aside, we will cheque if two/5 is greater than or less than 1/2. Since two/5 is less than 1/2, we will round the given mixed fraction to half dozen.
c.) 21/v is an improper fraction, and then we will catechumen it to a mixed fraction. This will brand it \(four \dfrac{one}{5}\). Now, nosotros will keep the whole number function aside and compare the fractional part with one/ii. So, keeping 4 aside, we will check if one/v is greater than or less than one/2. Since 1/five is less than ane/2, we volition circular the given fraction to 4.
How to Round Off Decimal Numbers?
A decimal number is a combination of a whole number part and a fractional function separated by a decimal point. Rounding decimal numbers works in the aforementioned way as we round whole numbers although we demand to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal betoken every bit well equally the digits given subsequently the decimal point. Observe the decimal identify value chart to empathise this better.
We usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values later the decimal point. However, sometimes we even need to circular a decimal to the nearest whole number. In this instance, nosotros cheque the tenths digit. If it is equal to or more than 5, and then the given number is rounded up, and if the tenths digit is less than 5 then the given number is rounded down.
Example 1: Round 5.62 to the nearest whole number.
Solution: Since we need to round this decimal to the nearest whole number, we will cheque the tenths digit. In this instance, the tenths digit is 6, which is more than v. So, the number will exist rounded to 6. In other words, five.62 ≈ vi
In the other cases, where we demand to round decimals to the nearest tenths, hundredths, or thousandths, we need to recollect the unproblematic rule of marking the number up to which nosotros are rounding and checking the number to its correct. For instance, when we round decimal numbers to the nearest hundredths, we need to check the thousandths place. Similarly, if we need to round decimal numbers to the nearest tenths, we demand to check the hundredths place. If the number to exist checked is less than 5, so the rounding number remains unchanged, and the post-obit digits are replaced with 0. Whereas, if the number to be checked is 5 or more 5, then the rounding number is increased by 1 and the post-obit digits are changed to 0. Allow us understand this with an example.
Instance two: Round 0.439 to the nearest hundredths.
Solution: In this case, the digit to the right of the hundredths place, that is, the thousandths place is 9, which is more than five. And so, we will add ane to the digit in the hundredths place, that is, 3 + 1 = 4, and write 0 in the digits to the right. So, 0.439 volition be rounded to 0.44
Note: Information technology should exist noted that when nosotros round a decimal number to the nearest hundredth, the round decimal fraction is said to be correct to 2 places of decimal. In other words, if nosotros are asked to round off a number to two decimal places, it means we demand to round it to the nearest hundredths. Similarly, when we are asked to round off a number to one decimal place, information technology means we demand to round it to the nearest tenths.
Tips on Rounding Numbers:
The following tips are helpful in solving questions related to rounding numbers.
- While rounding numbers, we always need to cheque the digit to the right of the rounding number. If it is less than 5, the rounding number remains the same and the following digits are changed to 0. If the digit to the right is equal to or more than five, we increase the rounding digit by ane and the following numbers are changed to 0.
- When we round decimal numbers, we usually come across terms like circular to the nearest tenths, hundredths, thousandths, and so on.
- When we are asked to round off a number to one decimal place, it means we need to round information technology to the nearest tenths, similarly, when nosotros are asked to round off a number up to two decimal places, it means nosotros need to circular information technology to the nearest hundredths.
- When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, so information technology is said to be rounded down.
Related Topics
Cheque out the following links related to rounding numbers.
- What are Numbers?
- Number Line
Rounding Numbers Examples
become to slidego to slide
Desire to build a stiff foundation in Math?
Go beyond memorizing formulas and understand the 'why' behind them. Experience Cuemath and become started.
Book a Complimentary Trial
Do Questions
go to slidego to slide
FAQs on Rounding Numbers
What is Rounding Numbers in Math?
Rounding a number means converting a number to a simpler value such that its value remains close to what it was. Rounding numbers makes adding simpler and converts figures to an estimate value which is easier to remember. For example, if the population of a town is 692,769, it can be rounded to 700,000, and it would be easier to think an approximate figure of 700,000 rather than the real figure.
What are the Rules for Rounding Off Decimal Numbers?
At that place are some bones rules that need to exist followed for rounding decimal numbers. They are similar to rounding the other numbers, however, nosotros demand to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal signal as well equally the digits given after the decimal signal. In other words, we unremarkably round decimal numbers to the nearest tenths, hundredths, thousandths, and and so on, which represent the identify values after the decimal betoken. Sometimes, we even round the decimal to the nearest whole number. In all these cases, we use the following rules.
- We first need to know what our rounding digit is. This digit is the one that will ultimately exist affected.
- After this, we need to bank check the digit to the right of this identify which will decide the fate of the rounding digit.
- If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.
- If the digit to the right is 5 or more than v, we increase the rounding digit past 1, and all the digits to the right of the rounding digit are changed to 0.
For example, if we demand to round 0.476 to the nearest tenths, information technology ways we will check the digit to its right, which is the hundredths digit. In this example, it is 7 which is more than 5. Therefore, 0.476 will be rounded up to 0.v to the nearest tenths.
What is 62 Rounded to the Nearest ten?
When 62 is rounded to the nearest 10, we need to check the digit in ones identify. Here, information technology is 2, which is less than 5. So, 6 will remain the same, and 2 will change to 0. Therefore, 62 rounded to the nearest ten will be 60.
Where do we Utilise Rounding of Numbers in Real Life?
In existent life, we usually circular numbers whenever the exact value is not so of import. For example, if we want to know the approximate amount that we spent in a grocery store, or the amount while estimating a budget, or while expressing larger figures similar the population of a town. We guess the amount to simpler numbers so that calculation becomes easier. For example, if nosotros know that our monthly expenditure would be around $590, we can easily circular the number to $600 which is a figure that is easier to retrieve.
How to Round Numbers to the Nearest Tenth?
If we need to round decimal numbers to the nearest 10th, nosotros need to cheque the digit to the right of the digit on the tenths place, which is the hundredths place. If the number in the hundredths identify is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to exist checked is 5 or more than five, then the rounding number is increased by 1 and the following digits are changed to 0. For example, to round 56.73 to the nearest tenth, nosotros will cheque the digit in the hundredths place, which is 3 in this case. Since three is less than 5, 7 will remain the same and the following digits will go 0. So, 56.73 rounded to the nearest tenths will go 56.seven
What is the Purpose of Rounding Numbers?
Rounding numbers means adjusting the digits of a number such that it gives an estimated upshot. Rounding a number gives an approximate value which is a simpler and a shorter representation of the given number. For example, if the population of a town is 498,821, information technology would be easier if information technology is expressed as 500,000. This helps in making calculations easier with a figure that is easy to remember and note. However, rounding of numbers is done in those cases where the exact value does not agree that much importance.
What is Rounding Numbers to the Nearest 10?
When we round numbers to the nearest ten, we outset mark the digit in the tens place. Then, nosotros discover the 'ones' place, which lies to the right of the tens column. According to the rules, if the digit in the ones place is five or more 5, we add 1 to the digit in the tens place, that is, we increase the tens place past 1 and write 0 in all the digits to the right. Notwithstanding, If the digit in the ones place is less than 5, nosotros write 0 in the ones identify and in all the places to its right, and the digit in the tens place remains the aforementioned. For case, if we demand to circular 389 to the nearest ten, we will check the digit in ones place. In this case, information technology is 9 which is more than five. So, 8 will change to 9, and 389 will be rounded to 390.
How to Round Numbers to the Nearest 100?
In guild to round numbers to the nearest hundred, we need to check the digit to its right, which is the tens place. For example, if we need to circular 3270 to the nearest 100, we will bank check the tens place. In this case, it is 7, which means the digit in the hundreds place volition be increased by 1, that is, 2 will get iii and the remaining digits to its correct will become cypher. Therefore, 3270 will exist rounded upwardly to 3300.
How to Round Numbers to the Nearest M?
When we round numbers to the nearest chiliad, we bank check the digit in the hundreds place. If the digit in the hundreds identify is 5 or more than than five, we increase the thousands place by 1 and write 0 in all the digits to the correct. In case, if the digit in the hundreds place is less than 5, we write 0 in the hundreds place and in all the places to its right, while the digit in the thousands place remains as it is. For example, allow us round 76431 to the nearest thousand. We volition outset bank check the digit in the hundreds identify. In this case, it is 4, which is less than v. So, 6 will remain as information technology is and all the digits to the right will become 0. Therefore, 76431 will exist rounded to 76000.
21 Thousandths As A Decimal,
Source: https://www.cuemath.com/numbers/rounding-numbers/
Posted by: gabbardfoready.blogspot.com
0 Response to "21 Thousandths As A Decimal"
Post a Comment