Decimals are a way of converting fractional numbers system into linear form of number systems i.e. Not in a pattern of writing a fractional number having a numerator and denominator. The dot (.) also called as 'period' or 'decimal point' between two digits in a number indicates that particular number to be a decimal number. The zero and the counting numbers (1,2,3,...) make up the set of whole numbers. But not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a symbol called the decimal point. As you move right from the decimal point, each place value is divided by 10. You can improve your skills using adding decimal calculator
For an example, fractional number '5/10' can be written as the decimal '0.5'.
The decimal 0.5 could be pronounced as 'Fifth Tenth' or as 'Zero Point five'. If a decimal is less than 1, place a zero before the decimal point. So, now it should be written as 0.5 not .5. There are other decimals numbers like hundredths or thousandths and many more. They all are based on the number ten just like our number system. A decimal number can be greater than one. The decimal 8.9 can be pronounced as 'eight and nine tenth'. Decimal numbers of Tenths have one digit after the decimal point. The decimal 0.5 is called as "five tenths" or "zero point five". It is equal to the fractional number 5/10. Decimal number of Hundredths have two digits after the decimal point. The decimal 0.97 is pronounced "ninety-seven hundredths" or "zero point nine seven". It is equal to the fractional number 97/100. Decimal number of Thousandths goes with the same trend. They have three digits after the decimal point. The decimal 0.123 is pronounced "one hundred twenty-three thousandths" or "zero point one two three". If it happens that a 'zero' is placed after the decimal point in a number. For example, a decimal number 0.021 is pronounced "twenty-one thousandths" or "zero point zero two one". Use this resource for more on decimals.
Our decimal system of numbers lets us write numbers as larger or smaller as per our choice. In number system, digits can be placed to the left and right of a decimal point. The number to the left of the decimal point indicates numbers greater than one and the right of the decimal point is less than one. The decimal point indicates where the "ones" place is located and it is placed to the right of the ones place. As we move right from the decimal point, each number place is divided by 10.
The decimal number 534.129 as "five hundred thirty four and one hundred twenty-nine thousandths". Normally read as "five hundred thirty four point one two nine."
Exercise:
Convert the following fraction into decimal:
1) 1/10
A. 0.01
B. 0.1
C. 1.0
D. 10.0
2)12/100
A. 0.012
B. 0.0012
C. 1.2
D. 0.12
3) 1/100 =
A. 0.01
B. 0.1
C. 1.0
D. 10.0
4) 1/1000=
A. 0.001
B. 0.0001
c. 0.01
D. 0.1
Conversion of decimals into fraction:
Decimals are a type of fractional number. The decimal number 0.2 is equal to the fraction 2/10. The decimal 0.017 represents the fraction 17/1000. Decimal when represented in fractional number always have a denominator that is in the power of 10.
50/100 is equivalent to 1/2 since 1/2 times 50/50 is 5/100. Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, and so on.
Some examples of Decimal numbers and Fractional numbers which are equivalent :
0.2 and 1/5
0.5 and 1/2
0.25 and 1/4
0.75 and 3/4
Two decimal numbers can be compared. A decimal number can be greater than, less than or equal to the other decimal number.
Comparing 0.5 and 0.05 is similar like comparing two fractional numbers 5/10 to 5/100. The fraction 5/10 is equivalent to 50/100 which is clearly larger than 5/100.
Steps:
Compare two decimal numbers start with tenths place and then hundredths place and so on. If a decimal number has a greater digit in the tenths place then it is larger than a decimal with lesser digit in tenths place.
If the tenths places of both the decimal numbers are equal check for the hundredths place of both the numbers. Compare the hundredths place of both the decimal numbers, then the thousandths place and so on.
If each decimal place value is the same then the decimals are equal.
For example;
Decimal numbers 0.05 and 0.005 if compared, then 0.05 is greater than 0.005.
Place Value of Decimal numbers:
1) Decimal numbers, let’s say 0.649, have three digits after the decimal point. Each digit is a different place value.
2) The next digit after the decimal point is called the tenths place value. There are six tenths in the number 0.649.
3) The second digit resembles hundredths that are located in the number. The number 0.649 has four hundredths.
4) The third digit is the thousandths place.
Therefore, there are six tenths, four hundredths and nine thousandths in the number 0.649.
Rounding decimal number is same as rounding other numbers. If the hundredths and thousandths places of a decimal is forty-nine or less, they can be eliminated and the tenths place does not change.
For example, rounding 0.542 to the nearest tenth would give 0.5.
If the hundredths and thousandths places are more than 50, the tenths place is brought up by 1. The decimal 0.78 rounded to the nearest tenth is 0.8.
Let’s say the thousandths place of a decimal is less than 4. then the 4 is dropped and the hundredths place is kept unchanged. For example, rounding 0.123 to the nearest hundredth would give 0.12.
If the thousandths place is more than 5, the hundredths place is increased by one. The decimal 0.127 rounded to the nearest hundredth is 0.13.
Addition and Subtraction of Two or more decimal numbers:
Arithmetic operations in decimal numbers is nearly similar with the operations in other forms of numbers.
Addition:
Adding Decimals numbers is just like adding other forms of numbers.
Steps:
1) Always line up the decimal points one above the other when adding decimal numbers.
For example: 0.75
+ 0.53
___________
___________
2) Put the decimal point in the proper place leaving space for the product digits for both left and right hand side of in your answer.
For example: 0.75
+ 0.53
___________
___________
3) Add the numbers as done normally with whole numbers.
For example: 0.75
+ 0.53
_____________
1.28
____________
* Note that 12 that is acquired after adding 7 and 5 happens to shift the 1 before the decimal dot and 2 is written after the dot. This is because the 1 is added to the column consisting the number 0.
In order to add Decimals that have different numbers of decimal places take the following steps
Steps:
1)Place one digit below the other so that the bottom decimal point is directly below the top decimal point.
2) Add each column starting at the right side.
Example: Add 9.275 + 15.57
9.275
+15.57
15.845
Subtraction:
Subtracting two Decimal numbers is similar in process as what done with whole numbers.
Steps:
1) Put the decimal points of the greater number over the smaller number when subtracting decimal numbers. (Also read fraction to decimal converter)
37.721
- 21.005
2) Subtract the numbers as done with whole numbers.
37.721
- 21.005
16.716
3) Put the decimal point in the proper place of the answer.
In order to multiply a three digit decimal by a one digit decimal number follow these steps
Steps:
1) Place one decimal number above the other so that they are placed on the right side sequentially vertical.
2) Avoid the decimal points for sometime and multiply the numbers like multiplying a three digit number by a one digit number.
0.529
0.7
3) Multiply the two numbers on the right side. (9 * 7 = 63). This number is larger than 10 so place 6 above the center column and place three below the line in the right column.
6
0.529
0.7
3
4) Multiply the digit in the top center column (2) by the digit in the center of the right column (7). The answer (2*7=14) is added to the 6 above the center column to give an answer of 20. The units place value (0) of 20 is placed below the line and the tens place value (2) of the 20 is placed above the five.
26
0.529
0.7
03
5) The 5 of the top number is multiplied by the 7 of the multiplier (5*7=35). The two that was previously carried is added and 37 is placed below the line. At the start we disregarded the decimal places. Count the decimal places and move the decimal place to its proper location. There are three decimal places in 0.529 and one in the decimal 0.7 so move the decimal four places to the left to give the final answer of 0.3703.
26
0.529
0.7
0.3703
In upcoming posts we will discuss about Fractions in Grade IV and adding and subtracting integers worksheets. Visit our website for information on CBSE computer science syllabus
For an example, fractional number '5/10' can be written as the decimal '0.5'.
The decimal 0.5 could be pronounced as 'Fifth Tenth' or as 'Zero Point five'. If a decimal is less than 1, place a zero before the decimal point. So, now it should be written as 0.5 not .5. There are other decimals numbers like hundredths or thousandths and many more. They all are based on the number ten just like our number system. A decimal number can be greater than one. The decimal 8.9 can be pronounced as 'eight and nine tenth'. Decimal numbers of Tenths have one digit after the decimal point. The decimal 0.5 is called as "five tenths" or "zero point five". It is equal to the fractional number 5/10. Decimal number of Hundredths have two digits after the decimal point. The decimal 0.97 is pronounced "ninety-seven hundredths" or "zero point nine seven". It is equal to the fractional number 97/100. Decimal number of Thousandths goes with the same trend. They have three digits after the decimal point. The decimal 0.123 is pronounced "one hundred twenty-three thousandths" or "zero point one two three". If it happens that a 'zero' is placed after the decimal point in a number. For example, a decimal number 0.021 is pronounced "twenty-one thousandths" or "zero point zero two one". Use this resource for more on decimals.
Our decimal system of numbers lets us write numbers as larger or smaller as per our choice. In number system, digits can be placed to the left and right of a decimal point. The number to the left of the decimal point indicates numbers greater than one and the right of the decimal point is less than one. The decimal point indicates where the "ones" place is located and it is placed to the right of the ones place. As we move right from the decimal point, each number place is divided by 10.
The decimal number 534.129 as "five hundred thirty four and one hundred twenty-nine thousandths". Normally read as "five hundred thirty four point one two nine."
Exercise:
Convert the following fraction into decimal:
1) 1/10
A. 0.01
B. 0.1
C. 1.0
D. 10.0
2)12/100
A. 0.012
B. 0.0012
C. 1.2
D. 0.12
3) 1/100 =
A. 0.01
B. 0.1
C. 1.0
D. 10.0
4) 1/1000=
A. 0.001
B. 0.0001
c. 0.01
D. 0.1
Conversion of decimals into fraction:
Decimals are a type of fractional number. The decimal number 0.2 is equal to the fraction 2/10. The decimal 0.017 represents the fraction 17/1000. Decimal when represented in fractional number always have a denominator that is in the power of 10.
50/100 is equivalent to 1/2 since 1/2 times 50/50 is 5/100. Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, and so on.
Some examples of Decimal numbers and Fractional numbers which are equivalent :
0.2 and 1/5
0.5 and 1/2
0.25 and 1/4
0.75 and 3/4
Two decimal numbers can be compared. A decimal number can be greater than, less than or equal to the other decimal number.
Comparing 0.5 and 0.05 is similar like comparing two fractional numbers 5/10 to 5/100. The fraction 5/10 is equivalent to 50/100 which is clearly larger than 5/100.
Steps:
Compare two decimal numbers start with tenths place and then hundredths place and so on. If a decimal number has a greater digit in the tenths place then it is larger than a decimal with lesser digit in tenths place.
If the tenths places of both the decimal numbers are equal check for the hundredths place of both the numbers. Compare the hundredths place of both the decimal numbers, then the thousandths place and so on.
If each decimal place value is the same then the decimals are equal.
For example;
Decimal numbers 0.05 and 0.005 if compared, then 0.05 is greater than 0.005.
Place Value of Decimal numbers:
1) Decimal numbers, let’s say 0.649, have three digits after the decimal point. Each digit is a different place value.
2) The next digit after the decimal point is called the tenths place value. There are six tenths in the number 0.649.
3) The second digit resembles hundredths that are located in the number. The number 0.649 has four hundredths.
4) The third digit is the thousandths place.
Therefore, there are six tenths, four hundredths and nine thousandths in the number 0.649.
Rounding decimal number is same as rounding other numbers. If the hundredths and thousandths places of a decimal is forty-nine or less, they can be eliminated and the tenths place does not change.
For example, rounding 0.542 to the nearest tenth would give 0.5.
If the hundredths and thousandths places are more than 50, the tenths place is brought up by 1. The decimal 0.78 rounded to the nearest tenth is 0.8.
Let’s say the thousandths place of a decimal is less than 4. then the 4 is dropped and the hundredths place is kept unchanged. For example, rounding 0.123 to the nearest hundredth would give 0.12.
If the thousandths place is more than 5, the hundredths place is increased by one. The decimal 0.127 rounded to the nearest hundredth is 0.13.
Addition and Subtraction of Two or more decimal numbers:
Arithmetic operations in decimal numbers is nearly similar with the operations in other forms of numbers.
Addition:
Adding Decimals numbers is just like adding other forms of numbers.
Steps:
1) Always line up the decimal points one above the other when adding decimal numbers.
For example: 0.75
+ 0.53
___________
___________
2) Put the decimal point in the proper place leaving space for the product digits for both left and right hand side of in your answer.
For example: 0.75
+ 0.53
___________
___________
3) Add the numbers as done normally with whole numbers.
For example: 0.75
+ 0.53
_____________
1.28
____________
* Note that 12 that is acquired after adding 7 and 5 happens to shift the 1 before the decimal dot and 2 is written after the dot. This is because the 1 is added to the column consisting the number 0.
In order to add Decimals that have different numbers of decimal places take the following steps
Steps:
1)Place one digit below the other so that the bottom decimal point is directly below the top decimal point.
2) Add each column starting at the right side.
Example: Add 9.275 + 15.57
9.275
+15.57
15.845
Subtraction:
Subtracting two Decimal numbers is similar in process as what done with whole numbers.
Steps:
1) Put the decimal points of the greater number over the smaller number when subtracting decimal numbers. (Also read fraction to decimal converter)
37.721
- 21.005
2) Subtract the numbers as done with whole numbers.
37.721
- 21.005
16.716
3) Put the decimal point in the proper place of the answer.
In order to multiply a three digit decimal by a one digit decimal number follow these steps
Steps:
1) Place one decimal number above the other so that they are placed on the right side sequentially vertical.
2) Avoid the decimal points for sometime and multiply the numbers like multiplying a three digit number by a one digit number.
0.529
0.7
3) Multiply the two numbers on the right side. (9 * 7 = 63). This number is larger than 10 so place 6 above the center column and place three below the line in the right column.
6
0.529
0.7
3
4) Multiply the digit in the top center column (2) by the digit in the center of the right column (7). The answer (2*7=14) is added to the 6 above the center column to give an answer of 20. The units place value (0) of 20 is placed below the line and the tens place value (2) of the 20 is placed above the five.
26
0.529
0.7
03
5) The 5 of the top number is multiplied by the 7 of the multiplier (5*7=35). The two that was previously carried is added and 37 is placed below the line. At the start we disregarded the decimal places. Count the decimal places and move the decimal place to its proper location. There are three decimal places in 0.529 and one in the decimal 0.7 so move the decimal four places to the left to give the final answer of 0.3703.
26
0.529
0.7
0.3703
In upcoming posts we will discuss about Fractions in Grade IV and adding and subtracting integers worksheets. Visit our website for information on CBSE computer science syllabus
