Basic Concept of Decimal<\/span><\/h2>\nThe decimal number system is called the base-ten positional number system. Generally, a decimal numeral refers to the notation of a number in the decimal numeral system. The representation of decimal numbers is known as decimal fractions.<\/p>\n
Decimal numbers do not allow the exact representation of the real numbers. Usually, there are two parts in decimal numbers one is the whole number part and the other is the fraction part. And the decimal point or point is represented by (.)<\/p>\n
Types of Decimals<\/h3>\n
The decimal numbers are of three types. They are
\n1. Recurring Decimal Numbers
\n2. Non-Recurring Decimal Numbers
\n3. Decimal Fraction<\/p>\n
1. Recurring Decimal Numbers:<\/strong>
\nRecurring Decimal Numbers are known as Repeating or Non-Terminal Decimals. It consists of finite or infinite numbers.
\nExample:
\n3.12 is Finite
\n3.2454… is Infinite
\n2. Non-Recurring Decimal Numbers:<\/strong>
\nNon-Recurring Decimal Numbers are known as Non-Repeating or Terminal Decimals with finite or infinite numbers.
\nExample:
\n4.534 is Finite
\n1.7321…is Infinite
\n3. Decimal Fraction:<\/strong>
\nThe decimal fraction represents the power of 10. The point means 1 and the numbers after the points will be zeros which are equal to the digits according to the place value.
\nExample:<\/strong> Convert the decimal 1.23 into the decimal fraction.
\nSolution:<\/strong>
\nThere are two numbers after the point
\nThe decimal point ‘.’ is equal to 1
\n‘2’ represents hundredths of positions
\n‘3’ represents tenths positions<\/p>\nConcept of Decimal Places<\/h3>\n
The place value<\/a> represents the position of the digits in a number. The Place values in decimals will determine its value or position. The position of the digit is important in decimals. So, it is necessary to know the place values in decimals.
\nExample:<\/strong>
\nWrite the place value in decimals for 12.36
\nSolution:<\/strong>
\nThe position of 1 is the tens place
\nThe position of 2 is the ones place.
\nThe position of 3 is the tenths place
\nThe position of 6 is hundredths place<\/p>\nProperties of Decimals<\/h3>\n
There are some properties of decimal numbers under arithmetic operations. The properties of decimals are as follows
\nProperty 1:<\/strong>
\nIf a decimal number or fraction is multiplied by 0, the product is 0.
\nExample:<\/strong> 1.2 \u00d7 0 = 0
\nProperty 2.<\/strong>
\nIf a decimal number or fraction is multiplied by 1, the product is the decimal fraction itself.
\nExample:<\/strong> 1.2 \u00d7 1 = 1.2
\nProperty 3:<\/strong>
\nIf any two decimal numbers are multiplied in any order, the product remains the same.
\nExample:<\/strong> 0.1 \u00d7 0.3 = 0.3 \u00d7 0.1
\nProperty 4:<\/strong>
\nIf 0 is divided by any decimal number, the quotient will be 0.
\nExample:<\/strong> 0 \u00f7 1.2 = 0
\nProperty 5:<\/strong>
\nIf a decimal number or fraction is divided by 1, the quotient is the decimal number.
\nExample:<\/strong> 1.2 \u00f7 1 = 1.2
\nProperty 6:<\/strong>
\nIf a decimal number or fraction is divided by the same number, then the quotient is 1.
\nExample:<\/strong> 1.24 \u00f7 1.24 = 1
\nProperty 8:<\/strong>
\nThe division of the decimal number or whole number is not possible.
\nExample:<\/strong> 1.2 \u00f7 0 = undefined<\/p>\nArithmetic Operations on Decimals<\/h3>\n
Arithmetic Operations are of four types such as addition, subtraction, multiplication, and division. Let us discuss how the arithmetic operations are applicable in decimal numbers with examples.
\n1. Addition:<\/strong> In decimal numbers, we line up the numbers according to the decimal points and then add the numbers.
\nExample:
\n1.2 + 1.2 = 2.4
\n2. Subtraction:<\/strong> In decimal numbers, we line up the numbers according to the decimal points and then subtract the numbers.
\nExample: 2.4 – 1.2 = 1.2
\n3. Multiplication:<\/strong> In multiplication, the numbers will be multiplied by ignoring the decimal points. After the result, we add the decimal points from left to right.
\nExample: Multiply 6.25 \u00d7 2.5
\n4. Division:<\/strong> In division operations, the decimal points will be shifted from right to left.
\nExample: 6.26 \u00f7 10 = 0.626<\/p>\nDecimal Examples<\/h3>\n
Example 1.<\/strong>
\nAdd two decimal numbers 17.52 and 14.25
\nSolution:\u00a0<\/strong>
\nFirst, add the hundredths place
\n2 + 5 = 7
\nNow add tenths place value
\n5 + 2 = 7
\nAdd ones place value
\n7 + 4 = 11
\nPut the 1 in ones place and carry 1 to the tens place.
\nAdd tens place value
\n1 + 1 + 1 = 3
\n![\"Concept](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Concept-of-Decimals-img_2-300x244.jpg\")
\nThus the sum of two decimal numbers 17.52 and 14.25 is 31.77<\/p>\nExample 2.<\/strong>
\nMultiply the numbers 1.464 and 0.245.
\nSolution:\u00a0<\/strong>
\nThere are six decimal places in both numbers.
\nIgnore the decimal places and then multiply the two given numbers.
\n![\"Concept](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Concept-of-Decimals-img_1-271x300.jpg\")
\nAnd then rewrite the product by placing six decimal places in the result.
\nThus the multiplication of two decimal numbers 1.464 and 0.245 is 0.358680<\/p>\nExample 3.<\/strong>
\nConvert 3\/100 in decimal form.
\nSolution:<\/strong>
\nIn the fraction 3\/100, 3 is the numerator and 100 is the denominator.
\nDivide 3 by 100.
\n3 \u00f7 100 = 0.03
\nHere one represents 1 and two zeros represent two numbers after the points.<\/p>\nExample 4.<\/strong>
\nWrite the decimal place value for the highlighted numbers.
\ni. 12.534
\n<\/strong>ii. 0.46<\/strong>24
\niii. 1.2<\/strong>467
\nSolution:<\/strong>
\ni. 12.534
\n<\/strong>Here we have to write the place value for 4.
\n4 is placed 3 numbers after the decimal point.
\nSo, the decimal place value is 4 \u00d7 thousandth = 4 \u00d7 1\/1000
\nii. 0.46<\/strong>24
\nHere we have to write the place value for 6.
\n6 is placed two numbers after the decimal point.
\nSo, the decimal place value is 6 \u00d7 hundredth = 6 \u00d7 1\/100
\niii. 1.2<\/strong>467
\nHere we have to write the place value for 2.
\n2 is placed one number after the decimal point.
\nSo, the decimal place value is 2 \u00d7 tenths = 2 \u00d7 1\/10<\/p>\nExample 5.<\/strong>
\nMultiply the two decimal numbers 46.789 with 100.
\nSolution:<\/strong>
\nGiven the decimal numbers 46.789 and 100.
\nThe concept to use here is multiplying decimal with part 100
\nWe know that,
\nThe decimal point will shift to the right when we multiply with 10, 100, 1000…
\nHere we have to multiply with 100 which means there are two zeros.
\nSo we have to place the decimal point after the two numbers.
\nThat means 46.789 \u00d7 100 = 4678.9<\/p>\nFAQs on Concept of Decimals<\/h3>\n
1. What is the decimal number?<\/strong><\/p>\nDecimals are the integer and non-integer numbers which consist of two parts whole numbers and fractions and these are separated by the decimal point.
\nExample: 1.24 is a decimal number.<\/p>\n
2. What are the types of decimals?<\/strong><\/p>\nThere are three types of decimals. They are
\ni. Recurring decimals(Non-Terminating or Repeating)
\nii. Non-Recurring decimals (Terminating or Non-Repeating)
\niii. Decimal Fraction<\/p>\n
3. What are decimal places?<\/strong><\/p>\nThe position of a digit to the right of the decimal point in a number written in decimal notation.<\/p>\n","protected":false},"excerpt":{"rendered":"
In Math, a decimal number system is a standard system that is the same as the whole number. The whole number part and fraction part is separated by a decimal point. The left side part of the number is the fraction part and the right side part of the number is a whole number part. … Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":117748,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Concept-of-Decimal.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117732"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=117732"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117732\/revisions"}],"predecessor-version":[{"id":135431,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117732\/revisions\/135431"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/117748"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=117732"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=117732"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=117732"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n1. Recurring Decimal Numbers
\n2. Non-Recurring Decimal Numbers
\n3. Decimal Fraction<\/p>\n
\nRecurring Decimal Numbers are known as Repeating or Non-Terminal Decimals. It consists of finite or infinite numbers.
\nExample:
\n3.12 is Finite
\n3.2454… is Infinite
\n2. Non-Recurring Decimal Numbers:<\/strong>
\nNon-Recurring Decimal Numbers are known as Non-Repeating or Terminal Decimals with finite or infinite numbers.
\nExample:
\n4.534 is Finite
\n1.7321…is Infinite
\n3. Decimal Fraction:<\/strong>
\nThe decimal fraction represents the power of 10. The point means 1 and the numbers after the points will be zeros which are equal to the digits according to the place value.
\nExample:<\/strong> Convert the decimal 1.23 into the decimal fraction.
\nSolution:<\/strong>
\nThere are two numbers after the point
\nThe decimal point ‘.’ is equal to 1
\n‘2’ represents hundredths of positions
\n‘3’ represents tenths positions<\/p>\n
Concept of Decimal Places<\/h3>\n
The place value<\/a> represents the position of the digits in a number. The Place values in decimals will determine its value or position. The position of the digit is important in decimals. So, it is necessary to know the place values in decimals. There are some properties of decimal numbers under arithmetic operations. The properties of decimals are as follows Arithmetic Operations are of four types such as addition, subtraction, multiplication, and division. Let us discuss how the arithmetic operations are applicable in decimal numbers with examples. Example 1.<\/strong> Example 2.<\/strong> Example 3.<\/strong> Example 4.<\/strong> Example 5.<\/strong> 1. What is the decimal number?<\/strong><\/p>\n Decimals are the integer and non-integer numbers which consist of two parts whole numbers and fractions and these are separated by the decimal point. 2. What are the types of decimals?<\/strong><\/p>\n There are three types of decimals. They are 3. What are decimal places?<\/strong><\/p>\n The position of a digit to the right of the decimal point in a number written in decimal notation.<\/p>\n","protected":false},"excerpt":{"rendered":" In Math, a decimal number system is a standard system that is the same as the whole number. The whole number part and fraction part is separated by a decimal point. The left side part of the number is the fraction part and the right side part of the number is a whole number part. … Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":117748,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/06\/Concept-of-Decimal.png","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117732"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=117732"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117732\/revisions"}],"predecessor-version":[{"id":135431,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/117732\/revisions\/135431"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media\/117748"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=117732"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=117732"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=117732"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nExample:<\/strong>
\nWrite the place value in decimals for 12.36
\nSolution:<\/strong>
\nThe position of 1 is the tens place
\nThe position of 2 is the ones place.
\nThe position of 3 is the tenths place
\nThe position of 6 is hundredths place<\/p>\nProperties of Decimals<\/h3>\n
\nProperty 1:<\/strong>
\nIf a decimal number or fraction is multiplied by 0, the product is 0.
\nExample:<\/strong> 1.2 \u00d7 0 = 0
\nProperty 2.<\/strong>
\nIf a decimal number or fraction is multiplied by 1, the product is the decimal fraction itself.
\nExample:<\/strong> 1.2 \u00d7 1 = 1.2
\nProperty 3:<\/strong>
\nIf any two decimal numbers are multiplied in any order, the product remains the same.
\nExample:<\/strong> 0.1 \u00d7 0.3 = 0.3 \u00d7 0.1
\nProperty 4:<\/strong>
\nIf 0 is divided by any decimal number, the quotient will be 0.
\nExample:<\/strong> 0 \u00f7 1.2 = 0
\nProperty 5:<\/strong>
\nIf a decimal number or fraction is divided by 1, the quotient is the decimal number.
\nExample:<\/strong> 1.2 \u00f7 1 = 1.2
\nProperty 6:<\/strong>
\nIf a decimal number or fraction is divided by the same number, then the quotient is 1.
\nExample:<\/strong> 1.24 \u00f7 1.24 = 1
\nProperty 8:<\/strong>
\nThe division of the decimal number or whole number is not possible.
\nExample:<\/strong> 1.2 \u00f7 0 = undefined<\/p>\nArithmetic Operations on Decimals<\/h3>\n
\n1. Addition:<\/strong> In decimal numbers, we line up the numbers according to the decimal points and then add the numbers.
\nExample:
\n1.2 + 1.2 = 2.4
\n2. Subtraction:<\/strong> In decimal numbers, we line up the numbers according to the decimal points and then subtract the numbers.
\nExample: 2.4 – 1.2 = 1.2
\n3. Multiplication:<\/strong> In multiplication, the numbers will be multiplied by ignoring the decimal points. After the result, we add the decimal points from left to right.
\nExample: Multiply 6.25 \u00d7 2.5
\n4. Division:<\/strong> In division operations, the decimal points will be shifted from right to left.
\nExample: 6.26 \u00f7 10 = 0.626<\/p>\nDecimal Examples<\/h3>\n
\nAdd two decimal numbers 17.52 and 14.25
\nSolution:\u00a0<\/strong>
\nFirst, add the hundredths place
\n2 + 5 = 7
\nNow add tenths place value
\n5 + 2 = 7
\nAdd ones place value
\n7 + 4 = 11
\nPut the 1 in ones place and carry 1 to the tens place.
\nAdd tens place value
\n1 + 1 + 1 = 3
\n
\nThus the sum of two decimal numbers 17.52 and 14.25 is 31.77<\/p>\n
\nMultiply the numbers 1.464 and 0.245.
\nSolution:\u00a0<\/strong>
\nThere are six decimal places in both numbers.
\nIgnore the decimal places and then multiply the two given numbers.
\n
\nAnd then rewrite the product by placing six decimal places in the result.
\nThus the multiplication of two decimal numbers 1.464 and 0.245 is 0.358680<\/p>\n
\nConvert 3\/100 in decimal form.
\nSolution:<\/strong>
\nIn the fraction 3\/100, 3 is the numerator and 100 is the denominator.
\nDivide 3 by 100.
\n3 \u00f7 100 = 0.03
\nHere one represents 1 and two zeros represent two numbers after the points.<\/p>\n
\nWrite the decimal place value for the highlighted numbers.
\ni. 12.534
\n<\/strong>ii. 0.46<\/strong>24
\niii. 1.2<\/strong>467
\nSolution:<\/strong>
\ni. 12.534
\n<\/strong>Here we have to write the place value for 4.
\n4 is placed 3 numbers after the decimal point.
\nSo, the decimal place value is 4 \u00d7 thousandth = 4 \u00d7 1\/1000
\nii. 0.46<\/strong>24
\nHere we have to write the place value for 6.
\n6 is placed two numbers after the decimal point.
\nSo, the decimal place value is 6 \u00d7 hundredth = 6 \u00d7 1\/100
\niii. 1.2<\/strong>467
\nHere we have to write the place value for 2.
\n2 is placed one number after the decimal point.
\nSo, the decimal place value is 2 \u00d7 tenths = 2 \u00d7 1\/10<\/p>\n
\nMultiply the two decimal numbers 46.789 with 100.
\nSolution:<\/strong>
\nGiven the decimal numbers 46.789 and 100.
\nThe concept to use here is multiplying decimal with part 100
\nWe know that,
\nThe decimal point will shift to the right when we multiply with 10, 100, 1000…
\nHere we have to multiply with 100 which means there are two zeros.
\nSo we have to place the decimal point after the two numbers.
\nThat means 46.789 \u00d7 100 = 4678.9<\/p>\nFAQs on Concept of Decimals<\/h3>\n
\nExample: 1.24 is a decimal number.<\/p>\n
\ni. Recurring decimals(Non-Terminating or Repeating)
\nii. Non-Recurring decimals (Terminating or Non-Repeating)
\niii. Decimal Fraction<\/p>\n