Page 1 Savita and Shama were going to market to buy some stationary items. Savita said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50 paise”. They knew how to write rupees and paise using decimals. So Savita said, I have Rs 5.75 and Shama said, “I have Rs 7.50”. Have they written correctly? We know that the dot represents a decimal point. In this chapter, we will learn more about working with decimals. 8.2 Tenths Ravi and Raju measured the lengths of their pencils. Ravi’s pencil was 7 cm 5mm long and Raju’s pencil was 8 cm 3 mm long. Can you express these lengths in centimetre using decimals? We know that 10 mm = 1 cm Therefore, 1 mm = 1 10 cm or one-tenth cm = 0.1 cm Now, length of Ravi’s pencil = 7cm 5mm = 7 5 10 cm i.e. 7cm and 5 tenths of a cm = 7.5cm The length of Raju’s pencil = 8 cm 3 mm = 8 3 10 cm i.e. 8 cm and 3 tenths of a cm = 8.3 cm 8.1 Introduction Chapter 8 D D De e ec c ci i im m ma a al l ls s s Page 2 Savita and Shama were going to market to buy some stationary items. Savita said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50 paise”. They knew how to write rupees and paise using decimals. So Savita said, I have Rs 5.75 and Shama said, “I have Rs 7.50”. Have they written correctly? We know that the dot represents a decimal point. In this chapter, we will learn more about working with decimals. 8.2 Tenths Ravi and Raju measured the lengths of their pencils. Ravi’s pencil was 7 cm 5mm long and Raju’s pencil was 8 cm 3 mm long. Can you express these lengths in centimetre using decimals? We know that 10 mm = 1 cm Therefore, 1 mm = 1 10 cm or one-tenth cm = 0.1 cm Now, length of Ravi’s pencil = 7cm 5mm = 7 5 10 cm i.e. 7cm and 5 tenths of a cm = 7.5cm The length of Raju’s pencil = 8 cm 3 mm = 8 3 10 cm i.e. 8 cm and 3 tenths of a cm = 8.3 cm 8.1 Introduction Chapter 8 D D De e ec c ci i im m ma a al l ls s s DECIMALS 165 Let us recall what we have learnt earlier. If we show units by blocks then one unit is one block, two units are two blocks and so on. One block divided into 10 equal parts means each part is 1 10 (one-tenth) of a unit, 2 parts show 2 tenths and 5 parts show 5 tenths and so on. A combination of 2 blocks and 3 parts (tenths) will be recorded as : Ones Tenths (1) ( 1 10 ) 2 3 It can be written as 2.3 and read as two point three. Let us look at another example where we have more than ‘ones’. Each tower represents 10 units. So, the number shown here is : i.e. 20 + 3 + 5 10 = 23.5 This is read as ‘twenty three point five’. 1. Can you now write the following as decimals? Hundreds Tens Ones Tenths (100) (10) (1) ( 1 10 ) 5 3 8 1 2 7 3 4 3 5 4 6 2. Write the lengths of Ravi’s and Raju’s pencils in ‘cm’ using decimals. 3. Make three more examples similar to the one given in question 1 and solve them. Tens Ones Tenths (10) (1) ( 1 10 ) 2 3 5 Page 3 Savita and Shama were going to market to buy some stationary items. Savita said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50 paise”. They knew how to write rupees and paise using decimals. So Savita said, I have Rs 5.75 and Shama said, “I have Rs 7.50”. Have they written correctly? We know that the dot represents a decimal point. In this chapter, we will learn more about working with decimals. 8.2 Tenths Ravi and Raju measured the lengths of their pencils. Ravi’s pencil was 7 cm 5mm long and Raju’s pencil was 8 cm 3 mm long. Can you express these lengths in centimetre using decimals? We know that 10 mm = 1 cm Therefore, 1 mm = 1 10 cm or one-tenth cm = 0.1 cm Now, length of Ravi’s pencil = 7cm 5mm = 7 5 10 cm i.e. 7cm and 5 tenths of a cm = 7.5cm The length of Raju’s pencil = 8 cm 3 mm = 8 3 10 cm i.e. 8 cm and 3 tenths of a cm = 8.3 cm 8.1 Introduction Chapter 8 D D De e ec c ci i im m ma a al l ls s s DECIMALS 165 Let us recall what we have learnt earlier. If we show units by blocks then one unit is one block, two units are two blocks and so on. One block divided into 10 equal parts means each part is 1 10 (one-tenth) of a unit, 2 parts show 2 tenths and 5 parts show 5 tenths and so on. A combination of 2 blocks and 3 parts (tenths) will be recorded as : Ones Tenths (1) ( 1 10 ) 2 3 It can be written as 2.3 and read as two point three. Let us look at another example where we have more than ‘ones’. Each tower represents 10 units. So, the number shown here is : i.e. 20 + 3 + 5 10 = 23.5 This is read as ‘twenty three point five’. 1. Can you now write the following as decimals? Hundreds Tens Ones Tenths (100) (10) (1) ( 1 10 ) 5 3 8 1 2 7 3 4 3 5 4 6 2. Write the lengths of Ravi’s and Raju’s pencils in ‘cm’ using decimals. 3. Make three more examples similar to the one given in question 1 and solve them. Tens Ones Tenths (10) (1) ( 1 10 ) 2 3 5 MATHEMATICS 166 Representing Decimals on number line We represented fractions on a number line. Let us now represent decimals too on a number line. Let us represent 0.6 on a number line. We know that 0.6 is more than zero but less than one. There are 6 tenths in it. Divide the unit length between 0 and 1 into 10 equal parts and take 6 parts as shown below : Write five numbers between 0 and 1 and show them on the number line. Can you now represent 2.3 on a number line? Check, how many ones and tenths are there in 2.3. Where will it lie on the number line? Show 1.4 on the number line. Example 1 : Write the following numbers in the place value table : (a) 20.5 (b) 4.2 Solution : Let us make a common place value table, assigning appropriate place value to the digits in the given numbers. We have, Tens (10) Ones (1) Tenths ( 1 10 ) 20.5 2 0 5 4.2 0 4 2 Example 2 : Write each of the following as decimals : (a) Two ones and five-tenths (b) Thirty and one-tenth Solution : (a) Two ones and five-tenths = 2 + 5 10 = 2.5 (b) Thirty and one-tenth = 30 + 1 10 = 30.1 Example 3 : Write each of the following as decimals : (a) 30 + 6 + 2 10 (b) 600 + 2 + 8 10 Solution : (a) 30 + 6 + 2 10 How many tens, ones and tenths are there in this number? We have 3 tens, 6 ones and 2 tenths. Therefore, the decimal representation is 36.2. (b) 600 + 2 + 8 10 Note that it has 6 hundreds, no tens, 2 ones and 8 tenths. Therefore, the decimal representation is 602.8 Page 4 Savita and Shama were going to market to buy some stationary items. Savita said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50 paise”. They knew how to write rupees and paise using decimals. So Savita said, I have Rs 5.75 and Shama said, “I have Rs 7.50”. Have they written correctly? We know that the dot represents a decimal point. In this chapter, we will learn more about working with decimals. 8.2 Tenths Ravi and Raju measured the lengths of their pencils. Ravi’s pencil was 7 cm 5mm long and Raju’s pencil was 8 cm 3 mm long. Can you express these lengths in centimetre using decimals? We know that 10 mm = 1 cm Therefore, 1 mm = 1 10 cm or one-tenth cm = 0.1 cm Now, length of Ravi’s pencil = 7cm 5mm = 7 5 10 cm i.e. 7cm and 5 tenths of a cm = 7.5cm The length of Raju’s pencil = 8 cm 3 mm = 8 3 10 cm i.e. 8 cm and 3 tenths of a cm = 8.3 cm 8.1 Introduction Chapter 8 D D De e ec c ci i im m ma a al l ls s s DECIMALS 165 Let us recall what we have learnt earlier. If we show units by blocks then one unit is one block, two units are two blocks and so on. One block divided into 10 equal parts means each part is 1 10 (one-tenth) of a unit, 2 parts show 2 tenths and 5 parts show 5 tenths and so on. A combination of 2 blocks and 3 parts (tenths) will be recorded as : Ones Tenths (1) ( 1 10 ) 2 3 It can be written as 2.3 and read as two point three. Let us look at another example where we have more than ‘ones’. Each tower represents 10 units. So, the number shown here is : i.e. 20 + 3 + 5 10 = 23.5 This is read as ‘twenty three point five’. 1. Can you now write the following as decimals? Hundreds Tens Ones Tenths (100) (10) (1) ( 1 10 ) 5 3 8 1 2 7 3 4 3 5 4 6 2. Write the lengths of Ravi’s and Raju’s pencils in ‘cm’ using decimals. 3. Make three more examples similar to the one given in question 1 and solve them. Tens Ones Tenths (10) (1) ( 1 10 ) 2 3 5 MATHEMATICS 166 Representing Decimals on number line We represented fractions on a number line. Let us now represent decimals too on a number line. Let us represent 0.6 on a number line. We know that 0.6 is more than zero but less than one. There are 6 tenths in it. Divide the unit length between 0 and 1 into 10 equal parts and take 6 parts as shown below : Write five numbers between 0 and 1 and show them on the number line. Can you now represent 2.3 on a number line? Check, how many ones and tenths are there in 2.3. Where will it lie on the number line? Show 1.4 on the number line. Example 1 : Write the following numbers in the place value table : (a) 20.5 (b) 4.2 Solution : Let us make a common place value table, assigning appropriate place value to the digits in the given numbers. We have, Tens (10) Ones (1) Tenths ( 1 10 ) 20.5 2 0 5 4.2 0 4 2 Example 2 : Write each of the following as decimals : (a) Two ones and five-tenths (b) Thirty and one-tenth Solution : (a) Two ones and five-tenths = 2 + 5 10 = 2.5 (b) Thirty and one-tenth = 30 + 1 10 = 30.1 Example 3 : Write each of the following as decimals : (a) 30 + 6 + 2 10 (b) 600 + 2 + 8 10 Solution : (a) 30 + 6 + 2 10 How many tens, ones and tenths are there in this number? We have 3 tens, 6 ones and 2 tenths. Therefore, the decimal representation is 36.2. (b) 600 + 2 + 8 10 Note that it has 6 hundreds, no tens, 2 ones and 8 tenths. Therefore, the decimal representation is 602.8 DECIMALS 167 Write 3 2 4 5 8 5 , , in decimal notation. Fractions as decimals We have already seen how a fraction with denominator 10 can be represented using decimals. Let us now try to find decimal representation of (a) 11 5 (b) 1 2 (a) We know that 11 5 = 22 10 = 20 2 10 + = 20 10 + 2 10 = 2 + 2 10 = 2.2 Therefore, 22 10 = 2.2 (in decimal notation.) (b) In 1 2 , the denominator is 2. For writing in decimal notation, the denominator should be 10. We already know how to make an equivalent fraction. So, 1 2 = 1 5 2 5 5 10 × × = = 0.5 Therefore, 1 2 is 0.5 in decimal notation. Decimals as fractions Till now we have learnt how to write fractions with denominators 10, 2 or 5 as decimals. Can we write a decimal number like 1.2 as a fraction? Let us see 12 1 2 10 . = + = 10 10 + = 2 10 12 10 EXERCISE 8.1 1. Write the following as numbers in the given table. (a) (b) T ens Ones T enths Hundreds T ens T enths Hundreds Tens Ones Tenths (100) (10) (1) ( 1 10 ) Page 5 Savita and Shama were going to market to buy some stationary items. Savita said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50 paise”. They knew how to write rupees and paise using decimals. So Savita said, I have Rs 5.75 and Shama said, “I have Rs 7.50”. Have they written correctly? We know that the dot represents a decimal point. In this chapter, we will learn more about working with decimals. 8.2 Tenths Ravi and Raju measured the lengths of their pencils. Ravi’s pencil was 7 cm 5mm long and Raju’s pencil was 8 cm 3 mm long. Can you express these lengths in centimetre using decimals? We know that 10 mm = 1 cm Therefore, 1 mm = 1 10 cm or one-tenth cm = 0.1 cm Now, length of Ravi’s pencil = 7cm 5mm = 7 5 10 cm i.e. 7cm and 5 tenths of a cm = 7.5cm The length of Raju’s pencil = 8 cm 3 mm = 8 3 10 cm i.e. 8 cm and 3 tenths of a cm = 8.3 cm 8.1 Introduction Chapter 8 D D De e ec c ci i im m ma a al l ls s s DECIMALS 165 Let us recall what we have learnt earlier. If we show units by blocks then one unit is one block, two units are two blocks and so on. One block divided into 10 equal parts means each part is 1 10 (one-tenth) of a unit, 2 parts show 2 tenths and 5 parts show 5 tenths and so on. A combination of 2 blocks and 3 parts (tenths) will be recorded as : Ones Tenths (1) ( 1 10 ) 2 3 It can be written as 2.3 and read as two point three. Let us look at another example where we have more than ‘ones’. Each tower represents 10 units. So, the number shown here is : i.e. 20 + 3 + 5 10 = 23.5 This is read as ‘twenty three point five’. 1. Can you now write the following as decimals? Hundreds Tens Ones Tenths (100) (10) (1) ( 1 10 ) 5 3 8 1 2 7 3 4 3 5 4 6 2. Write the lengths of Ravi’s and Raju’s pencils in ‘cm’ using decimals. 3. Make three more examples similar to the one given in question 1 and solve them. Tens Ones Tenths (10) (1) ( 1 10 ) 2 3 5 MATHEMATICS 166 Representing Decimals on number line We represented fractions on a number line. Let us now represent decimals too on a number line. Let us represent 0.6 on a number line. We know that 0.6 is more than zero but less than one. There are 6 tenths in it. Divide the unit length between 0 and 1 into 10 equal parts and take 6 parts as shown below : Write five numbers between 0 and 1 and show them on the number line. Can you now represent 2.3 on a number line? Check, how many ones and tenths are there in 2.3. Where will it lie on the number line? Show 1.4 on the number line. Example 1 : Write the following numbers in the place value table : (a) 20.5 (b) 4.2 Solution : Let us make a common place value table, assigning appropriate place value to the digits in the given numbers. We have, Tens (10) Ones (1) Tenths ( 1 10 ) 20.5 2 0 5 4.2 0 4 2 Example 2 : Write each of the following as decimals : (a) Two ones and five-tenths (b) Thirty and one-tenth Solution : (a) Two ones and five-tenths = 2 + 5 10 = 2.5 (b) Thirty and one-tenth = 30 + 1 10 = 30.1 Example 3 : Write each of the following as decimals : (a) 30 + 6 + 2 10 (b) 600 + 2 + 8 10 Solution : (a) 30 + 6 + 2 10 How many tens, ones and tenths are there in this number? We have 3 tens, 6 ones and 2 tenths. Therefore, the decimal representation is 36.2. (b) 600 + 2 + 8 10 Note that it has 6 hundreds, no tens, 2 ones and 8 tenths. Therefore, the decimal representation is 602.8 DECIMALS 167 Write 3 2 4 5 8 5 , , in decimal notation. Fractions as decimals We have already seen how a fraction with denominator 10 can be represented using decimals. Let us now try to find decimal representation of (a) 11 5 (b) 1 2 (a) We know that 11 5 = 22 10 = 20 2 10 + = 20 10 + 2 10 = 2 + 2 10 = 2.2 Therefore, 22 10 = 2.2 (in decimal notation.) (b) In 1 2 , the denominator is 2. For writing in decimal notation, the denominator should be 10. We already know how to make an equivalent fraction. So, 1 2 = 1 5 2 5 5 10 × × = = 0.5 Therefore, 1 2 is 0.5 in decimal notation. Decimals as fractions Till now we have learnt how to write fractions with denominators 10, 2 or 5 as decimals. Can we write a decimal number like 1.2 as a fraction? Let us see 12 1 2 10 . = + = 10 10 + = 2 10 12 10 EXERCISE 8.1 1. Write the following as numbers in the given table. (a) (b) T ens Ones T enths Hundreds T ens T enths Hundreds Tens Ones Tenths (100) (10) (1) ( 1 10 ) MATHEMATICS 168 2. Write the following decimals in the place value table. (a) 19.4 (b) 0.3 (c) 10.6 (d) 205.9 3. Write each of the following as decimals : (a) Seven-tenths (b) Two tens and nine-tenths (c) Fourteen point six (d) One hundred and two ones (e) Six hundred point eight 4. Write each of the following as decimals: (a) 5 10 (b) 3 + 7 10 (c) 200 + 60 + 5 + 1 10 (d) 70 + 8 10 (e) 88 10 (f) 4 2 10 (g) 3 2 (h) 2 5 (i) 12 5 (j) 3 3 5 (k) 4 1 2 5. Write the following decimals as fractions. Reduce the fractions to lowest form. (a) 0.6 (b) 2.5 (c) 1.0 (d) 3.8 (e) 13.7 (f) 21.2 (g) 6.4 6. Express the following as cm using decimals. (a) 2 mm (b) 30 mm (c) 116 mm (d) 4 cm 2 mm (e) 162 mm (f) 83 mm 7. Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number? (a) 0.8 (b) 5.1 (c) 2.6 (d) 6.4 (e) 9.1 (f) 4.9 8. Show the following numbers on the number line. (a) 0.2 (b) 1.9 (c) 1.1 (d) 2.5 9. Write the decimal number represented by the points A, B, C, D on the given number line. 10. (a) The length of Ramesh’s notebook is 9 cm 5 mm. What will be its length in cm? (b) The length of a young gram plant is 65 mm. Express its length in cm. 8.3 Hundredths David was measuring the length of his room. He found that the length of his room is 4 m and 25 cm. He wanted to write the length in metres. Can you help him? What part of a metre will be one centimetre?Read More

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### Chapter Notes - Decimals

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### NCERT Solutions(Part -1) - Decimals

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### NCERT Solutions(Part - 2) - Decimals

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### Understanding Tenths and Hundredths Place

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### Worksheet Question - Decimals

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### Representing Decimal Numbers on Number line

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- Addition and Subtraction of Unlike Fractions
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- Addition and Subtraction of Like Fractions
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