DecimalsDecimalsDecimals - NCERT

1 Savita and Shama were going to market to buy some stationary said, I have 5 rupees and 75 paise . Shama said, I have 7 rupeesand 50 paise .They knew how to write rupees and paise using Savita said, I have ` and Shama said, I have ` .Have they written correctly?We know that the dot represents a decimal this chapter, we will learn more about workingwith TenthsRavi and Raju measured the lengths of their pencils. Ravi s pencil was7 cm 5mm long and Raju s pencil was 8 cm 3 mm long. Can you expressthese lengths in centimetre using decimals?We know that 10 mm= 1 cmTherefore, 1 mm= 110 cm or one-tenth cm = cmNow, length of Ravi s pencil= 7cm 5mm= 7510cm 7cm and 5 tenths of a cm= length of Raju s pencil= 8 cm 3 mm= 8310 cm 8 cm and 3 tenths of a cm= 8 Chapter 8 Chapter 8 Chapter 8 Chapter 8 DecimalsDecimalsDecimalsDecimalsDecimals 2021-22 DECIMALS165 Let us recall what we have learnt we show units by blocks then one unit isone block, two units are two blocks and soon.

2 One block divided into 10 equal partsmeans each part is 110 (one-tenth) of a unit, 2 parts show 2 tenths and 5parts show 5 tenths and so on. A combination of 2 blocks and 3 parts(tenths) will be recorded as :OnesTenths(1)(110)23It can be written as and read as two point us look at another example where we have more than ones . Eachtower represents 10 units. So, the number shown here is 20 + 3 + 510 = is read as twenty three point five . you now write the following as decimals?HundredsTensOnesTenths(100)(10) (1)(110)538127 the lengths of Ravi s and Raju s pencils in cm using three more examples similar to the one given in question 1 andsolve them.

3 TensOnes Tenths (10) (1) (110) 2 3 52021-22 MATHEMA TICS166 Representing Decimals on number lineWe represented fractions on a number line. Let us now represent decimalstoo on a number line. Let us represent on a number know that is more than zero but less than one. There are 6 tenths init. Divide the unit length between 0 and 1 into 10 equal parts and take 6 partsas shown below :Write five numbers between 0 and 1 and show them on the number you now represent on a number line? Check, how many ones andtenths are there in Where will it lie on the number line?Show on the number 1 : Write the following numbers in the place value table : (a) (b) : Let us make a common place value table, assigning appropriate placevalue to the digits in the given numbers.

4 We have,Tens (10)Ones (1)Tenths (110) 2 : Write each of the following as decimals : (a) Two ones andfive-tenths (b) Thirty and one-tenthSolution :(a) Two ones and five-tenths = 2 + 510 = (b) Thirty and one-tenth = 30 + 110 = 3 : Write each of the following as decimals :(a) 30 + 6 + 210(b) 600 + 2 + 810 Solution : (a) 30 + 6 + 210 How many tens, ones and tenths are there in this number? We have3 tens, 6 ones and 2 , the decimal representation is (b) 600 + 2 + 810 Note that it has 6 hundreds, no tens, 2 ones and 8 , the decimal representation is 324585, , in as decimalsWe have already seen how a fraction with denominator 10 can be representedusing us now try to find decimal representation of (a) 115 (b) 12(a)We know that 115 = 2210 = 20 210+ = 2010 + 210 = 2 + 210 = , 2210 = (in decimal notation.)

5 (b)In 12, the denominator is 2. For writing in decimal notation, thedenominator should be 10. We already knowhow to make an equivalent fraction. So,12 = 1 52 5510 = = , 12 is in decimal as fractionsTill now we have learnt how to write fractions with denominators 10, 2 or 5 asdecimals. Can we write a decimal number like as a fraction?Let us see 1 2 +=1010+=2101210 EXERCISE the following as numbers in the given table.(a)(b)TensOnesTenthsHundredsTensTe nthsHundredsTensOnesTenths(100)(10)(1)(1 10)2021-22 MATHEMA the following decimals in the place value table.(a) (b) (c) (d) 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 each of the following as decimals:(a)510(b)3 + 710(c)200 + 60 + 5 + 110(d)70 + 810(e)8810(f)4210(g)32(h)25(i)125(j)335( k) the following decimals as fractions .

6 Reduce the fractions to lowest form.(a) (b) (c) (d) (e) (f) (g) 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 which two whole numbers on the number line are the given numbers lie?Which of these whole numbers is nearer the number?(a) (b) (c) (d) (e) (f) the following numbers on the number line.(a) (b) (c) (d) the decimal number represented by the points A, B, C, D on the givennumber (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 HundredthsDavid was measuring the length of his found that the length of his room is 4 mand 25 wanted to write the length in you help him?

7 What part of a metre willbe one centimetre?2021-22 DECIMALS1691 cm = ( )1100m or one-hundredth of a means 25 cm = 25100 mNow ( )1100 means 1 part out of 100 parts of a whole. As we have done for110, let us try to show this a square and divide it into ten equal part is the shaded rectangle of this square?It is 110 or one-tenth or , see Fig (i).Now divide each such rectangle into ten equal get 100 small squares as shown in Fig (ii).Then what fraction is each small square of the wholesquare?Each small square is ( )1100or one-hundredth of thewhole square. In decimal notation, we write ( )1100= read it as zero point zero part of the whole square is the shaded portion, ifwe shade 8 squares, 15 squares, 50 squares, 92 squares ofthe whole square?

8 Take the help of following figures to portionsOrdinary fractionDecimal number8 squares_____92 squares_____Fig (ii)Fig (i)2021-22 MATHEMA TICS170 Let us look at some more place value number shown in the table above is 2 + 4103100+. In decimals, it iswritten as , which is read as two point four three .Example 4 : Fill the blanks in the table using block information given belowand write the corresponding number in decimal :The number is 100 + 30 + 2 + 110 + 5100 = 5 : Fill the blanks in the table and write the corresponding number indecimal form using block information given (1)Tenths (110)Hundredths ( )1100243 HundredsTensOnesTenthsHundredths(100)(10 )(1)(110)( )110013215 OnesTenthsHundredths(1)(110)( )11002021-22 DECIMALS171 Solution :Example 6 : Given the place value table, write the number in decimal.

9 The number is 2 100 + 4 10 + 3 1 + 2 110 + 5 ( )1100 = 200 + 40 + 3 + 210 + 5100 = first digit 2 is multiplied by 100; thenext digit 4 is multiplied by 10 (110 of 100);the next digit 3 is multiplied by 1. After this,the next multipling factor is 110; and then it is1100 (110 of 110).The decimal point comes between ones place and tenths place in adecimal is now natural to extend the place value table further, from hundredths to110 of hundredths us solve some 7 : Write as decimals.(a)45(b)34(c)71000 Solution : (a) We have to find a fraction equivalent to 45 whose denominatoris = 4 25 2810 = = (100)(10)(1)(110)( )110024325We can see that as we go fromleft to right, at every step themultiplying factor becomes110 of the previous (1)(110)( )1100142 Therefore, the number is TICS172(b)Here, we have to find a fraction equivalent to 34 with denominator 10 or100.

10 There is no whole number that gives 10 on multiplying by 4, therefore,we make the demominator 100 and we have,34=3 254 2575100 = = (c) Here, since the tenth and the hundredth place is , we write 71000 = 8 : Write as fractions in lowest terms.(a) (b) (c) : (a) = 4100 = 125=(b) = 2 + 34100234 2100 22175021750= + = +=(c) = 3421000 = 342 21000 2171500 =Example 9 : Write each of the following as a decimal.(a)200 + 30 + 5 +2109100+(b) 50 + 1106100+(c)16 + 31051000+Solution : (a) 200 + 30 + 5 + 2109100+ =+ + 235 211091100 = (b)50 + 1106100+ = 50 + 1 110 + 6 1100 = (c)16 + 31051000+ = 16 + 310010051000++ = 16 + 3 110 + 0 1100 + 5 11000 = 10 : Write each of the following as a decimal.