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ID : in-5-Decimal-Numbers [1] Class 5 Decimal Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) What do you get when you subtract the sum of 661.15 and 26.32 f rom 736.81? (2) Which number is 71.16 larger than the largest 4-digit number? (3) What do you get when you multiply 6.5 and 9.42? (4) Fill in the blank with < , > , or = sign: 0.000606 ____ 0.0616 (5) What do you get when you add the f ollowing decimals: 325.33 and 5.89? Choose correct answer(s) f rom given choice (6) T he place value of 7 in 1860.7425 is a. 7 T enths b. T housandths c. 7 Hundreds d. 7 T en thousandths (7) What number do you get by adding 2 T housandths and 95 T en thousandths together to 21 T en T housands? (8) a. 210003.8115 b. 210000.0115 c. 21000001.15 d. 2100.000115 T ake away One T enths seven times f rom 1 and you are lef t with a. 0.1 b. 0.3 c. 0.7 d. none of these (9) At a construction site, there are 13.5 loads of bricks, and the total weight of all the loads together is 311.445 kgs. What is the weight of one load? a. 22.89 kg b. 23.14 kg c. 23.07 kg d. 23.18 kg (10) Which of the f ollowing represents the number two Hundredths in decimal f orm a. 0.02000 b. 0.000200 c. 0.20000 d. 2.00000 (11) Shilpa drove 44.802 kms to visit her grandmother. When she reached her grandmother's house she noticed the car had used up 3.93 litres of petrol. How many kilometers did she travel per litre of petrol? a. 11.38 km b. 11.4 km c. 11.56 km d. 11.26 km (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [2] Fill in t he blanks (12) A snail crawls 23 cm in 15 minutes. It crawls another 57 cm in 38 minutes. T he total distance it crawls is (13) metres. 127.88 + 40.79 + 0.2 = (14) How is the number thirty-one and sixteen T en thousandths written in decimal f orm as (15) Meenakshi bought the f ollowing things when she got her f irst salary of Rs.60000 A gaming system f or Rs.2276.95 A microwave f or Rs.6167.05 A computer f or Rs.21970.50. Now Rs. is lef t with her. © 2016 Edugain (www.edugain.com). All Rights Reserved (C) 2016 Edugain (www.Edugain.com) Many more such worksheets can be generated at www.edugain.com Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [3] Answers (1) 49.34 Step 1 Let us f irst f ind the sum of the Like Decimal numbers 661.15 and 26.32. Decimals with the same number of decimal places are called Like Decimals. Step 2 Let us add starting f rom the hundredths and carry over if needed. T he decimal point in the answer will be placed as being placed in the addends: T en T housands T housands Hundreds T ens Ones . T enth Hundredth 6 + 6 6 1 . 1 5 2 6 . 3 2 8 7 . 4 7 Step 3 Let us now subtract the sum 687.47 f rom 736.81 by placing the digits of these two Like Fractions according to their place values T en T housands T housands Hundreds T ens Ones . T enth Hundredth - 7 3 6 . 8 1 6 8 7 . 4 7 0 4 9 . 3 4 Step 4 Hence, when we subtract the sum of 661.15 and 26.32 f rom 736.81, we get 49.34. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [4] (2) 10070.16 Step 1 T he largest 4-digit number is 9999 (a whole number). Step 2 T he number 71.16 larger than 9999 can be f ound by adding the numbers 71.16 and 9999. Step 3 Let us f irst convert the whole number 9999 into decimal f orm. In decimal f orm, 9999 can be written as 9999.00. Decimals with the same number of decimal places are called like decimals. Step 4 Now, our task is to add the Like Decimals 71.16 and 9999.00. Let us add them starting f rom the hundredths and carry over if needed. T he decimal point in the answer will be placed as being placed in the addends: Hundred T housands T en T housands T housands Hundreds T ens Ones . T enth Hundredth 9 9 + 1 0 0 9 9 . 0 0 7 1 . 1 6 7 0 . 1 6 Step 5 Hence, the number 71.16 larger than the largest 4-digit number is 10070.16. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [5] (3) 61.230 Step 1 In order to multiply the two decimal numbers, let us f irst f ind out the position of the decimal point in the f inal product. Step 2 Let us f irst count the number of decimal places in both the multiplicands. T he total number of decimal places in the product will be the sum of the number of decimal places in both the multiplicands. Step 3 In the number 6.5, there is 1 decimal place and in 9.42 there are 2 decimal places. Hence, there will be a total of 3 decimal places in the f inal product. Step 4 Now, let us multiply the two numbers just like whole numbers, and in the f inal product place the decimal point such that there are 3 decimal places (i.e. af ter 3 places f rom the right): 9 4 2 x 6 5 4 7 1 0 5 6 5 2 0 6 1 2 3 0 Step 5 Now put the decimal point af ter three places f rom right. T heref ore, 9.42 × 6.5 = 61.230 (4) < Step 1 In the given problem we must f irst compare the whole numbers. Here, we see that the whole part f or both the numbers is ‘0’ and hence is equal. Step 2 However, we know that the given two numbers are not equal. So, let us compare the f ractional part. Step 3 Comparing the f ractional part of the two numbers, we f ind that .000606 < .0616. Step 4 Hence, 0.000606 < 0.0616. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [6] (5) 331.22 Step 1 Decimals with the same number of decimal places are called Like Decimals. T he numbers given here are theref ore Like Decimals. Step 2 In order to add the given Like Decimals, let us arrange the digits according to their place value, that is one below the other to make sure that the decimals are also placed exactly one below the other. T his way, we will place the ones below the ones, the tenths below the tenths and so on. Step 3 T he decimal point in the answer will be placed as being placed in the addends. Step 4 Let us add the numbers digit by digit starting f rom the hundredths and carry over if needed: T housands Hundreds T ens Ones . T enth Hundredth 3 2 + 3 3 5 . 3 3 5 . 8 9 1 . 2 2 Step 5 Hence, when we add the decimals 325.33 and 5.89, we get 331.22. (6) a. 7 T enths Step 1 Let’s use the place value chart and f ind where 7 is placed: 18607425 | Lakhs| T housands| | T L| L| Ones| T enths| Hundredths| T housandths| T en thousandths| T T H| T H| H| T | O| . (1/10)| 1 8 6 0 . 7 (1/100)| 4 (1/1000)| 2 (1/10000)| 5 Legend: T L - T en Lakhs, L - Lakhs, T T H - T en T housands, T H - T housands, H - Hundreds, T T ens, O - Ones. Step 2 From the above table, we observe that 7 is placed under the T enths place. Step 3 Hence, the place value of 7 in 1860.7425 is 7 T enths. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [7] (7) b. 210000.0115 Step 1 Let us f irst convert the number names into numerals: 2 T housandths = 2 ÷ 1000 = 0.002 95 T en thousandths = 95 ÷ 10000 = 0.0095 21 T en T housands = 21 × 10000 = 210000 Step 2 Let’s f irst add the decimal numbers as below: | T housands| Lakhs| | T L| L| Ones| T enths| Hundredths| T housandths| T en thousandths| T T H| T H| H| T | O| . (1/10)| T otal (1/100)| (1/1000)| (1/10000)| 0 . 0 0 2 0 0 . 0 0 9 5 0 . 0 1 1 5 Legend: T L - T en Lakhs, L - Lakhs, T T H - T en T housands, T H - T housands, H - Hundreds, T T ens, O - Ones. Step 3 Let us now add the decimal numbers with the whole number: | T housands| Ones| T enths| Hundredths| T housandths| T en thousandths| Lakhs| | T L| L| T otal T T H| T H| H| T | O| . (1/10)| (1/100)| (1/1000)| (1/10000)| 0 . 0 1 1 5 2 1 0 0 0 0 . 0 0 0 0 2 1 0 0 0 0 . 0 1 1 5 Step 4 T heref ore, by adding 2 T housandths and 95 T en thousandths together to 21 T en T housands, we get 210000.0115. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [8] (8) b. 0.3 Step 1 Look at the question caref ully and notice that One T enths of 1 = 1 , 10 and seven times of 1 10 = 7 10 = 0.7 Step 2 Now take One T enths seven times f rom 1 or subtracting 0.7 f rom 1 = 1 - 0.7 = 0.3 Step 3 T heref ore the lef t value with you, when you take away One T enths seven times f rom 1 is 0.3. (9) c. 23.07 kg Step 1 T he number of loads of bricks = 13.5 Step 2 T otal weight of all the loads together = 311.445 kgs Step 3 In order to f ind the weight of one load, we need to divide the total weight by the number of loads. Step 4 T heref ore, the weight of one load is 311.445 ÷ 13.5 = 23.07 kg. (10) a. 0.02000 Step 1 Let’s f irst convert the number name into number/f raction. So, two Hundredths can be written as: 2 100 Step 2 By converting the f raction into decimals, we get: 2 = 0.02 100 Step 3 T heref ore, the number two Hundredths in decimal f orm is 0.02. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [9] (11) b. 11.4 km Step 1 Distance that Shilpa drove to reach her grandmother's house = 44.802 kms Step 2 Number of litres used while driving = 3.93 litres Step 3 In order to know the number of kilometres per litre of petrol, we will need to divide the number of kilometers traveled Shilpa by the number of litres of petrol used. Step 4 T hus, the number of kilometers Shilpa travelled per litre of petrol = 44.802 ÷ 3.93 = 11.4 km/litre Step 5 T heref ore, the kilometres per litre of petrol (mileage of the car) is 11.4 km/liter. (12) 0.8 Step 1 T he total distance (in cm) the snail crawls: 23 cm + 57 cm = 80 cm Step 2 Let us now convert the distance 80 cm (centimetres) into distance in meters as below. We know that: 100 cm = 1 m T heref ore, 80 cm = 80 m = 0.8 m 100 Step 3 Hence, the snail crawls 0.8 m in the total time. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [10] (13) 168.87 Step 1 Decimals with the same number of decimal places are called Like Decimals. T he numbers given here are theref ore Like Decimals. Step 2 In order to add the given Like Decimals, let us arrange the digits according to their place value, that is one below the other to make sure that the decimals are also placed exactly one below the other. T his way, we will place the ones below the ones, the tenths below the tenths and so on. Step 3 T he decimal point in the answer will be placed as being placed in the addends. Step 4 Let us add the numbers digit by digit starting f rom the hundredths and carry over if needed: T housands Hundreds T ens Ones . T enth Hundredth 1 2 7 . 8 8 4 0 . 7 9 0 . 2 0 8 . 8 7 + 1 6 Step 5 Hence, when we add the decimals 127.88, 40.79, and 0.2 we get 168.87 (14) 31.0016 (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : in-5-Decimal-Numbers [11] (15) 29585.50 Step 1 Amount received by Meenakshi as salary = Rs.60000 Step 2 Let us add the amounts spent by Meenakshi f or purchasing various things: T en T housands Hundreds T ens Ones . T enth Hundredth T housands A gaming 2 2 7 6 . 9 5 6 1 6 7 . 0 5 system A microwave A computer 2 1 9 7 0 . 5 0 T otal 3 0 4 1 4 . 5 0 Expense Hence, Meenakshi's total expense is Rs.30414.50. Step 3 In order to f ind the amount lef t with Meenakshi, let us subtract her f irst salary with her total expense: Amount lef t with Meenakshi = Meenakshi's salary - Meenakshi's total expense = 60000 - 30414.50 = 60000.00 - 30414.50 ...(Writing 60000 in decimal f orm 60000.00 so that the two numbers are Like Decimals) Step 4 Now, let us subtract 30414.50 f rom 60000.00 by placing the digits of two decimal numbers according to their place values: T en T housands T housands Hundreds T ens Ones . T enth Hundredth - 6 0 0 0 0 . 0 0 3 0 4 1 4 . 5 0 2 9 5 8 5 . 5 0 Step 5 Hence, af ter shopping Meenakshi is lef t with Rs.29585.50. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited