Maths Measurement Worksheets PDF

# 8 Measurement ## Learning Objectives - To understand and use different units of length, mass and capacity - To write measurements using decimals - To solve word problems on length, mass and capacity - To estimate measures ## Let's Get Started The students of Class IV are doing some experiments...

# 8 Measurement ## Learning Objectives - To understand and use different units of length, mass and capacity - To write measurements using decimals - To solve word problems on length, mass and capacity - To estimate measures ## Let's Get Started The students of Class IV are doing some experiments in the Science lab while measuring various objects. Which statements do you think are correct? Give reasons for your answer. - No, no, you should drop just 1 ml. - I should drop 1 kg of liquid. - You should drop - 1 km of liquid. - This paper should be about 1 mm long. - This table should weigh only 1 g. - Oh! I am so tired. I walked 1 km to get to school today. ## Measurement of Length Various units for the measurement of length include: kilometre, hectometre, decametre, metre, decimetre, centimetre and millimetre. The basic unit for measuring length is metre. A few examples from real life where measurement of length occurs are: - The distance (the measurement of length between two points or locations) between any two cities is measured in kilometres. - The length of a pencil is approximately 16 centimetres. ### Conversion of Units of Lengths Centimetre and millimetre are smaller units of measurements. These units are commonly used for measuring smaller lengths. Bigger units can be converted to smaller and smaller units can be converted to bigger units as shown below. | Multiples | | | |----------------------|---|---| | kilometre | km | | | hectometre | hm | | | decametre | dam | | | metre | m | | | decimetre | dm | | | centimetre | cm | | | millimetre | mm | | To convert **a bigger unit to a smaller unit**: multiply the bigger unit by 10 or multiples of 10. To convert **a smaller unit to a bigger unit**: divide the smaller unit by 10 or multiples of 10. ### Solved Examples **Example 1:** Convert 2 dam to dm. **Solution:** In the chart given above, between dam and dm, there are two multiplications by 10 (dam to m and m to dm). So, we multiply with 10 × 10 = 100. Therefore, 2 dam = 2 × 100 = 200 dm. **Example 2:** Find 1/4 of 9 m in cm. **Solution:** 1 m = 10 x 10 cm = 100 cm 1/4 × 9m = 1/4 × 9 × 100 = 225 cm. Therefore, 1/4 of 9 m = 225 cm. **Example 3:** 8 km 2 hm 5 dam 9 m = ____m. **Solution:** 8 km = 8 × 1000 = 8000 m 2 hm = 2 × 100 = 200 m 5 dam = 5 × 10 = 50 m 9m = 9×1 = 9m Therefore, 8 km 2 hm 5 dam 9 m = 8000 m + 200 m + 50 m + 9 m = 8259 m. **Go Easy!** - 1 km = 1000 m - 1/2 km = 500 m - 1/4 km = 250 m - 3/4 km = 750 m ### Exercise 8A 1. **Fill in the blanks.** - The length of my eraser is about 2 ___. - The height of a table is approximately 1 ___. 2. **Solve the following.** - 4 km = 4000 m - 1/3 of 6 m = ___ cm - 3/4 of 16 dm = ___ mm - 5 km 23 m = ___ m - 7 m 25 cm = ___ cm - 3 m 4 cm = ___ cm - 7 km 3 dam 2 m = ___ m - 5629 m = 5 km 120 m ___ m ## Measurement of Mass and Weight The mass of an object is the amount of matter that the object has. The weight of an object is the measure of the heaviness of the object. | Multiples | | | |----------------------|---|---| | kilogram | kg | | | hectogram | hg | | | decagram | dag | | | gram | g | | | decigram | dg | | | centigram | cg | | | milligram | mg | | Kilogram, hectogram, decagram, gram, decigram, centigram and milligram various units for the measurement of mass and weight of objects. The basic unit for measuring mass is gram. A few real-life examples where measurement of mass and weight occurs are: - The spices used in the kitchen are usually measured in milligrams or grams. - Fruit and vegetables are normally measured in grams or kilograms. - A teaspoon of salt is around 5 g. - A tablespoon of salt is around 15 g. - The weight of a Class IV boy would be around 30 kg. ### Conversion of Units of Mass To convert a bigger unit to a smaller unit, multiply by 10 or multiples of 10. To convert a smaller unit to a bigger unit, divide by 10 or multiples of 10. ### Solved Examples **Example 4:** Convert 5 kg to g. **Solution:** To convert a bigger unit to a smaller unit, we multiply. In the chart given above, between kg and g, there are three multiplications by 10 (kg to hg, hg to dag and dag to g). So, we multiply with 10 × 10 × 10 = 1000. So, 1 kg = 1000 g Therefore, 5 kg = 5 × 1000 = 5000 g. **Example 5:** Find 2/5 of 6 kg in g. **Solution:** 2/5 of 6 × 1000 (To convert kg to g, multiply by 1000.) 2/5 × 6 × 1000 = 2400 g. Therefore, 2/5 of 6 kg = 2400 g. **Example 6:** Solve 25 g 7 cg = ___ cg. **Solution:** 25 g = 25 × 100 = 2500 cg (To convert g to cg, multiply by 100.) Now, 2500 cg + 7 cg = 2507 cg So, 25 g 7 cg = 2507 cg. **Common Errors** - 25 g 7 cg = 2507 cg - 25 g 7 cg = 257 cg ### Exercise 8B 1. **Fill in the blanks.** - I bought 3 kg ___ apples from the market. - 7 kg = 1000 g - 1/5 of 9 kg = ___g - 3 kg 275 g = 3775 g - 1/5 of 4 kg = ___g - 5 kg 2 hg 1 dag 3 g = ___g - 2350 g = ___ kg - 2359 g = ___ kg - 8kg 9 hg 3 g = ___g ## Measurement of Capacity Kilolitre, hectolitre, decalitre, litre, decilitre, centilitre and millilitre are various units of measuring capacity. The basic unit for measuring capacity is litre. | Multiples | | | |----------------------|---|---| | kilolitre | kl | | | hectolitre | hl | | | decalitre | dal | | | litre | l | | | decilitre | dl | | | centilitre | cl | | | millilitre | ml | | A few real-life examples where measurement of capacity occurs are: - A bottle contains around 1 l of water. - A glass contains approximately 200 ml of water. - A bucket contains 15 l of water. Measuring spoons are used to measure ingredients while baking cookies and cakes. ### Conversion of Units of Capacity Follow the chart given below to convert the units of measurement of capacity. Bigger to smaller: multiply Smaller to Bigger: divide | | | | | | | | |---|---|---|---|---|---|---| | kl | hl | dal | l | dl | cl | ml | |× 10 | × 10 | × 10 | × 10 | × 10 | × 10 | × 10 | |÷ 10 | ÷ 10 | ÷ 10 | ÷ 10 | ÷ 10 | ÷ 10 | ÷ 10 | ### Solved Examples **Example 7:** Convert 4 l to ml. **Solution:** Based on the chart for the units of capacity, to move from l to ml, we need to multiply by 10 three times. So, we multiply with 10 × 10 × 10 = 1000. 1 l = 1000 ml 4 l = 4×1000 = 4000 ml ### Exercise 8C 1. **Fill in the blanks.** - This jar contains about ___ of milk. - A glass contains approximately ___ ml of water. - 9 kl = 9000 l - 6700 l = ___ kl - 1/5 of 4 kl = ___ l - 6701 l = ___ kl - 1/4 of 5 hl = ___ ml - 9 kl 2 hl 3 l = ___ l ## Understanding Measures in Decimals Consider a case where 38.579 kg is to be expressed in kg, hg, dag and g. - The number before the decimal, that is, 38 will be kg. - The first digit after the decimal, that is, 5 will be hectogram. - The next digit 7 will be decagram and the digit 9 will be gram. Therefore, 38.579 kg = 38 kg 5 hg 7 dag 9 g. **Note:** The units should be in the same order as in the charts. ## Mental Maths 1. Express 98 km 4 m in km. 2. Express 30 g 9 dg 5 mg in grams. ### Do you know? In ancient times, people used body parts as units of measurement. The length of a foot, the width of a finger and the distance of a step were some of the units of measurement. ## Solved Examples **Example 8:** Express 739.209 km in km, hm, dam and m. **Solution:** 739.209 km = 739 km 2 hm 0 dam 9 m **Example 9:** Express 231.587 l in l, dl, cl and ml **Solution:** 231.587 l = 231 l 5 dl 8 cl 7 ml **Example 10:** Express 162 g 9 dg 6 cg 1 mg in grams. **Solution:** Following the same pattern used above, but in the reverse order, we 162 g 9 dg 6 cg 1 mg = 162.961 g **Example 11:** Express 162 l 9 dl 1 ml in litres. **Solution:** 162 l 9 dl 1 ml = 162.901 l **Example 12:** Express 13 km 8 hm 5 dam 3 m in km. **Solution:** 13 km 8 hm 5 dam 3 m = 13.853 km **Example 13:** Express 52 g 7 mg in g. **Solution:** 52 g 7 mg = 52.007 g ### Exercise 8D 1. **Express the following in hg, dag and g.** - 25.726 kg - 29.31 kg - 482.305 kg 2. **Express the following in hm, dam and m.** - 35.763 km - 296.14 km - 5.009 km 3. **Express the following in hl, dal and l.** - 19.68 kl - 5.247 kl - 625.803 kl ## Word Problems on Measurements Let us now look at some examples from real life where measurements take place. ### Solved Examples **Example 14:** Vibhav bought 3 kg 250 g of apples, 2 kg of mangoes, 350 g of grapes and 30 g of mint leaves. What is the total mass of all the items that Vibhav bought? **Solution:** | | | | |---|---|---| | Apples | 3.250 kg | 2 kg will be written like this | | Mangoes | 2.000 kg | | | Grapes | 0.350 kg | 30 g will be written like this | | Mint leaves | 0.030 kg | | | **Total** | **5.630 kg** | | The total mass of all the items is 5 kg 630 g. **Example 15:** Ram travelled 15 km 270 m by car, 12 km by cycle and 825 m by foot. What was the total distance travelled by Ram? **Solution:** | | | | |---|---|---| | km | m | | | 15 | 270 | 825 m will be written like this. | | 12 | 000 | | | +00 | 825 | | | **28** | **095** | 12 km will be written like this. | The total distance travelled by Ram is 28 km 95 m. **Example 16:** Out of 5 l 270 ml of water in a bucket, Seema used 1 l 8 ml of water. How much water was left in the bucket? **Solution:** | | | | |---|---|---| | l | ml | | | 5 | 270 | 8 ml will be written like this. | | -1 | 008 | | | **4** | **262** | | 4 l 262 ml of water was left in the bucket. ### Exercise 8E Solve the following word problems. 1. The weights of Ajay, Vijay and Sumit are 46 kg 375 g, 51 kg 7 g and 49 kg 25 g, respectively. - Who is the heaviest among these three boys? - Who is the lightest among these three boys? - What is the total weight of these three boys? 2. Bharat bought 10 kg 200 g of mangoes. Later he bought 5 kg 150 g of more mangoes. What is the total mass of mangoes that he bought? 3. A tank had 35 l 750 ml of water. The gardener used up 7 l 200 ml of water. How much water is left in the tank? 4. Out of a distance of 49 km 105 m, Krishna covered 11 km 795 m. How much distance is left to be covered? 5. Farha bought 5 m 75 cm of a red cloth and 18 m 6 cm of a blue cloth. What is the total length of the clothes that she bought? 6. Meher's weight is 49.750 kg and Zehras weight is 32.520 kg. Whose weight is more and by how much? 7. The capacity of two buckets of water is 15 l 275 ml. If the capacity of one bucket is 10 l 195 ml, what is the capacity of the second bucket? 8. The distance from Mumbai to Lonavla is 82 km 725 m. The distance from Lonavla to Pune is 68 km 980 m. What is the total distance from Mumbai to Pune? 9. The mass of an empty box is 3 kg. If it is filled with toys, the mass becomes 12 kg 509 g. What is the mass of the toys? 10. Samira bought 3 l 745 ml of orange juice, 4 l 70 ml of guava juice and 5 l 8 ml of pineapple juice. What is the total amount of juice that she bought? ## Chapter Revision ### Choose the correct option. 1. 27.81 km = - 27.81 m - 278.1 m - 27810 m - 27081 m 2. 1/5 of 18 m = - 360 cm - 18 cm - 5 cm - 3.6 cm 3. 5 kg 5 g = - 5500 g - 5050 g - 5000 g - 5005 g 4. 23 kl 7 l = - 23007 l - 2307 l - 237 l - 23700 l 5. 4 km 5 hm 8 m = - 4058 m - 4580 m - 45080 m - 4508 m 6. 7234 g = - 72340 kg - 7234 kg - 7.234 kg - 72.34 kg 7. 17.95 l = - 17 l 950 ml - 1 l 795 ml - 179 l 5 ml - 1795 ml 8. 85.327 km = ___ km ___ hm ___ dam ___ m - 85 km 3 hm 2 dam 7 m - 8 km 53 hm 2 dam 7 m - 8 km 5 hm 32 dam 7 m - 8 km 5 hm 3 dam 27 m 9. 12 kg 725 g more than 125 kg 8 g = - 137 kg 8 g - 138 kg 525 g - 137 kg 733 g - 138 kg 8 g 10. Anita bought 7 kg of apples and 1 kg 350 g of mangoes. How many more kg of apples did she buy than mangoes? - 7.350 kg - 5.650 kg - 2.350 kg - 1.750 kg ### Fill in the blanks. 1. To convert kg to dg, multiply by ___. 2. To convert cm to hm, we ___ by 10,000. 3. 1 dal = ___ dl 4. 1 m = ___ cm 5. 1 glass contains 200 ___ of water. 6. The tailor needs 2 ___ of cloth to make my shirt. 7. Mother cooked 1 ___ of potatoes for lunch. 8. The school is about 3 ___ away from my house.