Decimals

Decimals are a way of writing parts of a whole using place value. When one unit is divided into 10 equal parts, each part is one-tenth, written 0.1, and when it is divided into 100 equal parts, each part is one-hundredth, written 0.01. In this chapter you will extend the place value table to the right of the decimal point, read and write numbers such as 23.45 as 2 tens, 3 ones, 4 tenths and 5 hundredths, show decimals on a number line, and convert fractions with denominators 10 and 100 into decimals and back. You will then learn to compare decimals by looking first at the whole part and then at the tenths and hundredths. The chapter shows how decimals are used in daily life: money (Rs 7.50 means 7 rupees 50 paise), length (35 cm = 0.35 m) and weight (250 g = 0.25 kg). Finally, you will add and subtract decimals by lining up the decimal points and filling empty places with zeros.

Detailed Worksheet: Decimals Section A - Definitions (10 marks) 1. What is a decimal? Explain what the decimal point separates in the number 46.27. (2 marks) 2. What are tenths and hundredths? Write one-tenth and seven-hundredths as decimals. (2 marks) 3. Write the place value of each digit in 305.68. (2 marks) 4. What are like decimals? Convert 3.5, 2.75 and 4.125 into like decimals. (2 marks) 5. Why is 0.5 equal to 0.50? Explain using a hundredths grid. (2 marks) Section B - Calculations and Applications (15 marks) 6. Write as decimals: (i) 3/10 (ii) 47/100 (iii) 7/2 (iv) 3/5 (v) 2 and 3/4 (vi) 205/100. (3 marks) 7. Write as fractions in lowest form: (i) 0.6 (ii) 2.5 (iii) 0.04 (iv) 1.25 (v) 0.75 (vi) 3.2. (3 marks) 8. Express as rupees using decimals: (i) 5 paise (ii) 75 paise (iii) Rs 20 and 7 paise. Express in metres: (iv) 9 cm (v) 254 cm. Express in kilograms: (vi) 3 kg 70 g. (3 marks) 9. Find: (i) 16.25 + 3.7 + 0.86 (ii) 25.3 - 9.48 (iii) 20 - 12.37. (3 marks) 10. Namita travels 20 km 50 m by bus, 500 m by auto and 1 km 800 m on foot. Find the total distance in km using decimals. Also find how much more she travels by bus than by auto and on foot together. (3 marks) Section C - Diagrams (10 marks) 11. Draw a number line from 0 to 2 divided into tenths. Mark the points 0.3, 0.9, 1.2 and 1.8 on it. Which of these is closest to 1? (4 marks) 12. Draw two 10 x 10 grids. Shade 0.45 of the first grid and 0.7 of the second grid. Write each shaded part as a fraction with denominator 100. (3 marks) 13. Draw a place value table with columns Hundreds, Tens, Ones, Tenths and Hundredths, and enter the numbers 207.05, 64.3 and 0.89. Write each number in expanded form. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Rahul says 0.25 is greater than 0.3 because 25 is greater than 3. (i) Explain his mistake. (ii) Compare the two numbers correctly using a place value table. (iii) Arrange 0.3, 0.25, 0.05 and 0.52 in ascending order. (iv) State the rule for comparing decimals. (5 marks) 15. Radhika bought vegetables: tomatoes Rs 34.50, potatoes Rs 27.75, onions Rs 42 and peas Rs 18.25. (i) Find her total bill. (ii) She paid with a Rs 200 note; how much change should she get? (iii) Which two items together cost exactly Rs 60.25? (5 marks) 16. A ribbon 5 m long is used to make bows. Each bow needs 0.35 m. (i) Find the length used for 10 bows by repeated addition. (ii) Find the length of ribbon left after making 10 bows. (iii) If another 2.65 m piece is added to the leftover, find the total length now. (iv) Explain why lining up decimal points is necessary while adding. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Always line up the decimal points when adding or subtracting, and show all working.