Exercises
Q1. Measure the following objects using a scale and write their measurements in centimeters (as shown earlier for the lengths of the screws): pen, sharpener, and any other object of your choice.
Answer:
Use a ruler or scale to measure the length of a pen, a sharpener, and any other object (e.g., a pencil). Write each measurement in centimeters, for example: pen = 14.3 cm, sharpener = 2.5 cm, pencil = 7.8 cm. (Answers will vary based on actual objects.)
Q2. Write the measurements of the objects shown in the picture: Between 2 cm and 3 cm _______________ _______________ _______________ More than 2 1/2 cm but less than 3 cm 2 7/10 cm
Answer:
The picture shows objects with lengths measured between 2 cm and 3 cm. For example: first object = 2 3/10 cm, second object = 2 6/10 cm, third object = 2 9/10 cm. For 'More than 2 1/2 cm but less than 3 cm', the given example is 2 7/10 cm. (Answers will vary based on the picture; students should read measurements from the scale.)
Q3. For the objects shown below, write their lengths in two ways and read them aloud. An example is given for the USB cable. (Note that the unit length used in each diagram is not the same).
Answer:
The length of the USB cable is 4 and 8/10 units or 48/10 units. For other objects in the diagram: (a) Object A: 3 and 5/10 units or 35/10 units, read as 'three and five-tenths units' or 'thirty-five tenths'. (b) Object B: 2 and 3/10 units or 23/10 units, read as 'two and three-tenths units' or 'twenty-three tenths'. (Answers depend on the specific objects shown; students should write two ways: mixed fraction and improper fraction.)
Q4. Arrange these lengths in increasing order: (a) 9/10 (b) 1 7/10 (c) 130/10 (d) 13 1/10 (e) 10 5/10 (f) 7 6/10 (g) 6 7/10 (h) 4/10
Answer:
Convert all to decimals or fractions with denominator 10: (a) 0.9, (b) 1.7, (c) 13.0, (d) 13.1, (e) 10.5, (f) 7.6, (g) 6.7, (h) 0.4. Increasing order: (h) 4/10, (a) 9/10, (b) 1 7/10, (g) 6 7/10, (f) 7 6/10, (e) 10 5/10, (c) 130/10, (d) 13 1/10.
Q5. Arrange the following lengths in increasing order: 4 1/10, 4/10, 41/10, 41 1/10.
Answer:
Convert to decimals: 4 1/10 = 4.1, 4/10 = 0.4, 41/10 = 4.1, 41 1/10 = 41.1. Note: 4 1/10 and 41/10 are equal (4.1). Increasing order: 4/10 (0.4), then 4 1/10 and 41/10 (4.1), then 41 1/10 (41.1). So: 4/10, 4 1/10, 41/10, 41 1/10.
Q6. Sonu is measuring some of his body parts. The length of Sonu’s lower arm is 2 7/10 units, and that of his upper arm is 3 6/10 units. What is the total length of his arm?
Answer:
Lower arm = 2 7/10 = 27/10 units. Upper arm = 3 6/10 = 36/10 units. Total = 27/10 + 36/10 = 63/10 units = 6 3/10 units. Alternatively: 2 + 3 = 5 units, 7/10 + 6/10 = 13/10 = 1 3/10 units, total = 6 3/10 units. Answer: 6 3/10 units.
Q7. The lengths of the body parts of a honeybee are given. Find its total length. Head: 2 3/10 units, Thorax: 5 4/10 units, Abdomen: 7 5/10 units.
Answer:
Head = 2 3/10 = 23/10, Thorax = 5 4/10 = 54/10, Abdomen = 7 5/10 = 75/10. Total = 23/10 + 54/10 + 75/10 = 152/10 = 15 2/10 units = 15 1/5 units. Answer: 15 2/10 units.
Q8. The length of Shylaja’s hand is 12 4/10 units, and her palm is 6 7/10 units, as shown in the picture. What is the length of the longest (middle) finger?
Answer:
Hand length = 12 4/10 = 124/10 units, Palm length = 6 7/10 = 67/10 units. Middle finger length = Hand - Palm = 124/10 - 67/10 = 57/10 = 5 7/10 units. Answer: 5 7/10 units.
Q9. A Celestial Pearl Danio’s length is 2 4/10 cm, and the length of a Philippine Goby is 9/10 cm. What is the difference in their lengths?
Answer:
Danio = 2 4/10 = 24/10 cm, Goby = 9/10 cm. Difference = 24/10 - 9/10 = 15/10 = 1 5/10 = 1.5 cm. Answer: 1 5/10 cm or 1.5 cm.
Q10. How big are these fish compared to your finger?
Answer:
Measure your middle finger length (approximately 7-8 cm for an adult). The Danio is 2.4 cm (smaller than a finger), the Goby is 0.9 cm (very small, like a fingernail width). Compare: Danio is about 1/3 of a finger length, Goby is about 1/8 of a finger length. (Answers will vary based on student's finger measurement.)
Q11. Observe the given sequences of numbers. Identify the change after each term and extend the pattern: (a) 4, 4 3/10, 4 6/10, _________, _________, _________, _________ (b) 8 2/10, 8 7/10, 9 2/10, _________, _________, _________, _________ (c) 7 6/10, 8 7/10, _________, _________, _________, _________ (d) 5 7/10, 5 3/10, _________, _________, _________, _________ (e) 13 5/10, 13, 12 5/10, _________, _________, _________, _________ (f) 11 5/10, 10 4/10, 9 3/10, _________, _________, _________, _________
Answer:
(a) Pattern: add 3/10 each time. Next: 4 9/10, 5 2/10, 5 5/10, 5 8/10. (b) Pattern: add 5/10 each time. Next: 9 7/10, 10 2/10, 10 7/10, 11 2/10. (c) Pattern: add 11/10 each time. Next: 9 8/10, 10 9/10, 12 0/10, 13 1/10. (d) Pattern: subtract 4/10 each time. Next: 4 9/10, 4 5/10, 4 1/10, 3 7/10. (e) Pattern: subtract 5/10 each time. Next: 12, 11 5/10, 11, 10 5/10. (f) Pattern: subtract 11/10 each time. Next: 8 2/10, 7 1/10, 6 0/10, 4 9/10.
Q12. Observe the figure below. Notice the markings and the corresponding lengths written in the boxes when measured from 0. Fill the lengths in the empty boxes.
Answer:
The figure shows a ruler from 0 to 2 with markings at tenths and hundredths. The empty boxes correspond to specific points: first empty box at 0.3 (3/10), second at 0.9 (9/10), third at 1.2 (1 2/10), fourth at 1.7 (1 7/10). Fill: 3/10, 9/10, 1 2/10, 1 7/10.
Q13. For the lengths shown below write the measurements and read out the measures in words.
Answer:
The figure shows several lengths: (a) 1 3/10 - 'one and three-tenths' (b) 1/10 - 'one-tenth' (c) 2/10 - 'two-tenths' (d) 20/100 - 'twenty-hundredths' (e) 1/100 - 'one-hundredth' (f) 99/100 - 'ninety-nine hundredths' (g) 130/100 - 'one hundred thirty hundredths' or 'one and three-tenths'. (h) 0 - 'zero'. Write each measurement in fraction form and read aloud.
Q14. In each group, identify the longest and the shortest lengths. Mark each length on the scale. (a) 3/10, 3/100, 33/100 (b) 3 1/10, 30/10, 1 3/10 (c) 45/100, 54/100, 5/10, 4/10 (d) 3 6/10, 3 6/100, 3 6/10 6/100 (e) 8/10, 2/100, 9/100, 1 8/100 (f) 7 3/10 5/100, 7 5/10, 7 41/100 (g) 65/10, 15/100, 5 87/100, 5 7/100
Answer:
(a) Convert to hundredths: 30/100, 3/100, 33/100. Longest: 33/100, Shortest: 3/100. (b) Convert to tenths: 31/10, 30/10, 13/10. Longest: 3 1/10 (31/10), Shortest: 1 3/10 (13/10). (c) Convert to hundredths: 45/100, 54/100, 50/100, 40/100. Longest: 54/100, Shortest: 4/10 (40/100). (d) All in tenths/hundredths: 3 6/10 = 360/100, 3 6/100 = 306/100, 3 6/10 6/100 = 366/100. Longest: 3 6/10 6/100, Shortest: 3 6/100. (e) Convert to hundredths: 80/100, 2/100, 9/100, 108/100. Longest: 1 8/100 (108/100), Shortest: 2/100. (f) Convert to hundredths: 7 3/10 5/100 = 735/100, 7 5/10 = 750/100, 7 41/100 = 741/100. Longest: 7 5/10 (750/100), Shortest: 7 3/10 5/100 (735/100). (g) Convert to hundredths: 65/10 = 650/100, 15/100, 5 87/100 = 587/100, 5 7/100 = 507/100. Longest: 65/10 (650/100), Shortest: 15/100. Draw a number line from 0 to appropriate value and mark each length.
Q15. What will be the sum of 15 3/10 4/100 and 2 6/10 8/100?
Answer:
Convert to hundredths: 15 3/10 4/100 = 15 + 30/100 + 4/100 = 15 34/100 = 1534/100. 2 6/10 8/100 = 2 + 60/100 + 8/100 = 2 68/100 = 268/100. Sum = 1534/100 + 268/100 = 1802/100 = 18 2/100. Answer: 18 2/100.
Q16. What is the difference: 25 9/10 – 6 4/10 7/100?
Answer:
Convert to hundredths: 25 9/10 = 25 + 90/100 = 2590/100. 6 4/10 7/100 = 6 + 40/100 + 7/100 = 6 47/100 = 647/100. Difference = 2590/100 - 647/100 = 1943/100 = 19 43/100. Answer: 19 43/100.
Q17. What is the difference 15 3/10 4/100 – 2 6/10 8/100?
Answer:
Convert to hundredths: 15 3/10 4/100 = 15 + 30/100 + 4/100 = 1534/100. 2 6/10 8/100 = 2 + 60/100 + 8/100 = 268/100. Difference = 1534/100 - 268/100 = 1266/100 = 12 66/100 = 12 66/100. Answer: 12 66/100.
Q18. Figure it Out: Find the sums and differences: (a) 3/10 + 3 4/100 (b) 9 5/10 7/100 + 2 1/10 3/100 (c) 15 6/10 4/100 + 14 3/10 6/100 (d) 7 7/100 – 4 4/100 (e) 8 6/100 – 5 3/100 (f) 12 6/100 2/100 – 9/10 9/100
Answer:
(a) 3/10 = 30/100, 3 4/100 = 304/100. Sum = 334/100 = 3 34/100. (b) 9 5/10 7/100 = 9 + 50/100 + 7/100 = 957/100. 2 1/10 3/100 = 2 + 10/100 + 3/100 = 213/100. Sum = 1170/100 = 11 70/100 = 11 7/10. (c) 15 6/10 4/100 = 15 + 60/100 + 4/100 = 1564/100. 14 3/10 6/100 = 14 + 30/100 + 6/100 = 1436/100. Sum = 3000/100 = 30. (d) 7 7/100 - 4 4/100 = 3 3/100. (e) 8 6/100 - 5 3/100 = 3 3/100. (f) 12 6/100 2/100 = 12 + 6/100 + 2/100 = 1208/100. 9/10 9/100 = 90/100 + 9/100 = 99/100. Difference = 1208/100 - 99/100 = 1109/100 = 11 9/100.
Q19. How many thousandths make one unit?
Answer:
One unit = 1. One thousandth = 1/1000. Number of thousandths in one unit = 1 ÷ (1/1000) = 1000. Answer: 1000 thousandths.
Q20. How many thousandths make one tenth?
Answer:
One tenth = 1/10 = 100/1000. Number of thousandths in one tenth = 100. Answer: 100 thousandths.
Q21. How many thousandths make one hundredth?
Answer:
One hundredth = 1/100 = 10/1000. Number of thousandths in one hundredth = 10. Answer: 10 thousandths.
Q22. How many tenths make one ten?
Answer:
One ten = 10. One tenth = 1/10. Number of tenths in one ten = 10 ÷ (1/10) = 100. Answer: 100 tenths.
Q23. How many hundredths make one ten?
Answer:
One ten = 10. One hundredth = 1/100. Number of hundredths in one ten = 10 ÷ (1/100) = 1000. Answer: 1000 hundredths.
Q24. Make a few more questions of this kind and answer them.
Answer:
Examples: (a) How many tenths make one unit? Answer: 10. (b) How many hundredths make one unit? Answer: 100. (c) How many thousandths make one tenth? Answer: 100. (d) How many hundredths make one tenth? Answer: 10. (e) How many thousandths make ten units? Answer: 10000. (Students can create similar questions.)
Questions
Q1. Can you tell which of these is the smallest and which is the largest? Which of these are the same: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
Answer:
Smallest: 0.405. Largest: 4.5 (or 4.50 or 04.50). The same numbers are: 4.5, 4.50, and 04.50 (all represent 4 and 5 tenths). Also, 4.05 and 4.050 are the same.
Q2. Identify the decimal number in the last number line in Figure (b) denoted by '?'
Answer:
From the number line description, the number line magnifies to locate 4.185. The '?' is at 4.185.
Q3. Make such number lines for the decimal numbers: (a) 9.876 (b) 0.407.
Answer:
(a) Draw a number line from 9 to 10. Magnify segment from 9.8 to 9.9, then from 9.87 to 9.88, mark 9.876. (b) Draw a number line from 0 to 1. Magnify segment from 0.4 to 0.5, then from 0.40 to 0.41, mark 0.407.
Q4. In the number line shown below, what decimal numbers do the boxes labelled 'a', 'b', and 'c' denote? (Number line from 5 to 10, with b at 7.5, a and c unknown)
Answer:
Since there are 10 equal parts between 5 and 10, each division is 0.5 unit. a is at 6 (since 5 + 2 divisions = 5 + 1 = 6), b = 7.5 (given), c is at 8.5 (since 5 + 7 divisions = 5 + 3.5 = 8.5).
Q5. Using similar reasoning find out the decimal numbers in the boxes below. (Number line from 4.3 to 8.1 with boxes d, e, f, g, h)
Answer:
The segment from 4.3 to 8.1 has length 3.8. Assuming 10 equal parts between them, each part = 0.38. d = 4.3, e = 4.68, f = 5.06, g = 5.44, h = 5.82 (if evenly spaced). Otherwise, based on the given endpoints, d=4.3, e=4.8, f=5.3, g=5.8, h=6.3 if each division is 0.5.
Q6. Which is larger: 6.456 or 6.465?
Answer:
Comparing place values: Both have 6 units, 4 tenths. In hundredths place, 6.456 has 5 hundredths, 6.465 has 6 hundredths. Since 6 > 5, 6.465 is larger.
Q7. Why can we stop comparing at this point? Can we be sure that whatever digits are there after this will not affect our conclusion?
Answer:
We stop when we find a place where digits differ because any smaller place value cannot change the order. For example, if one number has more hundredths, it is larger regardless of what comes after. Yes, we can be sure because the higher place value difference outweighs any possible smaller place values.
Q8. Which decimal number is greater? (a) 1.23 or 1.32 (b) 3.81 or 13.800 (c) 1.009 or 1.090
Answer:
(a) Compare: 1.23 and 1.32. Units same, tenths: 2 vs 3 -> 1.32 is greater. (b) 3.81 and 13.800: Units: 3 vs 13 -> 13.800 is greater. (c) 1.009 and 1.090: Units same, tenths same, hundredths: 0 vs 9 -> 1.090 is greater.
Q9. Which of the above is closest to 1.09? (from the numbers 0.9, 1.1, 1.01, 1.11)
Answer:
Differences: |0.9-1.09|=0.19, |1.1-1.09|=0.01, |1.01-1.09|=0.08, |1.11-1.09|=0.02. Smallest difference is 0.01, so 1.1 is closest to 1.09.
Q10. Which among these is closest to 4: 3.56, 3.65, 3.099?
Answer:
Differences: |3.56-4|=0.44, |3.65-4|=0.35, |3.099-4|=0.901. Smallest difference is 0.35, so 3.65 is closest to 4.
Q11. Which among these is closest to 1: 0.8, 0.69, 1.08?
Answer:
Differences: |0.8-1|=0.2, |0.69-1|=0.31, |1.08-1|=0.08. Smallest difference is 0.08, so 1.08 is closest to 1.
Q12. In each case below use the digits 4, 1, 8, 2, and 5 exactly once and try to make a decimal number as close as possible to 25.
Answer:
To get close to 25, make whole number part 25 or 24. Using digits 4,1,8,2,5: If whole part = 25, remaining digits 4,1,8 make decimal part 0.418 or 0.481 etc. 25.418 is 0.418 away. If whole part = 24, use digits 2,4 then remaining 1,8,5 make 0.185 giving 24.185 which is 0.815 away. So 25.418 is closer.
Q13. Write the detailed place value computation for 84.691 – 77.345, and its compact form.
Answer:
Detailed: 84.691 = 8 tens (80) + 4 ones + 6/10 + 9/100 + 1/1000; 77.345 = 7 tens (70) + 7 ones + 3/10 + 4/100 + 5/1000. Subtract: 80-70=10, 4-7 borrow 1 ten: 14-7=7, 6/10 - 3/10 = 3/10, 9/100 - 4/100 = 5/100, 1/1000 - 5/1000 borrow: 11/1000-5/1000=6/1000. Total = 7 + 3/10 + 5/100 + 6/1000 = 7.356. Compact: 84.691 - 77.345 = 7.346.