Chapter 3: A Peek Beyond the Point

Time Allowed: 45 Minutes

Maximum Marks: 30

SECTION A: 1-MARK QUESTIONS (5 Marks)

Answer all questions. Each question carries 1 mark.

Q1. Write the quantity "5 ones, 3 tenths, and 8 hundredths" in its standard decimal form.

Q2. Which fraction is greater: $\frac{10}{1000}$ or $\frac{1}{10}$?

Q3. How many thousandths make up exactly one hundredth ($\frac{1}{100}$)?

Q4. Fill in the blank to continue the simple increasing sequence:

$4, \; 4\frac{3}{10}, \; 4\frac{6}{10}, \; \_\_\_\_\_\_$

Q5. Convert $4.59\text{ kg}$ into an gram form

SECTION B: 2-MARK QUESTIONS (10 Marks)

Show your steps clearly. Each question carries 2 marks.

Q6. Arrange the following decimal lengths in descending order (largest to smallest):

$11.01, \; 1.011, \; 1.101, \; 11.10, \; 1.01$

Q7. Perform the following fractional addition and write your answer in both mixed fraction and decimal forms:

$8\frac{7}{10} + 5\frac{6}{10}$

Q8. Solve the following fractional subtraction by borrowing from the whole number spot:

$12\frac{6}{10} - \frac{99}{100}$

Q9. State whether the following statement is True or False, and provide a reason:

"A decimal number with more digits after the decimal point is always greater than a decimal number with fewer digits."

Q10. [Word Problem] Mahi goes to the local market and buys $0.25\text{ kg}$ of fresh green beans, $0.5\text{ kg}$ of potatoes, and $0.05\text{ kg}$ of ginger. Find the combined total weight of the items she purchased.

SECTION C: 5-MARK QUESTIONS (15 Marks)

Complete step-by-step calculations must be written down. Each question carries 5 marks.

Q11. Using each of the digits 1, 4, 0, 8, and 6 exactly once, complete the tasks below:

• (a) Form the smallest possible decimal number that lies between $100$ and $1000$. (2 Marks)
• (b) Form the decimal number closest to the whole number $30$. (1 Mark)
• (c) Draw a small Place Value Table (with columns for Hundreds, Tens, Ones, Tenths, Hundredths, and Thousandths) and map out the digits of the number you formed in part (a). (2 Marks)

Q12. Pinto is a dairy distributor who tracks milk supply over a week:

• (a) He delivers $3.79\text{ Litres}$ of milk on Monday, $4.2\text{ Litres}$ on Tuesday, and $4.25\text{ Litres}$ on Wednesday. Calculate the total quantity of milk delivered in these first three days. (2 Marks)
• (b) If his total delivery across a 6-day workweek sums up to exactly $25\text{ Litres}$, find the total quantity of milk supplied during the remaining last three days of that week. (3 Marks)

Q13. (a) Analyze the step differences and fill in the missing blanks to extend the alternating pattern: (3 Marks)

$5.5, \; 6.4, \; 6.39, \; 7.29, \; 7.28, \; 6.18, \; 6.17, \; \_\_\_\_\_, \; \_\_\_\_\_$

(b) Indian Railways provides optional travel insurance on e-tickets costing $45\text{ paise}$ per passenger. If $100$ passengers purchase this insurance on a small tour bus booking, show your steps to find the total insurance fee collected in Rupees (₹). (2 Marks)

ANSWER KEY & MARKING SCHEME

(For Evaluation and Grading Reference)

SECTION A

Q1. $5.38$ (1 Mark) Q2. $\frac{1}{10}$ (since $\frac{10}{1000} = \frac{1}{100}$ and $0.1 > 0.01$) (1 Mark) Q3. $10$ thousandths (since $\frac{1}{100} \div \frac{1}{1000} = 10$) (1 Mark) Q4. $4\frac{9}{10}$ (or $4.9$) (1 Mark) Q5. $4\frac{59}{100}$ (1 Mark) ### SECTION B

Q6. Vertically align using equal decimal places ($11.100, 11.010, 1.101, 1.011, 1.010$).

• Correct Order: $11.10 > 11.01 > 1.101 > 1.011 > 1.01$ (2 Marks for full correct sequence; 1 mark if one minor error exists) Q7. Summing whole components: $8 + 5 = 13$. Fractional components: $\frac{7 + 6}{10} = \frac{13}{10} = 1\frac{3}{10}$.

• Total sum = $13 + 1\frac{3}{10} = 14\frac{3}{10}$ or $14.3$ (1 Mark for fraction form, 1 Mark for decimal form) Q8. Convert tenths to hundredths: $12\frac{60}{100} - \frac{99}{100}$. Borrow $1$ whole unit: $11\frac{160}{100} - \frac{99}{100}$.

• Final evaluation = $11\frac{61}{100}$ (or $11.61$) (1 Mark for correct borrowing steps, 1 Mark for accurate answer) Q9. False. (1 Mark) Value is determined column by column from left to right based on place value position, not by digit count. For instance, $0.2$ is larger than $0.1555$. (1 Mark for proper justification) Q10. Align the decimal points vertically:

  \begin{array}{r@{\quad}l} 0.25 & \text{kg} \\ 0.50 & \text{kg} \\ + \, 0.05 & \text{kg} \\ \hline 0.80 & \text{kg} \end{array}

• Total Weight = $0.8\text{ kg}$ (or $0.80\text{ kg}$) (1 Mark for column alignment/setup, 1 Mark for correct total sum) ### SECTION C

  Q11. * (a) To locate it between $100$ and $1000$, select $1$ for the hundreds slot, then place remaining digits in ascending order: $104.68$ (2 Marks) * (b) Proximity to $30$ yields choices starting with $40$ or $18$. $40.168$ is closest ($10.168$ away). Answer: $40.168$ (1 Mark) * (c) Place value alignment table for $104.68$: (2 Marks) | Hundreds ($100$) | Tens ($10$) | Ones ($1$) | . | Tenths ($\frac{1}{10}$) | Hundredths ($\frac{1}{100}$) | Thousandths ($\frac{1}{1000}$) |

  | :—: | :—: | :—: | :—: | :—: | :—: | :—: |

  | 1 | 0 | 4 | . | 6 | 8 | 0 |

Q12. * (a) Days 1–3 Sum = $3.79 + 4.20 + 4.25 = \mathbf{12.24\text{ Litres}}$ (2 Marks for step and addition total) * (b) Days 4–6 Balance calculation: $25.00 - 12.24$ (1 Mark for setup)

\begin{array}{r@{\quad}l} 25.00 & \text{L} \\ - \, 12.24 & \text{L} \\ \hline 12.76 & \text{L} \end{array}

• Milk supplied in the last three days = $12.76\text{ Litres}$ (2 Marks for accurate subtraction validation) Q13. * (a) The pattern consists of shifting steps: $+0.90$, then $-0.01$.

  $5.5 + 0.9 = 6.4 \to 6.4 - 0.01 = 6.39 \to 6.39 + 0.9 = 7.29 \to 7.29 - 0.01 = 7.28$.

  The last known step was $6.18 \to 6.17$ (which is $-0.01$).

  Next step requires $+0.90 \implies 6.17 + 0.90 = \mathbf{7.07}$. (1.5 Marks) Following step requires $-0.01 \implies 7.07 - 0.01 = \mathbf{7.06}$. (1.5 Marks) * (b) Metric progression breakdown:

• $1\text{ km} = 1000\text{ meters}$

• $1\text{ meter} = 100\text{ centimeters}$

• $1\text{ cm} = 10\text{ millimeters}$

• Calculation: $1000 \times 100 \times 10 = \mathbf{1,000,000\text{ mm}}$ (2 Marks for step conversion path)