Practice Questions

Justify whether the statement "A decimal number is always a quantity less than 1" is true or false. Propose a counterexample if it is false.

Define a decimal number.

Identify the place value of the digit 8 in the number $45.678$.

Demonstrate how to express 35 paise as rupees using decimal notation.

Recall how many millimeters are in one centimeter.

Name the symbol used to separate the whole number part from the fractional part in a decimal number.

Explain how to convert 75 millimeters into centimeters.

Summarize the relationship between a rupee and paise. Convert 65 paise into rupees.

Convert the measurement 8 m 5 cm into meters using decimal notation.

Analyze the decimal numbers 4.505 and 4.55 to determine which one is greater.

The heights of three friends are 1.52 m, 155 cm, and 1.49 m. Arrange their heights in descending order, expressing all heights in meters.

A car travels 12.5 km on Monday, 15.75 km on Tuesday, and 9.8 km on Wednesday. Calculate the total distance the car traveled in three days.

Ayan claims that $7.100$ is greater than $7.1$ because $100$ is greater than $1$. Critique his reasoning.

Design a scenario for a school cafeteria selling three food items: a sandwich, a juice box, and a fruit cup. Create a price for each item (using decimals, e.g., ₹25.50). Your scenario should require a student to buy one of each item, pay with a ₹100 note, and calculate the change received. Present the full problem and its solution.

A tailor has $12.5$ meters of fabric. He needs to cut two pieces: one of length $5.75$ m and another of length $6.9$ m. He estimates the total required length by rounding each measurement to the nearest whole number and concludes he has enough fabric. Evaluate his estimation method and justify whether his conclusion is correct using exact calculations.

The daily rainfall in a city for three consecutive days was recorded as 12.5 mm, 8.7 mm, and 15.3 mm. Calculate the total rainfall over the three days in centimeters.

Describe the steps to compare the decimal numbers $8.45$ and $8.41$.

Explain how to express 250 grams in kilograms using decimal notation.

Calculate the value of $15.01 - 9.1$.

A shopkeeper's bill shows an item for ₹25.75 and another for ₹15.5. He manually calculates the total as ₹40.80. Critique his calculation by identifying the place value error.

Analyze the sequence: $3.2, 3.5, 3.8, \dots$ and determine the next term.

Rohan bought a notebook for ₹25.75, a pen for ₹15.50, and an eraser for ₹4.25. If he paid with a ₹50 note, calculate the amount of change he received.

Design a word problem that requires subtracting decimal numbers to compare the weights of two objects, where borrowing is needed from the units place. Solve the problem you designed.

Formulate a step-by-step procedure to convert a measurement given in millimeters (mm) to kilometers (km). Use your procedure to convert $5,678$ mm to km.

The perimeter of a triangle is 15.6 cm. If two of its sides measure 5.4 cm and 6.8 cm, calculate the length of the third side.

A water tank has a capacity of 200 liters. It already contains 85.75 liters of water. An additional 45.5 liters of water is poured into it. Later, 62.8 liters of water is used for gardening. Calculate the quantity of water remaining in the tank.

A tailor has a piece of cloth measuring 10 m. He uses 3.45 m for a shirt and 4.8 m for trousers. Calculate the length of the cloth that is left.

Create a decimal number using the digits 3, 0, 5, and 9 exactly once, such that the number is greater than 3.5 but less than 3.9.

From the following list, identify the numbers that are equal in value: $4.8, 4.08, 4.80, 0.48, 4.800$.

List the place values for the first three digits to the right of the decimal point.

Describe how to write the number $54.321$ in expanded form.

Rina is asked to arrange $0.9$, $0.099$, and $1.01$ in ascending order. Her answer is $1.01, 0.9, 0.099$. Critique her answer by explaining the correct method of comparison based on place value.

Explain how the Indian place value system is extended to represent numbers smaller than one. Describe the relationship between one unit, one-tenth, and one-hundredth.

Summarize the conversion rules for the following units by stating the relationship and providing an example for each conversion. a) Millimeters to Centimeters b) Centimeters to Meters c) Grams to Kilograms

Evaluate the claim: "When you convert a length from centimeters to meters, the numerical value of the measurement always becomes smaller." Justify your conclusion.

Explain why $0.6$ is equal to $0.60$.

A sequence is generated starting with the number $20.0$. The rule to get the next term is: "Subtract $2.5$, then add $0.25$." Formulate the first five terms of this sequence and propose what the tenth term might be.

Describe the procedure for adding two decimal numbers, for example, $27.45 + 8.9$. Use a place value table to illustrate your explanation and explain the concept of regrouping (carrying over).

Formulate a general rule to find a decimal number that lies exactly halfway between any two given decimal numbers, 'a' and 'b'. Justify your rule using the concept of an average. Apply your rule to find the number exactly halfway between (i) $2.8$ and $2.9$, and (ii) $4.55$ and $4.56$.

Sunita went to the market with ₹500. She purchased 2.5 kg of potatoes at ₹22.50 per kg, 1.5 kg of tomatoes at ₹40.80 per kg, and 0.5 kg of onions at ₹35.00 per kg. Calculate the total amount she spent and the money she has left.

Using the digits 7, 2, 9, and 4 exactly once, form the largest and smallest possible decimal numbers with two decimal places. Then, solve for the difference between them.

The table shows the weight of different fruits in a basket.

The text mentions that in cricket, '5.5 overs' means 5 overs and 5 balls, not $5 \frac{1}{2}$ overs. Evaluate why a base-6 system (for balls) is used after the decimal point instead of a standard base-10 decimal system. Then, create a similar 'non-decimal' system for representing hours and minutes (1 hour = 60 minutes). Propose how you would write '2 hours and 30 minutes' and '1 hour and 15 minutes' in your system and calculate their sum using your notation.

Using the digits 1, 4, 6, and 9 exactly once, create two decimal numbers, one in the format $X.X$ and the other in $X.X$, whose sum is the largest possible value. Justify your placement of the digits.

Justify why the standard algorithm for subtracting whole numbers works for decimals. Use the example $15.2 - 8.7$ to explain the 'borrowing' process in terms of place value (tenths and units).