Practice Questions

Identify the place value of the digit 7 in the number $54.372$.

Calculate the product: $2.45 \times 1000$.

State the rule for multiplying any decimal number by 100.

Solve: $135.8 \div 100$.

Define a decimal fraction.

Convert the fraction $\frac{9}{1000}$ to its decimal form.

A rectangular park is $45.5$ m long and $20.2$ m wide. Calculate the area of the park.

Create a realistic word problem involving the multiplication of a decimal number (with two decimal places) by another decimal number (with one decimal place), such that the final product is a whole number. Provide the full solution.

List the decimal equivalents for the following fractions: $\frac{7}{10}$, $\frac{23}{100}$, and $\frac{5}{1000}$.

A ribbon of length $15.75$ m is cut into $7$ equal pieces. What is the length of each piece?

Justify why dividing a number by $100$ produces the same result as multiplying it by $0.01$.

Evaluate the statement: "The product of two decimal numbers, each less than 1, is always less than both of the original numbers." Justify your answer with an example.

Recall what happens to the position of the decimal point when a number is divided by 1000.

The side of a regular hexagon is $7.2$ cm. Calculate its perimeter.

Mr. Sharma bought $12.5$ litres of petrol for his car at ₹$96.80$ per litre. He also bought $3.5$ kg of apples at ₹$120.40$ per kg. If he gave the cashier two ₹$1000$ notes, how much change should he receive?

Given that $24 \times 13 = 312$, explain how you can find the product of $2.4 \times 1.3$ without performing the full multiplication again.

Summarize the rules for multiplying and dividing a decimal number by powers of 10 (10, 100, 1000). Provide one example for multiplication and one for division using the number $52.84$.

Explain how to express 75 grams in kilograms, showing the conversion first as a fraction and then as a decimal.

Describe the steps to find the product of $3.2 \times 0.4$.

Write the decimal number $47.205$ in expanded form as a sum of fractions.

Summarize the rule for dividing a decimal number by a whole number, using $15.5 \div 5$ as an example.

Describe the decimal place value system. For the number $36.819$, explain what each digit to the right of the decimal point represents.

If $145 \times 32 = 4640$, analyze and find the value of $1.45 \times 3.2$.

Calculate the product of $0.07$ and $0.6$.

Express the fraction $\frac{17}{8}$ in its decimal form.

A car consumes $8.5$ litres of petrol to travel $153$ km. How many kilometres can it travel on $1$ litre of petrol?

Sunita bought $3.5$ kg of onions at ₹$24.50$ per kg and $2.25$ kg of tomatoes at ₹$40.00$ per kg. Calculate the total amount she spent.

A student solved $4.2 \times 0.03$ and got the answer $1.26$. Critique the student's answer and explain the error in their reasoning.

A shop sells two sizes of juice. A $0.35$ litre bottle costs ₹28 and a $0.5$ litre bottle costs ₹35. Evaluate which bottle is a better value for money and justify your conclusion.

Without performing the complete division, justify whether the quotient of $45.15 \div 0.15$ is the same as the quotient of $451.5 \div 1.5$.

The area of a rectangular painting is $2.88 \text{ m}^2$. Propose two different pairs of possible dimensions (length and breadth in metres) for the painting, where both dimensions are decimal numbers.

A student states, "Dividing a number by a decimal always makes the result larger than the original number." Critique this statement. Is it always true, sometimes true, or never true? Provide examples to support your critique.

Two methods are proposed to solve $7.2 \div 0.04$.

• Method A: Convert to fractions: $\frac{72}{10} \div \frac{4}{100}$.
• Method B: Shift decimals: $\frac{7.2 \times 100}{0.04 \times 100} = \frac{720}{4}$. Evaluate both methods by solving the problem with each. Which method do you find more direct and why?

Design a word problem about planning a school event. The problem must require a student to perform both a decimal division and a decimal multiplication to find the final answer. The scenario should be realistic and all necessary values must be provided. Solve the problem you have designed.

Based on the calculation $15.6 \div 1.2 = 13$, formulate a general rule about how the decimal point in the dividend and divisor can be shifted without changing the quotient.

Explain what happens to the product when a number greater than 1 is multiplied by a number between 0 and 1. Use the example $12 \times 0.5$.

Justify why the decimal representation of $\frac{2}{7}$ must be a repeating decimal by analyzing the possible remainders during the long division of $2 \div 7$.

The actual length of a year is approximately $365.2422$ days. The Gregorian calendar uses the following rule for leap years: a year is a leap year if it is divisible by 4, except for years divisible by 100 unless they are also divisible by 400.

1. Formulate an expression for the average number of days in a year over a 400-year cycle according to this rule.
2. Evaluate this average.
3. Justify how well this system approximates the actual length of a year by calculating the difference.

Analyze the following and find the missing number: $43.2 \div \_\_\_\_ = 0.0432$.

A courier company charges ₹$32.50$ for the first kilogram and ₹$15.75$ for each additional kilogram or part thereof. A person sends a parcel weighing $4.8$ kg. Analyze the cost structure and calculate the total charge.

A baker uses $0.375$ kg of flour to bake one cake. He has a large sack containing $15$ kg of flour. (a) Calculate the maximum number of full cakes he can bake. (b) After baking the maximum number of cakes, calculate how much flour will be left over.

A pile of 25 identical cardboard sheets has a thickness of $4.75$ cm. Calculate the thickness of a single sheet in millimetres.

Explain the complete procedure for dividing a decimal number by another decimal number. Use the problem $15.75 \div 0.25$ to illustrate the steps.

Create a multi-step word problem where a shopkeeper mixes three items to sell. Your problem must require a student to:

1. Calculate the total cost of the mixture using decimal multiplication.
2. Calculate the cost per kilogram of the mixture using decimal division.
3. Propose a selling price per kg to achieve a specific decimal profit amount. Provide a full solution to the problem you have created.

Using the digits 2, 3, 5, and 8 exactly once, formulate a multiplication of the form $\square.\square \times \square.\square$ that yields the maximum possible product. Justify your placement of the digits.