Test: A Peek Beyond the Point - Class 7 MCQ

The decimal point is crucial because it clarifies whether a number is a whole number or a fraction. Without it, the distinction between these two types of numbers would be ambiguous.

Explanation of Incorrect Options

• Option A: While the decimal point can help in identifying currency values, this is not its primary purpose. Currency values can be represented without decimals in whole numbers.
• Option B: The decimal point does not allow for longer numbers to be written; rather, it serves to separate the whole number from the fractional part.
• Option C: Although calculations may be easier with decimals, the primary function of the decimal point is to indicate the separation between whole and fractional parts.

To determine which decimal represents four and one-tenth, we need to understand the meaning of the decimal notation.

Explanation of Correct Answer

The decimal 4.1 represents four and one-tenth, as it indicates 4 whole units and 1 tenth of a unit. Similarly, 4.10 also represents the same value because the trailing zero does not change the value of the decimal. Therefore, both A and B are correct.

Explanation of Incorrect Options

• Option C (4.01): This represents four and one-hundredth, which is not the same as four and one-tenth.

To determine which decimal is closest to 1, we can compare the distances of each option from the number 1:

• 1.5 is 0.5 away from 1.
• 0.9 is 0.1 away from 1.
• 1.01 is 0.01 away from 1.
• 1.1 is 0.1 away from 1.

Among these options, 1.01 is the closest to 1, as it is only 0.01 away. Therefore, the correct answer is C.

The correct relationship between centimetres and millimetres is given by option A: 1 cm = 10 mm. This means that one centimetre is equal to ten millimetres. To further clarify:

Explanation of Correct Answer

Centimetres and millimetres are both units of length in the metric system. The metric system is based on powers of ten, which makes conversions straightforward. Since 1 centimetre is defined as being equal to 10 millimetres, this is the correct answer.

Explanation of Incorrect Options

• Option B: 1 cm = 50 mm - This is incorrect because it overestimates the number of millimetres in a centimetre.
• Option C: 1 cm = 100 mm - This is incorrect as it suggests that there are 100 millimetres in a centimetre, which is not true.
• Option D: 1 cm = 5 mm - This is also incorrect because it underestimates the number of millimetres in a centimetre.

The correct way to read the decimal number 2.35 is as follows:

Explanation of Correct Answer

Option A: Two point three five is correct because we read the whole number part (2) followed by the word 'point' and then each digit after the decimal separately (3 and 5).

Explanation of Incorrect Options

• Option B: Two and thirty-five is incorrect because it implies a whole number (2) and a fraction (35), which does not accurately represent the decimal.
• Option C: Two hundred thirty-five is incorrect as it represents the whole number 235, not the decimal 2.35.
• Option D: Two point thirty-five is misleading; while it is close, the correct reading is to state each digit after the decimal point individually.

To convert hours into minutes, we multiply the number of hours by 60, as there are 60 minutes in an hour. Therefore, to convert 0.5 hours into minutes:

• 0.5 hours = 0.5 × 60 = 30 minutes.

Thus, the correct answer is 30 minutes.

Explanation of Incorrect Options

• A. 50 minutes - This option is incorrect because 0.5 hours does not equal 50 minutes; it is less than that.
• B. 45 minutes - This option is also incorrect as 0.5 hours is not equal to 45 minutes.
• C. 25 minutes - This option is incorrect because 0.5 hours is greater than 25 minutes.

The decimal number 0.02 can be understood in terms of fractions by examining its place value. It is composed of:

• 0 units
• 0 tenths
• 2 hundredths

Thus, 0.02 is equivalent to 2 hundredths, which is represented as the fraction 2/100 or simplified to 1/50.

Explanation of Incorrect Options

• Option A: 2 thousandths - This is incorrect because 0.02 represents 2 hundredths, not 2 thousandths (which would be 0.002).
• Option B: 2 tenths - This is incorrect as 0.2 represents 2 tenths, not 0.02.
• Option C: 2 units - This is incorrect because 0.02 is much less than 1, so it cannot represent 2 units.

To solve the expression 4 + 45/100, we first convert the fraction into decimal form. The fraction 45/100 is equal to 0.45.

Now, we can add this decimal to 4:

• 4 + 0.45 = 4.45

Thus, the correct answer is A. 4.45.

Explanation of Incorrect Options

• B. 4.54: This option is incorrect because it suggests that the sum is greater than the actual value.
• C. 4.5: This option is incorrect as it does not account for the full value of the fraction.
• D. 4.045: This option is incorrect as it suggests a value less than the actual sum.

To convert rupees into paise, we multiply the amount in rupees by 100, since 1 rupee is equal to 100 paise.

For 3.75 rupees:

• 3.75 rupees × 100 = 375 paise.

Explanation of Incorrect Options

• Option B: 37.5 paise is incorrect because it represents 0.375 rupees, not 3.75 rupees.
• Option C: 300.75 paise is incorrect because it is an incorrect conversion of 3.75 rupees.
• Option D: 3.75 paise is incorrect because it does not represent the correct conversion of 3.75 rupees.

0.01 is the correct representation of one-hundredth in decimal form.

Explanation of Incorrect Options

• 0.001: This represents one-thousandth, not one-hundredth.
• 1.0: This represents one whole, not a fraction of a hundred.
• 0.1: This represents one-tenth, which is larger than one-hundredth.

To determine which of the given decimal numbers is the smallest, we can compare them directly:

• 4.5 is equivalent to 4.50, as trailing zeros do not affect the value.
• 4.05 is less than 4.5 and 4.50.
• 4.005 is less than 4.05, 4.5, and 4.50.

Thus, the smallest number among the options is 4.005, which corresponds to option C.

Explanation of Incorrect Options

• A. 4.5: This number is larger than 4.005.
• B. 4.05: This number is larger than 4.005.
• D. 4.50: This number is equivalent to 4.5 and is larger than 4.005.

Explanation of Correct Answer

The correct answer is D. When adding or subtracting decimal numbers, the result will indeed lie between the sum of their whole number parts and that sum plus two. This is because the decimal parts can add up to less than 2, thus ensuring the final result remains within this range.

Explanation of Incorrect Options

• A. The result will always be less than the whole number sum. This is incorrect because the sum of the decimal numbers can exceed the whole number sum, depending on the decimal parts.
• B. The result will always be more than the whole number sum. This is also incorrect as the decimal parts can be negative or zero, which may lead to a result that is less than the whole number sum.
• C. The result will not involve whole numbers. This is misleading because the result of adding or subtracting decimal numbers can certainly involve whole numbers, especially when the decimal parts add up to a whole number.

Adding zeros after a decimal number does not change its value. For example, 0.2, 0.20, and 0.200 all represent the same quantity: two tenths. The zeros simply indicate precision in measurement but do not affect the actual value of the number.

Explanation of Correct Answer

Option B is correct because adding zeros to the right of a decimal does not change the value of the number. It remains the same quantity, just expressed with more decimal places.

Explanation of Incorrect Options

• Option A: This is incorrect because adding zeros does not increase the value of the number; it remains the same.
• Option C: This option is misleading. While it may seem that the decimal place value changes, the actual value of the number remains unchanged.
• Option D: This is incorrect as well. Adding zeros does not increase the value of the number; it simply adds more precision to the representation of the same value.

The measurement of the pencil is given as 3 units and 4 tenths. To express this in decimal form, we need to convert the fractional part (4 tenths) into its decimal equivalent. Since 4 tenths is equal to 0.4, we can combine this with the whole number (3) to get:

3.4

Explanation of Incorrect Options

• Option A: 3.0004 - This option incorrectly adds extra zeros after the decimal point, which does not represent the measurement accurately.
• Option C: 3.4 - This option is actually correct and represents the measurement accurately.
• Option D: 3.004 - This option incorrectly suggests that there are additional hundredths, which is not the case.

The correct answer is C: A ruler marked in tenths and hundredths. This type of ruler provides the most precise measurements for small objects, as it allows for measurements to be taken in smaller increments than whole numbers or halves.

Explanation of Incorrect Options

• A: A ruler with only whole numbers does not allow for precise measurements of small objects, as it lacks subdivisions.
• B: A ruler marked in halves allows for some level of measurement but is not as precise as one marked in tenths and hundredths.
• D: A ruler marked in kilometres is not suitable for measuring small objects, as it is designed for larger distances.