CBSE Class 7 Mathematics Another Peek beyond the Point MCQs Set 11

Answer: (c) 7 thousandths

Explanation:
1. After the decimal point the places are tenths, hundredths, thousandths.
2. In 46.207, 2 is in the tenths place, 0 in the hundredths place and 7 in the thousandths place.
3. So 7 stands for \( \frac{7}{1000} \), that is 7 thousandths.

Teacher's Note:
1. Count places to the right of the point: tenths, hundredths, thousandths.
2. Do not mix up the place of 7 with its value.

Answer: (b) 0.309

Explanation:
1. A denominator of 1000 means the number must have three digits after the decimal point.
2. \( \frac{309}{1000} \) = \( \frac{3}{10} \) + \( \frac{0}{100} \) + \( \frac{9}{1000} \).
3. So the decimal is 0.309.

Teacher's Note:
1. Number of zeroes in the denominator = number of digits after the point.
2. 3.09 would need a denominator of 100.

Answer: (a) 45.6

Explanation:
1. Multiplying by 10 shifts the decimal point one place to the right.
2. 4.56 → 45.6.
3. So 4.56 × 10 = 45.6.

Teacher's Note:
1. One zero in 10 means one place to the right.
2. The answer must be bigger than 4.56.

Answer: (d) 306

Explanation:
1. Multiplying by 1000 shifts the decimal point three places to the right.
2. In 0.306 there are exactly three digits after the point, so the point moves past all of them.
3. So 0.306 × 1000 = 306, a whole number.

Teacher's Note:
1. Three zeroes, three places to the right.
2. The leading 0 simply drops away.

Answer: (b) 3

Explanation:
1. 3.4 has 1 decimal digit and 2.17 has 2 decimal digits.
2. The product has 1 + 2 = 3 decimal digits.
3. Check: 34 × 217 = 7378, so 3.4 × 2.17 = 7.378, which has 3 digits after the point.

Teacher's Note:
1. Add the decimal digits of the two numbers.
2. Here no zero at the end disturbs the count.

Answer: (c) 1.875

Explanation:
1. 7 Ones ÷ 4 gives 1 One with 3 Ones left over.
2. 3 Ones and 5 Tenths make 35 Tenths; 35 ÷ 4 = 8 Tenths, remainder 3 Tenths. Going on with Hundredths and Thousandths gives 7 Hundredths and 5 Thousandths.
3. So 7.5 ÷ 4 = 1.875. Check: 1.875 × 4 = 7.5.

Teacher's Note:
1. Keep regrouping the remainder into the next smaller place.
2. Always check by multiplying back.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. 0.5 × 0.6 = \( \frac{5}{10} \) × \( \frac{6}{10} \) = \( \frac{30}{100} \) = 0.30, which is less than 0.5 and less than 0.6. So A is true.
2. R is the true general rule for numbers between 0 and 1.
3. R gives exactly the reason for A, so both are true and R is the correct explanation of A.

Teacher's Note:
1. Taking a part of a part gives something smaller.
2. Here R is the rule and A is one example of it.

Answer: (d) A is false, but R is true.

Explanation:
1. Dividing by 100 moves the point two places to the left, e.g. 7.2 ÷ 100 = 0.072. So A is false.
2. Dividing by 100 is the same as multiplying by \( \frac{1}{100} \), so R is true.
3. Hence A is false but R is true.

Teacher's Note:
1. Dividing makes the number smaller, so the point moves left.
2. Test any rule with a small example.

Answer: (c) Only Statement I is true

Explanation:
1. 2.5 × 4 = 10 is a whole number, so Statement I is true.
2. 2.5 × 0.4 = 1.00 = 1, a whole number made from two decimals, so Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. One counter-example is enough to show a 'never' statement is false.
2. Zeroes at the end of a decimal can make it a whole number.

Answer: (b) ₹75

Explanation:
1. 12.50 × 6 = \( \frac{1250}{100} \) × 6 = \( \frac{7500}{100} \).
2. 7500 ÷ 100 = 75.
3. So 6 pens cost ₹75.

Teacher's Note:
1. Multiply as whole numbers, then place the point.
2. ₹75.00 is the same as ₹75.

Answer: (a) (i)-(q), (ii)-(s), (iii)-(r), (iv)-(p)

Explanation:
1. Multiplying moves the point right: 2.5 × 10 = 25 (q), 2.5 × 100 = 250 (s).
2. Dividing moves the point left: 2.5 ÷ 10 = 0.25 (r), 2.5 ÷ 100 = 0.025 (p).
3. So the matching is (i)-(q), (ii)-(s), (iii)-(r), (iv)-(p).

Teacher's Note:
1. Multiply: right; divide: left.
2. Count the zeroes to know how many places.

Answer: (d) 0.12 square unit

Explanation:
1. Each small square is one-hundredth of the unit square.
2. The shaded part has 3 × 4 = 12 small squares, that is \( \frac{12}{100} \) = 0.12 square unit.
3. This is the area model of 0.3 × 0.4 = 0.12 square unit.

Teacher's Note:
1. Count the shaded squares and divide by 100.
2. 0.7 is the sum 0.3 + 0.4, not the product.

Answer: (c) Ones are regrouped into Tenths

Explanation:
1. In long division we move from Ones to Tenths only by regrouping.
2. That is exactly where the quotient crosses from the whole-number part to the decimal part.
3. So the point goes in when Ones are regrouped into Tenths.

Teacher's Note:
1. The decimal point separates Ones from Tenths.
2. Write the point in the quotient as soon as you start on Tenths.

Answer: (a) 10 ÷ 3

Explanation:
1. 10 ÷ 3: every step leaves remainder 1, so the digit 3 repeats for ever: 3.333 …
2. The others stop: 10 ÷ 4 = 2.5, 10 ÷ 5 = 2, 10 ÷ 8 = 1.25.
3. So the never-ending one is 10 ÷ 3.

Teacher's Note:
1. A division ends only when the remainder becomes 0.
2. A repeating remainder means repeating digits.

Answer: (d) 0.45 × 0.6

Explanation:
1. The product is less than both numbers only when both lie between 0 and 1.
2. Only 0.45 and 0.6 are both between 0 and 1: 0.45 × 0.6 = 0.27.
3. In (a) the product 4.8 is greater than both; in (b) 4.8 and (c) 1.08 the product lies between the two numbers. So the answer is 0.45 × 0.6.

Teacher's Note:
1. Compare each number with 1 first.
2. Both less than 1 gives a product smaller than both.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. 7.2 ÷ 0.8 = 72 ÷ 8 = 9, so A is true.
2. R is a true rule; it tells us 9 must be bigger than 7.2.
3. But R does not tell how the value 9 is found, so both are true but R is not the correct explanation of A.

Teacher's Note:
1. A is a calculation; R is only a size check.
2. Multiply both numbers by 10 to divide by a decimal.

Answer: (c) A is true, but R is false.

Explanation:
1. Both 4.68 and 1.3 have been multiplied by 10, so the quotient does not change: both equal 3.6. A is true.
2. If only the divisor is multiplied by 10, the quotient becomes 10 times smaller. So R is false.
3. Hence A is true but R is false.

Teacher's Note:
1. The quotient stays the same only when BOTH numbers are multiplied by the same number.
2. Changing one number alone changes the answer.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. 2.250 = 2 + \( \frac{2}{10} \) + \( \frac{5}{100} \) + \( \frac{0}{1000} \); the last zero adds nothing, so 2.250 = 2.25 and the bill is the same. A is true.
2. R is the true general rule about end zeroes.
3. R is exactly why A holds, so both are true and R is the correct explanation of A.

Teacher's Note:
1. Trailing zeroes after the point add nothing.
2. Zeroes between digits, like in 2.05, do matter.

Answer: (d) Neither statement is true

Explanation:
1. Multiplying by 100 moves the point two places to the right, so Statement I is false.
2. Dividing by 10 moves the point one place to the left, so Statement II is false.
3. So neither statement is true.

Teacher's Note:
1. Both statements have the directions swapped.
2. Multiplying makes bigger (right), dividing makes smaller (left).

Answer: (b) Only Statement II is true

Explanation:
1. 3 ÷ 8 is not a counting number, so Statement I is false.
2. \( \frac{3}{8} \) = \( \frac{3 × 125}{8 × 125} \) = \( \frac{375}{1000} \) = 0.375, so Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. Make the denominator 1000 to change eighths into decimals.
2. One example like 3 ÷ 8 disproves 'always'.

Answer: (a) Only Statement I is true

Explanation:
1. 25 ÷ 0.1 = \( \frac{250}{1} \) = 250 = 25 × 10, so Statement I is true.
2. 25 ÷ 0.01 = 2500, which equals 25 × 100, not 25 ÷ 100 = 0.25. So Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. Dividing by 0.1 is like multiplying by 10.
2. Dividing by 0.01 is like multiplying by 100.

Answer: (c) 1460.9688

Explanation:
1. Days for 4 revolutions = 4 × 365.2422.
2. Without the point: 4 × 3652422 = 14609688; the product keeps 4 decimal digits.
3. So the answer is 1460.9688 days.

Teacher's Note:
1. 1461 is the calendar count, not the true time.
2. Keep all four decimal digits.

Answer: (d) (i)-(q), (ii)-(s), (iii)-(p), (iv)-(r)

Explanation:
1. Count the decimal digits and place the point in 360.
2. 2.4 × 1.5: 2 places → 3.60 = 3.6 (q); 0.24 × 1.5: 3 places → 0.360 = 0.36 (s).
3. 2.4 × 0.015: 4 places → 0.0360 = 0.036 (p); 0.24 × 0.015: 5 places → 0.00360 = 0.0036 (r). So the answer is (i)-(q), (ii)-(s), (iii)-(p), (iv)-(r).

Teacher's Note:
1. Place the point in 360 first, then drop the end zero.
2. Total decimal digits decide the place of the point.

Answer: (b) ₹306

Explanation:
1. Rice: 2.5 × 48 = ₹120; sugar: 1.5 × 44 = ₹66.
2. Tea leaves: 0.25 × 480 = ₹120.
3. Total = 120 + 66 + 120 = ₹306.

Teacher's Note:
1. Find each item's cost separately, then add.
2. 0.25 kg is a quarter of a kilogram.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Dividing 1 by 7, the remainders come as 1, 3, 2, 6, 4, 5 and then 1 again, so 0 never appears.
2. So the digits 142857 repeat for ever: 0.142857142857 … Both A and R are true.
3. The repeating remainders are exactly why the decimal never ends, so R is the correct explanation of A.

Teacher's Note:
1. A division stops only when the remainder is 0.
2. Once a remainder repeats, the digits repeat too.

Answer: (d) Only Statement I is true

Explanation:
1. 0.942368 lies between 0 and 1.
2. Dividing by a number between 0 and 1 gives a bigger result, so Statement I is true.
3. Multiplying by a number less than 1 gives a smaller result, so Statement II is false. Hence only Statement I is true.

Teacher's Note:
1. Compare the divisor or multiplier with 1.
2. No calculation is needed here.

Answer: (b) 8 km

Explanation:
1. Distance in 8 rounds = 2.75 × 8 = 22 km.
2. Distance left = 30 − 22 = 8 km.
3. So she must cycle 8 km more.

Teacher's Note:
1. 22 km is what she has done, not what is left.
2. Read the question to the end.

Answer: (c) 8

Explanation:
1. Other number = 0.72 ÷ 0.09.
2. Multiply both by 100: 72 ÷ 9 = 8.
3. Check: 0.09 × 8 = 0.72. So the other number is 8.

Teacher's Note:
1. Missing factor = product ÷ known factor.
2. Make the divisor whole before dividing.

Answer: (a) (i)-(r), (ii)-(q), (iii)-(s), (iv)-(p)

Explanation:
1. Make each divisor 32 by multiplying both numbers by the same power of 10.
2. 86.4 ÷ 3.2 = 864 ÷ 32 = 27 (r); 8.64 ÷ 3.2 = 86.4 ÷ 32 = 2.7 (q).
3. 864 ÷ 0.32 = 86400 ÷ 32 = 2700 (s); 8.64 ÷ 0.032 = 8640 ÷ 32 = 270 (p). So the answer is (i)-(r), (ii)-(q), (iii)-(s), (iv)-(p).

Teacher's Note:
1. Scale dividend and divisor together.
2. Then compare the new dividend with 864.

Answer: (d) 2.7 cm

Explanation:
1. Other side = area ÷ known side = 20.25 ÷ 7.5.
2. Multiply both by 10: 202.5 ÷ 75 = 2.7.
3. Check: 7.5 × 2.7 = 20.25. So the other side is 2.7 cm.

Teacher's Note:
1. Area = length × breadth, so divide to find the missing side.
2. 12.75 is a subtraction, not a division.