CBSE Class 7 Mathematics Another Peek beyond the Point Worksheet Set 01

Very Short Answer Questions

Question 1. Write the fraction \( \frac{23}{1000} \) as a decimal number.
Answer:
Denominator 1000 needs three decimal digits, so \( \frac{23}{1000} \) = 0.023.

Teacher's Note:
1. Fill the empty place with a zero.
2. Three zeroes, three decimal places.

Question 2. In the number 38.405, what does the digit 5 stand for?
Answer:
5 is in the thousandths place, so it stands for 5 thousandths, that is \( \frac{5}{1000} \) = 0.005.

Teacher's Note:
1. Places after the point: tenths, hundredths, thousandths.
2. The 0 holds the hundredths place.

Question 3. Find the value of 6.3 × 10.
Answer:
Multiplying by 10 moves the point one place right: 6.3 × 10 = 63.

Teacher's Note:
1. One zero, one place.
2. The answer is bigger than 6.3.

Question 4. Find the value of 0.78 × 100.
Answer:
Multiplying by 100 moves the point two places right: 0.78 × 100 = 78.

Teacher's Note:
1. Two zeroes, two places right.
2. The leading 0 drops away.

Question 5. Find the value of 14.5 × 1000.
Answer:
Multiplying by 1000 moves the point three places right; fill with zeroes: 14.5 × 1000 = 14500.

Teacher's Note:
1. Add zeroes when digits run out.
2. Three zeroes, three places.

Question 6. Find the value of 32.6 ÷ 10.
Answer:
Dividing by 10 moves the point one place left: 32.6 ÷ 10 = 3.26.

Teacher's Note:
1. Dividing makes the number smaller.
2. One zero, one place left.

Question 7. Find the value of 0.45 ÷ 100.
Answer:
Dividing by 100 moves the point two places left: 0.45 ÷ 100 = 0.0045.

Teacher's Note:
1. Put zeroes in front when needed.
2. Count the places carefully.

Question 8. Find 7 × 0.4 first in tenths and then write the answer as a decimal.
Answer:
0.4 = 4 tenths, so 7 × 4 tenths = 28 tenths = \( \frac{28}{10} \) = 2.8.

Teacher's Note:
1. Multiply the counting numbers, keep the unit 'tenths'.
2. 10 tenths make 1 one.

Question 9. Find the value of 1.25 × 4.
Answer:
125 × 4 = 500; keep 2 decimal digits: 1.25 × 4 = 5.00 = 5.

Teacher's Note:
1. End zeroes after the point can be dropped.
2. 1.25 is one and a quarter; four of them make 5.

Question 10. Find the value of 8.4 ÷ 4.
Answer:
84 ÷ 4 = 21; keeping one decimal digit, 8.4 ÷ 4 = 2.1.

Teacher's Note:
1. Divide as whole numbers, then keep the decimal place.
2. Check: 2.1 × 4 = 8.4.

Question 11. State the rule for finding how many digits come after the decimal point in the product of two decimal numbers.
Answer:
Multiply the numbers without their decimal points; then the number of decimal digits in the product = total number of decimal digits in the two numbers.

Teacher's Note:
1. Add the decimal digits of both numbers.
2. Place the point counting from the right.

Question 12. Express 250 g in kilograms as a decimal.
Answer:
1 kg = 1000 g, so 250 g = \( \frac{250}{1000} \) kg = 0.25 kg.

Teacher's Note:
1. Grams to kilograms: divide by 1000.
2. 0.250 and 0.25 are equal.

Question 13. Given that 43 × 26 = 1118, write the value of 4.3 × 2.6 without multiplying again.
Answer:
The two numbers have 1 + 1 = 2 decimal digits, so put the point two places from the right in 1118: 4.3 × 2.6 = 11.18.

Teacher's Note:
1. The digits stay the same; only the point is placed.
2. Estimate: 4 × 3 = 12, close to 11.18.

Question 14. Find the product 2.4 × 3.5.
Answer:
24 × 35 = 840; 1 + 1 = 2 decimal digits, so 2.4 × 3.5 = 8.40 = 8.4.

Teacher's Note:
1. Place the point before dropping the end zero.
2. Estimate: 2 × 4 = 8.

Question 15. Find the product 0.6 × 0.07.
Answer:
6 × 7 = 42; 1 + 2 = 3 decimal digits are needed, so 0.6 × 0.07 = 0.042.

Teacher's Note:
1. Add a zero in front to make three places.
2. The product is smaller than both numbers.

Question 16. Find 0.8 × 0.9 and state whether the product is greater or smaller than both the numbers multiplied.
Answer:
0.8 × 0.9 = 0.72. Both numbers lie between 0 and 1, so the product is smaller than both 0.8 and 0.9.

Teacher's Note:
1. A part of a part is smaller still.
2. Compare 0.72 with 0.8 and 0.9.

Question 17. Find the value of 9.6 ÷ 8.
Answer:
96 ÷ 8 = 12; keeping one decimal digit, 9.6 ÷ 8 = 1.2. Check: 1.2 × 8 = 9.6.

Teacher's Note:
1. Divide as whole numbers first.
2. Check by multiplying back.

Question 18. Express the fraction \( \frac{7}{8} \) in decimal form.
Answer:
Make the denominator 1000: \( \frac{7}{8} \) = \( \frac{7 × 125}{8 × 125} \) = \( \frac{875}{1000} \) = 0.875.

Teacher's Note:
1. 8 × 125 = 1000.
2. You can also divide 7 by 8 by long division.

Question 19. Find 3.6 ÷ 0.4, showing the first step that makes the divisor a whole number.
Answer:
Multiply both numbers by 10: 3.6 ÷ 0.4 = 36 ÷ 4 = 9.

Teacher's Note:
1. Multiplying both by 10 keeps the quotient the same.
2. Dividing by a number less than 1 gives a bigger answer.

Question 20. By what number must both the numbers in 5.76 ÷ 0.24 be multiplied to make the divisor a whole number? Also write the quotient.
Answer:
0.24 × 100 = 24, so both must be multiplied by 100. Then 5.76 ÷ 0.24 = 576 ÷ 24 = 24.

Teacher's Note:
1. Two decimal digits in the divisor need × 100.
2. Check: 0.24 × 24 = 5.76.

Question 21. A ribbon of length 7.5 m is cut into 6 pieces of equal length. Find the length of each piece.
Answer:
Each piece = 7.5 ÷ 6. Since 75 ÷ 6 = 12.5, we get 7.5 ÷ 6 = 1.25 m.

Teacher's Note:
1. Equal pieces means division.
2. Check: 1.25 × 6 = 7.5.

Question 22. One litre of milk costs ₹58. Find the cost of 2.5 litres of milk.
Answer:
Cost = 58 × 2.5 = 145, so 2.5 litres cost ₹145.

Teacher's Note:
1. 2.5 litres = 2 litres + half a litre: 116 + 29.
2. Multiply rate by quantity.

Question 23. Express 68.5 cm in metres.
Answer:
1 m = 100 cm, so divide by 100: 68.5 cm = 0.685 m.

Teacher's Note:
1. Centimetres to metres: divide by 100.
2. Move the point two places left.

Question 24. The Earth needs 365.2422 days for one revolution around the Sun. How many days more than 365 × 10 does it need for 10 revolutions?
Answer:
Extra time each year = 0.2422 day. For 10 revolutions: 0.2422 × 10 = 2.422 days more.

Teacher's Note:
1. Only the extra part needs to be multiplied.
2. × 10 moves the point one place right.

Question 25. Given that 918 ÷ 27 = 34, write the values of 9.18 ÷ 0.27 and 91.8 ÷ 2.7.
Answer:
Multiply both by 100: 9.18 ÷ 0.27 = 918 ÷ 27 = 34.
Multiply both by 10: 91.8 ÷ 2.7 = 918 ÷ 27 = 34.

Teacher's Note:
1. Scaling both numbers by the same amount keeps the quotient.
2. Both answers are 34.

Question 26. Fill in the blank: 48 ÷ ____ = 480.
Answer:
The missing number is 0.1, because 48 ÷ 0.1 = 480 ÷ 1 = 480, the same as 48 × 10.

Teacher's Note:
1. The answer is bigger, so the divisor is less than 1.
2. Dividing by 0.1 = multiplying by 10.

Question 27. Without dividing, say which is greater, 36.4 ÷ 0.7 or 36.4 ÷ 7, and give the reason.
Answer:
36.4 ÷ 0.7 is greater. The smaller the divisor, the bigger the quotient; 0.7 is less than 1, so 36.4 ÷ 0.7 (= 52) is even bigger than 36.4, while 36.4 ÷ 7 = 5.2.

Teacher's Note:
1. Same dividend: smaller divisor, bigger quotient.
2. Compare the divisor with 1.

Question 28. Explain why 10 ÷ 3 cannot be written using a finite number of digits after the decimal point.
Answer:
At every step the remainder is 1; regrouping it as 10 of the next smaller unit again gives digit 3 and remainder 1.
The remainder never becomes 0, so the division never stops: 10 ÷ 3 = 3.333 …

Teacher's Note:
1. A division ends only when the remainder is 0.
2. Same remainder means same step again.

Question 29. Arrange in increasing order: 56.8 × 0.8, 56.8, 56.8 ÷ 0.8.
Answer:
56.8 × 0.8 = 45.44 and 56.8 ÷ 0.8 = 71.
Increasing order: 56.8 × 0.8, 56.8, 56.8 ÷ 0.8 (45.44 < 56.8 < 71).

Teacher's Note:
1. × 0.8 makes smaller; ÷ 0.8 makes bigger.
2. This can be decided without calculating.

Question 30. In 4 calendar years with one leap year there are 1461 days, while the Earth needs 1460.9688 days for 4 revolutions. By how many days does the calendar overshoot?
Answer:
Overshoot = 1461 − 1460.9688 = 0.0312 day in 4 years.

Teacher's Note:
1. Write 1461 as 1461.0000 to subtract.
2. The calendar is slightly too long.