CBSE Class 7 Mathematics A Peek Beyond the Poin Assignment Set 01

Very Short Answer Questions

Question 1. Two screws look exactly the same but one of them does not fit. Why do we need units smaller than a centimetre to describe such a difference?
Answer:
Their lengths differ by less than one centimetre, so whole centimetres cannot show the difference. We split a centimetre into 10 equal parts and measure in tenths.

Teacher's Note:
1. Small differences need small units.
2. Tenths of a centimetre are millimetres.

Question 2. Into how many equal parts is the length between two consecutive numbers of an ordinary centimetre scale divided? What is each part called?
Answer:
It is divided into 10 equal parts. Each part is one-tenth (\( \frac{1}{10} \)) of the unit, written 0.1.

Teacher's Note:
1. Each small part on a ruler is 1 mm = 0.1 cm.
2. Ten such parts make 1 cm.

Question 3. Write “two and seven-tenths” first as a mixed number with a fractional unit and then in decimal form.
Answer:
Mixed number: \( 2\frac{7}{10} \); decimal form: 2.7.

Teacher's Note:
1. 'and' separates the whole part from the fractional part.
2. The point plays the role of 'and'.

Question 4. How many one-tenths make one unit?
Answer:
10 one-tenths make one unit, because 10 × \( \frac{1}{10} \) = 1.

Teacher's Note:
1. Ten equal parts fill the whole.
2. 10 × 0.1 = 1.

Question 5. How many one-hundredths make one unit?
Answer:
100 one-hundredths make one unit, since each of the 10 tenths holds 10 hundredths (10 × 10 = 100).

Teacher's Note:
1. A hundredth is a tenth of a tenth.
2. 100 × 0.01 = 1.

Question 6. Write \( \frac{7}{100} \) in decimal form.
Answer:
\( \frac{7}{100} \) = 0.07, with 0 in the tenths place and 7 in the hundredths place.

Teacher's Note:
1. Hundredths need two places after the point.
2. Do not write 0.7, which is seven tenths.

Question 7. Name the symbol used to separate the whole-number part of a number from its fractional part.
Answer:
It is the decimal point, as in 7.05.

Teacher's Note:
1. Left of the point: whole part; right of it: fractional part.
2. Some countries use a comma instead.

Question 8. Write 1 mm in metres, in decimal form.
Answer:
1 m = 1000 mm, so 1 mm = \( \frac{1}{1000} \) m = 0.001 m.

Teacher's Note:
1. A millimetre is a thousandth of a metre.
2. 'milli' means one-thousandth.

Question 9. Convert 250 paise into rupees.
Answer:
100 paise = 1 rupee, so 250 paise = \( \frac{250}{100} \) rupees = Rs 2.50.

Teacher's Note:
1. Divide paise by 100 to get rupees.
2. Rupee amounts keep two decimal places.

Question 10. Between which two whole numbers does the decimal number 3.6 lie?
Answer:
3.6 is 3 units and 6 tenths, which is more than 3 but less than 4. So it lies between 3 and 4.

Teacher's Note:
1. The whole-number part gives the lower whole number.
2. Add 1 to get the upper one.

Question 11. Which is greater: 2.46 or 2.64?
Answer:
Both have 2 units; 2.64 has 6 tenths and 2.46 has 4 tenths. So 2.64 is greater.

Teacher's Note:
1. Compare from the highest place.
2. Stop at the first place where the digits differ.

Question 12. Find the sum 5.4 + 3.2.
Answer:
Tenths: 4 + 2 = 6; units: 5 + 3 = 8. So 5.4 + 3.2 = 8.6.

Teacher's Note:
1. Add tenths to tenths and units to units.
2. Keep the points in a line.

Question 13. Write 48 tenths first as a number in units and tenths and then in decimal form.
Answer:
48 tenths = \( \frac{48}{10} \) = 4 units and 8 tenths = 4.8.

Teacher's Note:
1. Every 10 tenths make one unit.
2. Dividing by 10 moves the point one place left.

Question 14. Add 2 units and 8 tenths to 3 units and 5 tenths. Give the answer in units and tenths.
Answer:
Units: 2 + 3 = 5; tenths: 8 + 5 = 13.
13 tenths = 1 unit and 3 tenths, so the sum is 6 units and 3 tenths (6.3).

Teacher's Note:
1. Regroup 10 tenths as 1 unit.
2. Just like carrying in whole-number addition.

Question 15. A length is 4 units, 4 tenths and 5 hundredths. Write it as a number of hundredths and also in decimal form.
Answer:
4 units = 400 hundredths and 4 tenths = 40 hundredths.
Total = 400 + 40 + 5 = 445 hundredths = 4.45.

Teacher's Note:
1. 1 unit = 100 hundredths; 1 tenth = 10 hundredths.
2. 445 hundredths = 445 ÷ 100 = 4.45.

Question 16. Write the expanded forms of 70.5 and 7.05 and state why the two numbers are different.
Answer:
70.5 = \( 7 \times 10 + 0 \times 1 + 5 \times \frac{1}{10} \) and 7.05 = \( 7 \times 1 + 0 \times \frac{1}{10} + 5 \times \frac{1}{100} \).
They differ because the same digits 7 and 5 sit in different places.

Teacher's Note:
1. The position of the point changes each digit's value.
2. 70.5 is ten times 7.05.

Question 17. Write in decimal form: 3 ones, 0 tenths and 8 hundredths.
Answer:
3.08 (3 in the ones place, 0 in the tenths place, 8 in the hundredths place).

Teacher's Note:
1. Keep the zero to hold the tenths place.
2. 3.8 would be a different number.

Question 18. Write 160 tenths in decimal form.
Answer:
160 tenths = \( \frac{160}{10} \) = 16, written 16.0.

Teacher's Note:
1. Every 10 tenths make one unit.
2. 16.0 and 16 are equal.

Question 19. Convert 408 cm into metres.
Answer:
1 cm = 0.01 m, so 408 cm = \( \frac{408}{100} \) m = 4.08 m.

Teacher's Note:
1. Divide centimetres by 100 to get metres.
2. 8 cm is 0.08 m, so keep the zero.

Question 20. Express 1 kg 7 g in kilograms, in decimal form.
Answer:
7 g = \( \frac{7}{1000} \) kg = 0.007 kg, so 1 kg 7 g = 1.007 kg.

Teacher's Note:
1. Grams take three places after the point.
2. 1.7 kg would mean 1 kg 700 g.

Question 21. The gap between 2.3 and 2.4 on a number line is divided into 10 equal parts. Write any three decimal numbers marked on these divisions.
Answer:
Each division is one hundredth, so the marks are 2.31, 2.32, …, 2.39.
Any three, for example 2.31, 2.35 and 2.38.

Teacher's Note:
1. A tenth cut into 10 parts gives hundredths.
2. All the marks start with 2.3.

Question 22. Arrange in ascending order: 1.101, 11.01, 1.01, 1.011.
Answer:
Comparing place by place (1.010, 1.011, 1.101, 11.010): 1.01 < 1.011 < 1.101 < 11.01.

Teacher's Note:
1. Look at the whole-number part first.
2. Then compare tenths, hundredths and thousandths.

Question 23. Find the difference 20 − 7.35.
Answer:
Write 20 as 20.00: 20.00 − 7.35 = 12.65.

Teacher's Note:
1. Add a point and zeros to the whole number first.
2. Check: 12.65 + 7.35 = 20.

Question 24. Write the next two terms of the sequence 6.2, 6.35, 6.5, …
Answer:
Each term is 0.15 more than the one before.
Next two terms: 6.5 + 0.15 = 6.65 and 6.65 + 0.15 = 6.8.

Teacher's Note:
1. Find the change between terms first.
2. 6.35 − 6.2 = 0.15.

Question 25. Which of the numbers 5.6, 5.65 and 6.04 is closest to 6? Give the reason in one line.
Answer:
6.04 is closest: it is only 0.04 away, while 5.65 is 0.35 away and 5.6 is 0.4 away.

Teacher's Note:
1. Find each distance from 6.
2. The closest number may be greater than 6.

Question 26. Without actually adding, state the two whole numbers between which the sum 14.6 + 7.8 must lie.
Answer:
The sum is more than 14 + 7 = 21 and less than 21 + 2 = 23, so it lies between 21 and 23 (the exact sum is 22.4).

Teacher's Note:
1. Each fractional part is less than 1.
2. So together they add less than 2.

Question 27. A nurse has to give 0.05 mg of a medicine but reads the prescription as 0.5 mg. How many times the prescribed dose will the patient receive?
Answer:
0.5 mg is 50 hundredths and 0.05 mg is 5 hundredths, so the patient gets 10 times the dose.

Teacher's Note:
1. Moving the point one place right multiplies by 10.
2. Decimal mistakes in medicine are dangerous.

Question 28. A cricket scoreboard shows “Overs left: 4.3”. What does this mean, and why is 4.3 here not a true decimal number?
Answer:
It means 4 complete overs and 3 balls, that is \( 4\frac{3}{6} \) overs.
It is not a true decimal because an over has 6 balls; it is not split into 10 equal parts.

Teacher's Note:
1. A true decimal splits the unit into 10 equal parts.
2. Here the digit after the point counts balls.

Question 29. How many millimetres make 1 km? Show the two steps you use.
Answer:
1 km = 1000 m and 1 m = 1000 mm.
So 1 km = 1000 × 1000 = 10,00,000 mm.

Teacher's Note:
1. Convert one step at a time.
2. Ten lakh millimetres make a kilometre.

Question 30. Using each of the digits 3, 1, 0, 9 and 7 exactly once, write the decimal number closest to 30 that has two digits before the decimal point.
Answer:
Using 3 and 0 makes the whole part exactly 30; the other digits 1, 7, 9 in increasing order keep the fractional part smallest.
The number is 30.179 (only 0.179 away from 30).

Teacher's Note:
1. Make the whole part as near to 30 as possible.
2. Then make the decimal part as small as possible.