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

Short Answer Questions

Question 1. A carpenter picks up two nails from a box. On a ruler marked only in whole centimetres, both nails look “about 4 cm long”, yet only one of them fits the hole. Explain why whole centimetres are not enough here, and state what each part is called when one centimetre is divided into 10 equal parts.
Answer:
Both nails lie between 4 cm and 5 cm but can still differ in length; a ruler marked only in whole centimetres cannot show that difference.
For an exact measure we need a smaller unit, so each centimetre is divided into 10 equal parts.
Each part is one-tenth of a centimetre, written \( \frac{1}{10} \) cm or 0.1 cm (that is, 1 mm).
With these marks the carpenter could find, for example, that one nail is 4.3 cm and the other is 4.7 cm.
In simple words: Whole centimetres are too big; tenths of a centimetre show the small difference.

Teacher's Note:
1. Accuracy needs smaller units.
2. 0.1 cm is the same as 1 mm.

Question 2. The length of a ribbon is 5 units and 8 one-tenths.
(i) Write this length in two different fractional forms and in decimal form.
(ii) Read out both fractional forms in words.
Answer:
(i) As a mixed number: \( 5\frac{8}{10} \) units. Since 5 units = 50 one-tenths, it is also \( \frac{58}{10} \) units. Decimal form: 5.8 units.
(ii) \( 5\frac{8}{10} \) is read “five and eight-tenths”; \( \frac{58}{10} \) is read “fifty-eight tenths”.
In simple words: 5 and 8 tenths = 58 tenths = 5.8.

Teacher's Note:
1. One length can be written in several equal ways.
2. Multiply the units by 10 to change them to tenths.

Question 3. Write each of the following quantities in decimal form and then state which two of them are equal in value.
(i) \( 8\frac{5}{10} \)
(ii) \( \frac{5}{10} \)
(iii) \( \frac{85}{10} \)
(iv) \( 85\frac{5}{10} \)
Answer:
(i) \( 8\frac{5}{10} \) = 8.5
(ii) \( \frac{5}{10} \) = 0.5
(iii) \( \frac{85}{10} \) = 8 + \( \frac{5}{10} \) = 8.5
(iv) \( 85\frac{5}{10} \) = 85.5
Quantities (i) and (iii) are equal, because 85 one-tenths is the same as 8 units and 5 one-tenths.
In simple words: 85 tenths and 8 and 5 tenths are both 8.5.

Teacher's Note:
1. Split an improper fraction into units and tenths.
2. Then compare the decimal forms.

Question 4. Answer the following and give a short reason for each, using the idea of splitting a part into 10 equal pieces.
(i) How many one-hundredths make one-tenth?
(ii) How many one-thousandths make one unit?
(iii) How many one-thousandths make one-hundredth?
Answer:
(i) 10, because each one-tenth is split into 10 equal parts to get one-hundredths.
(ii) 1000: a unit gives 10 tenths, each tenth gives 10 hundredths (100 in all), and each hundredth gives 10 thousandths (100 × 10 = 1000).
(iii) 10, because a hundredth is itself split into 10 equal parts to give thousandths.
In simple words: Each step down splits a part into 10, so neighbours differ by 10.

Teacher's Note:
1. Each place is 10 times the next one to its right.
2. Two steps apart means 100 times; three steps means 1000 times.

Question 5. Write in decimal form and then read the second number aloud in words.
(i) 3 ones, 0 tenths and 7 hundredths
(ii) 2 tens, 4 ones, 5 tenths, 0 hundredths and 9 thousandths
Answer:
(i) 3 + \( \frac{0}{10} \) + \( \frac{7}{100} \) = 3.07.
(ii) 20 + 4 + \( \frac{5}{10} \) + \( \frac{0}{100} \) + \( \frac{9}{1000} \) = 24.509.
It is read as “twenty-four point five zero nine”, not as “twenty-four point five hundred and nine”.
In simple words: 3.07 and 24.509; digits after the point are read one by one.

Teacher's Note:
1. Zeros hold empty places.
2. After the point, read each digit separately.

Question 6. Convert as directed and show the fraction step in each case.
(i) 85 mm into cm
(ii) 7 cm into m
(iii) 2.4 m into cm
Answer:
(i) 1 mm = \( \frac{1}{10} \) cm, so 85 mm = \( \frac{85}{10} \) cm = 8.5 cm.
(ii) 1 cm = \( \frac{1}{100} \) m, so 7 cm = \( \frac{7}{100} \) m = 0.07 m.
(iii) 2.4 m = 2 m + \( \frac{4}{10} \) m = 200 cm + 40 cm = 240 cm.
In simple words: Divide by 10 for mm to cm, by 100 for cm to m, and multiply by 100 for m to cm.

Teacher's Note:
1. Bigger unit, smaller number.
2. Smaller unit, bigger number.

Question 7. Zara thinks that writing extra zeros on the right of a decimal number changes its value, so she says 0.4, 0.40 and 0.400 are three different numbers. Use place value to say whether she is right, and also state whether 0.4 and 0.04 are equal.
Answer:
Zara is not right.
In 0.4, 0.40 and 0.400 the digit 4 is in the tenths place each time; the extra zeros only say there are 0 hundredths and 0 thousandths.
So all three mean 4 tenths: 0.4 = 0.40 = 0.400.
But in 0.04 the 4 is in the hundredths place, so it means 4 hundredths. Hence 0.4 and 0.04 are not equal; 0.4 is ten times 0.04.
In simple words: Zeros at the end change nothing, but a zero right after the point moves the digit.

Teacher's Note:
1. Look at the place of the non-zero digit.
2. End zeros add nothing; middle zeros matter.

Question 8. Find the following, writing the numbers one below the other with the decimal points in a line.
(i) 6.4 + 3.75
(ii) 9.2 − 4.86
Answer:
Write the points one below the other so that tenths are under tenths and hundredths under hundredths.
(i) 6.40 + 3.75: hundredths 0 + 5 = 5; tenths 4 + 7 = 11, that is 1 unit and 1 tenth; units 6 + 3 + 1 = 10. Sum = 10.15.
(ii) 9.20 − 4.86 = 4.34. Check: 4.34 + 4.86 = 9.20.
In simple words: Line up the points, fill gaps with zeros, then add or subtract.

Teacher's Note:
1. Write 6.4 as 6.40 and 9.2 as 9.20.
2. Check a subtraction by adding back.

Question 9. A toy train has three coaches of lengths \( 2\frac{6}{10} \) units, \( 3\frac{8}{10} \) units and \( 4\frac{9}{10} \) units. Find the total length of the train by adding the units and the one-tenths separately, and explain how the extra tenths are regrouped.
Answer:
Units: 2 + 3 + 4 = 9 units.
Tenths: 6 + 8 + 9 = 23 one-tenths.
23 one-tenths = 20 one-tenths + 3 one-tenths = 2 units and 3 one-tenths.
Total = 9 + 2 units and 3 one-tenths = \( 11\frac{3}{10} \) units = 11.3 units.
The regrouping is done because 10 one-tenths always make one whole unit.
In simple words: 9 units plus 23 tenths gives 11.3 units.

Teacher's Note:
1. Carry every 10 tenths into the units.
2. This is like carrying in whole numbers.

Question 10. Find 20.4 − 7.68. Write the subtraction step by step and explain clearly why a tenth has to be broken into 10 hundredths before the hundredths column can be subtracted.
Answer:
Write 20.4 as 20.40 so both numbers have hundredths.
Hundredths: 0 is less than 8, so one of the 4 tenths is broken into 10 hundredths. Now there are 3 tenths and 10 hundredths; 10 − 8 = 2 hundredths.
Tenths: 3 − 6 is not possible, so one unit is broken into 10 tenths, giving 19 units and 13 tenths; 13 − 6 = 7 tenths.
Units: 19 − 7 = 12.
So 20.4 − 7.68 = 12.72. Check: 12.72 + 7.68 = 20.40.
A tenth is broken because there were 0 hundredths to take 8 from, and 1 tenth = 10 hundredths.
In simple words: Borrow just as in whole numbers: 1 tenth = 10 hundredths, 1 unit = 10 tenths.

Teacher's Note:
1. Borrowing works the same way across the point.
2. Always check by adding back.

Question 11. Write each of these quantities in decimal form, showing one middle step for each.
(i) 347 tenths
(ii) 506 hundredths
(iii) 2075 thousandths
Answer:
(i) 347 tenths = \( \frac{347}{10} \) = 30 + 4 + \( \frac{7}{10} \) = 34.7.
(ii) 506 hundredths = \( \frac{506}{100} \) = 5 + \( \frac{6}{100} \) = 5.06.
(iii) 2075 thousandths = \( \frac{2075}{1000} \) = 2 + \( \frac{75}{1000} \) = 2.075.
In simple words: Divide by 10, 100 or 1000 by moving the point 1, 2 or 3 places left.

Teacher's Note:
1. The number of zeros tells how far the point moves.
2. Keep zeros that hold places, as in 5.06.

Question 12. Answer the following about rupees and paise.
(i) Write 8 paise, 40 paise and 375 paise in rupees using decimal notation.
(ii) Write ₹0.09 and ₹12.05 in paise.
Answer:
Since 100 paise make one rupee, 1 paisa = \( \frac{1}{100} \) rupee = ₹0.01.
(i) 8 paise = \( \frac{8}{100} \) rupee = ₹0.08; 40 paise = \( \frac{40}{100} \) rupee = ₹0.40; 375 paise = \( \frac{375}{100} \) rupees = ₹3.75.
(ii) ₹0.09 is 9 hundredths of a rupee = 9 paise; ₹12.05 = 12 rupees and 5 paise = 1200 + 5 = 1205 paise.
In simple words: Divide paise by 100 for rupees; multiply rupees by 100 for paise.

Teacher's Note:
1. Paise are hundredths of a rupee.
2. ₹0.09 is 9 paise, not 90 paise.

Question 13. On a number line, the gap between 7.3 and 7.4 is divided into 10 equal parts.
(i) What decimal number does each small part stand for?
(ii) Write the numbers at the 3rd mark and at the 7th mark, counted from 7.3.
Answer:
(i) The gap from 7.3 to 7.4 is one-tenth. One-tenth divided into 10 equal parts gives hundredths, so each part stands for 0.01.
(ii) 3rd mark: 7.3 + 0.03 = 7.33; 7th mark: 7.3 + 0.07 = 7.37.
In simple words: Each small part is 0.01, so count hundredths from 7.3.

Teacher's Note:
1. Find the value of one part first.
2. Then add that many parts to the starting mark.

Question 14. Compare 9.087 and 9.09.
(i) State which is greater, comparing the digits place by place and naming the place where the decision is made.
(ii) Write one decimal number that lies between these two numbers.
Answer:
(i) Write 9.09 as 9.090. Both have 9 units and 0 tenths. In the hundredths place the first has 8 and the second has 9. Since 9 > 8, 9.09 is greater; the digits after this place cannot change the result.
(ii) 9.088 lies between them, since 9.087 < 9.088 < 9.090.
In simple words: The hundredths place decides: 9.09 > 9.087.

Teacher's Note:
1. More digits does not mean bigger.
2. Add zeros to make the same number of places when comparing.

Question 15. For each sequence, find the change after every term and write the next two terms.
(i) 7.2, 7.55, 7.9, …
(ii) 20.4, 19.65, 18.9, …
Answer:
(i) The change is +0.35 each time (7.2 + 0.35 = 7.55, 7.55 + 0.35 = 7.9). Next two terms: 8.25 and 8.6.
(ii) The change is −0.75 each time (20.4 − 0.75 = 19.65, 19.65 − 0.75 = 18.9). Next two terms: 18.15 and 17.4.
In simple words: Find the fixed step and keep adding or subtracting it.

Teacher's Note:
1. Check the step between every pair of terms.
2. A sequence can decrease too.

Question 16. A bank clerk once paid out a huge sum because the amounts stored in paise were treated as rupees, and an aircraft was once loaded with fuel measured in pounds instead of kilograms. In your own words, explain what went wrong in such cases and write two habits that help us avoid decimal and unit mistakes.
Answer:
In both cases the number was right but its unit (or the place of the point) was wrong.
Amounts in paise were paid as if they were rupees, so every payment became 100 times too large.
Fuel measured in pounds was loaded as if it were kilograms, so the aircraft got far less than half the fuel it needed.
Two safe habits: always write the unit next to a number, and check the position of the decimal point (and the number of zeros) before using a value.
In simple words: Wrong units or a misplaced point can multiply or shrink a value hugely.

Teacher's Note:
1. A number without a unit can be misread.
2. Re-check the point before using a value.

Question 17. Using each of the digits 4, 9, 7 and 2 exactly once, together with one decimal point placed so that at least one digit comes after it, make the decimal number that is closest to 50. Write the two best candidates, give the distance of each from 50, and state the answer.
Answer:
The whole-number part should be as close to 50 as possible, so it should be 49.
With 4 and 9 before the point, the two candidates are 49.72 and 49.27.
50 − 49.72 = 0.28 and 50 − 49.27 = 0.73.
Any other arrangement, such as 47.92 (distance 2.08) or 42.79 (distance 7.21), is much farther away.
So the required number is 49.72.
In simple words: Use 49 before the point and the bigger fraction .72 to get closest to 50.

Teacher's Note:
1. Fix the whole part first.
2. Below the target, a larger decimal part brings you closer.

Question 18. In a subtraction, a number is taken away from 15.3 and the answer is 8.75. Find the missing number and verify your result by adding it back to the answer.
Answer:
Missing number = 15.3 − 8.75.
Writing 15.3 as 15.30: 15.30 − 8.75 = 6.55.
Check: 6.55 + 8.75 = 15.30 = 15.3, the number we started with. So the number taken away is 6.55.
In simple words: The missing number is 15.3 − 8.75 = 6.55.

Teacher's Note:
1. Taken-away number = start − answer.
2. Add back to check.

Question 19. A parcel contains 1.25 kg of wheat, 750 g of rice and 0.08 kg of salt. Find the total weight of the parcel first in kilograms and then in grams.
Answer:
First change all weights to kilograms: 750 g = \( \frac{750}{1000} \) kg = 0.75 kg.
Total = 1.25 + 0.75 + 0.08 = 2.08 kg.
In grams: 2.08 kg = 2000 g + 80 g = 2080 g.
Check: 1250 + 750 + 80 = 2080 g, which agrees.
In simple words: Use one unit for all weights, then add.

Teacher's Note:
1. Never add kg and g directly.
2. 0.08 kg is 80 g, not 8 g.

Question 20. A doctor prescribes 0.25 mL of a medicine, but the helper reads the label as 2.5 mL and gives that much.
(i) How many times the prescribed dose was actually given, and how many mL extra was it?
(ii) Write one simple writing habit that would have prevented this mistake.
Answer:
(i) Moving the decimal point one place to the right makes a number 10 times bigger, so 2.5 mL is 10 times the prescribed 0.25 mL. Extra given = 2.5 − 0.25 = 2.25 mL.
(ii) Always write a zero before the decimal point (0.25, never .25) and read the digits after the point one by one with the unit. This makes a lost or misplaced point easy to notice.
In simple words: 2.5 mL is ten times 0.25 mL, that is 2.25 mL too much.

Teacher's Note:
1. One place shift means ten times.
2. A leading zero makes the point visible.