CBSE Class 7 Mathematics A Peek Beyond the Point MCQs Set 11

Answer: (b) one-tenth

Explanation:
1. Cutting one unit into 10 equal parts gives parts of size \( \frac{1}{10} \) each.
2. Such a part is called one-tenth, written \( \frac{1}{10} \) or 0.1.
3. A one-hundredth appears only when a tenth is again split into 10 parts.

Teacher's Note:
1. Ten equal parts of a unit give tenths.
2. Hundredths need a second splitting into 10.

Answer: (c) zero point two seven four

Explanation:
1. 0.274 means 2 tenths, 7 hundredths and 4 thousandths.
2. Each digit after the point has its own place, so the digits are read one at a time.
3. So it is read as zero point two seven four.

Teacher's Note:
1. Digits after the point are read one by one.
2. Never read the part after the point as a whole number.

Answer: (d) ten

Explanation:
1. Our place value system is built on 10.
2. The Latin word decem means ten, so the system is called the decimal system.
3. It is related to the Sanskrit word dasha, which also means ten.

Teacher's Note:
1. Decimal means 'based on ten'.
2. Each place is 10 times the place on its right.

Answer: (a) Rs 0.01

Explanation:
1. 100 paise make 1 rupee.
2. So 1 paisa = \( \frac{1}{100} \) of a rupee.
3. One hundredth is written 0.01, so 1 paisa = Rs 0.01.

Teacher's Note:
1. Paise are hundredths of a rupee.
2. That is why rupee amounts have two digits after the point.

Answer: (c) 10

Explanation:
1. One-hundredths are made by cutting each one-tenth into 10 equal parts.
2. So \( \frac{1}{10} \) = \( \frac{10}{100} \), that is, 10 one-hundredths make one-tenth.
3. 100 one-hundredths would make a whole unit, not a tenth.

Teacher's Note:
1. Each place is 10 times the next smaller place.
2. Do not confuse 'make a tenth' with 'make a unit'.

Answer: (d) 0.5 cm

Explanation:
1. 1 cm = 10 mm, so 1 mm = \( \frac{1}{10} \) cm.
2. 5 mm = \( \frac{5}{10} \) cm = 0.5 cm.

Teacher's Note:
1. A millimetre is one-tenth of a centimetre.
2. Going to a bigger unit gives a smaller number.

Answer: (a) 8.84

Explanation:
1. Line up the points and write 5.6 as 5.60.
2. Hundredths: 4 + 0 = 4; tenths: 2 + 6 = 8; ones: 3 + 5 = 8.
3. So 3.24 + 5.60 = 8.84.

Teacher's Note:
1. Always keep the decimal points in one column.
2. Fill empty places with zeros before adding.

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

Explanation:
1. 0.5 is 5 tenths; 0.50 is 5 tenths and 0 hundredths, which is the same amount. So A is true.
2. A zero added at the right end only says that a smaller place is empty, so R is true.
3. R is exactly why 0.5 and 0.50 are equal, so R correctly explains A.

Teacher's Note:
1. Zeros at the right end of the decimal part add nothing.
2. 0.5 = 0.50 = 0.500.

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

Explanation:
1. 1 kg = 1000 g, so 1 g = \( \frac{1}{1000} \) kg = 0.001 kg. A is true.
2. 1 kilogram is 1000 grams, not 100 grams. R is false.
3. So A is true but R is false.

Teacher's Note:
1. Kilo means one thousand.
2. A gram is a thousandth of a kilogram.

Answer: (c) Only Statement I is true.

Explanation:
1. 10 × \( \frac{1}{10} \) = 1, so Statement I is true.
2. 100 × \( \frac{1}{1000} \) = \( \frac{100}{1000} \) = \( \frac{1}{10} \), only one-tenth. A unit needs 1000 thousandths. Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. 10 tenths, 100 hundredths, 1000 thousandths each make one unit.
2. 100 thousandths make only a tenth.

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

Explanation:
1. 1 mm = 0.1 cm, so (i)-(r).
2. 1 cm = 0.01 m, so (ii)-(s).
3. 1 g = 0.001 kg, so (iii)-(p); 1 paisa = Rs 0.01, so (iv)-(q).
4. Answer: (i)-(r), (ii)-(s), (iii)-(p), (iv)-(q).

Teacher's Note:
1. mm to cm: tenths; cm to m and paise to rupees: hundredths; g to kg: thousandths.
2. Also check that the units match.

Answer: (c) 3.7 cm

Explanation:
1. The gap from 3 to 4 is cut into 10 equal parts, so each small division is \( \frac{1}{10} \) cm.
2. P is at the 7th division after the mark 3.
3. Length = 3 + \( \frac{7}{10} \) = 3.7 cm.

Teacher's Note:
1. First find the value of one small division.
2. Then count divisions from the last whole number.

Answer: (b) 0

Explanation:
1. After the point: 4 is in the tenths place, 0 in the hundredths place, 8 in the thousandths place.
2. So the hundredths digit is 0.

Teacher's Note:
1. Count places starting just after the point.
2. A zero also holds a place.

Answer: (b) \( 3 \times 10 + 7 \times \frac{1}{100} \)

Explanation:
1. In 30.07, 3 is in the tens place and 0 in the ones place.
2. After the point, the tenths place has 0 and the hundredths place has 7.
3. So 30.07 = \( 3 \times 10 + 7 \times \frac{1}{100} \).

Teacher's Note:
1. Write the place of each non-zero digit.
2. The zero in the tenths place pushes 7 to hundredths.

Answer: (c) 4.5, 4.50, 04.50

Explanation:
1. Zeros before the whole-number part or after the last decimal digit do not change a number.
2. So 4.5 = 4.50 = 04.50, and group (c) has three equal numbers.
3. In the other groups the digits move to different places, so the numbers differ.

Teacher's Note:
1. Zeros at the ends do not change the value.
2. Zeros between the point and a digit do change it.

Answer: (d) 1.85

Explanation:
1. 185 hundredths = \( \frac{185}{100} \) = \( \frac{100}{100} \) + \( \frac{80}{100} \) + \( \frac{5}{100} \).
2. That is 1 + \( \frac{8}{10} \) + \( \frac{5}{100} \), which is 1.85.

Teacher's Note:
1. 100 hundredths make one unit.
2. Dividing by 100 moves the point two places left.

Answer: (d) 3.075 kg

Explanation:
1. Grams are thousandths of a kilogram, so 75 g = \( \frac{75}{1000} \) kg = 0.075 kg.
2. Adding 3 kg: 3 kg 75 g = 3.075 kg.

Teacher's Note:
1. Grams need three places after the point.
2. 75 g is 0.075 kg, not 0.75 kg.

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

Explanation:
1. Both have 12 units; 12.5 has 5 tenths and 12.45 has 4 tenths, so A is true.
2. 12.5 does have fewer digits after the point, so R is true as a fact.
3. But fewer digits is not why a number is bigger (2.05 < 2.5 though it has more digits). So R is not the correct explanation of A.

Teacher's Note:
1. Compare place by place, not by counting digits.
2. Here the tenths place decides.

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

Explanation:
1. 0.5 hour is 5 of the 10 equal parts of an hour, that is half an hour = 30 minutes. So R is true.
2. 4.5 hours after noon is 4 hours 30 minutes after 12, that is 4:30 p.m., not 4:50 p.m. So A is false.
3. So A is false but R is true.

Teacher's Note:
1. An hour has 60 minutes, not 100.
2. 0.5 hour is half an hour = 30 minutes.

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

Explanation:
1. Splitting a hundredth into 10 equal parts gives a thousandth, the third place after the point. R is true.
2. So one-thousandth has 1 in the third place: 0.001. A is true.
3. R explains why A is written that way, so R is the correct explanation of A.

Teacher's Note:
1. Tenths, hundredths, thousandths are the 1st, 2nd and 3rd places after the point.
2. 0.001 = 1/1000.

Answer: (b) Only Statement II is true.

Explanation:
1. 1 m = 100 cm = 100 × 10 mm = 1000 mm, so Statement II is true.
2. 1 km = 1000 m = 1000 × 1000 mm = 10,00,000 mm, not 1,00,000 mm. Statement I is false.
3. So only Statement II is true.

Teacher's Note:
1. Go step by step: km to m to mm.
2. 1 km is ten lakh millimetres.

Answer: (c) Both statements are true.

Explanation:
1. Distances from 3: 0.54, 0.36 and 0.901. The smallest is 0.36, so 2.64 is closest. Statement I is true.
2. Distances from 1: 0.3, 0.41 and 0.06. The smallest is 0.06, so 1.06 is closest. Statement II is true.
3. So both statements are true.

Teacher's Note:
1. Find each distance, then pick the smallest.
2. The closest number can be bigger than the target.

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

Explanation:
1. 0.09 is nine hundredths: (i)-(r).
2. 0.9 is nine tenths: (ii)-(p).
3. 0.009 is nine thousandths: (iii)-(q); 9.009 is nine and nine thousandths: (iv)-(s).
4. Answer: (i)-(r), (ii)-(p), (iii)-(q), (iv)-(s).

Teacher's Note:
1. The place of 9 after the point gives its name.
2. 1st place tenths, 2nd hundredths, 3rd thousandths.

Answer: (d) 8.5

Explanation:
1. The gap from 5 to 10 is 5 units, cut into 10 equal parts, so each division is 5 ÷ 10 = 0.5.
2. M is 7 divisions after 5.
3. M = 5 + 7 × 0.5 = 5 + 3.5 = 8.5.

Teacher's Note:
1. A division is not always 0.1; find it first.
2. Here each division is half a unit.

Answer: (a) 74 mm and 0.074 m

Explanation:
1. 1 cm = 10 mm, so 7.4 cm = 7.4 × 10 = 74 mm.
2. 1 cm = 0.01 m, so 7.4 cm = \( \frac{7.4}{100} \) m = 0.074 m.
3. Answer: 74 mm and 0.074 m.

Teacher's Note:
1. To a smaller unit the number grows; to a bigger unit it shrinks.
2. cm to m: divide by 100.

Answer: (c) 1.55 m

Explanation:
1. Cloth received = 3.45 + 4.20 + 2.80 = 10.45 m.
2. Still to come = 12.00 − 10.45 = 1.55 m.
3. Quick check: 3 + 4 + 2 = 9, which is less than 12, so some cloth is surely still due.

Teacher's Note:
1. First add what has come, then subtract from the order.
2. Write 12 as 12.00 before subtracting.

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

Explanation:
1. 2.02 − 2 = 0.02 = \( \frac{2}{100} \), and 2 − 1.8 = 0.2 = \( \frac{20}{100} \). So R is true.
2. 2 hundredths is less than 20 hundredths, so 2.02 is closer. A is true.
3. The distances in R are the reason for A, so R is the correct explanation of A.

Teacher's Note:
1. Closeness is decided by distance, not by being bigger or smaller.
2. Change both gaps to hundredths to compare.

Answer: (d) Only Statement II is true.

Explanation:
1. 2.5 has fewer digits than 2.05 but is greater, so Statement I is false.
2. Extra zeros at the right end only fill empty smaller places, so Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. One counter-example is enough to show a statement is false.
2. 2.5 = 2.50 > 2.05.

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

Explanation:
1. 2 m 5 cm = 2.05 m: (i)-(r).
2. 2 kg 50 g = 2.050 kg = 2.05 kg: (ii)-(p).
3. 205 paise = Rs 2.05: (iii)-(q); 2 cm 5 mm = 2.5 cm: (iv)-(s).
4. Answer: (i)-(r), (ii)-(p), (iii)-(q), (iv)-(s).

Teacher's Note:
1. Match the units first, then the digits.
2. 50 g is 0.050 kg, which equals 0.05 kg.

Answer: (b) 0.468 kg

Explanation:
1. In grams the masses are P 1250 g, Q 1205 g, R 1520 g and S 1052 g.
2. Heaviest is R (1520 g) and lightest is S (1052 g).
3. Difference = 1520 − 1052 = 468 g = 0.468 kg.

Teacher's Note:
1. Change all masses to one unit before comparing.
2. 1.52 kg is 1520 g, not 152 g.