Class 7 Maths Ganita Prakash Part 2 Chapter 4 MCQs – Another Peek Beyond the Point

The first digit to the right of the decimal point is in the tenths place.
In 27.53, the digit 5 represents 5 tenths.
5/10 = 0.5
The following digit 3 is in the hundredths place, not the tenths place.

1 kg = 1000 g
25 g = 25/1000 kg
= 0.025 kg
The kilogram amount is smaller numerically because a kilogram is a larger unit than a gram. Three decimal places are needed when dividing 25 by 1000.

254/1000 = 200/1000 + 50/1000 + 4/1000
= 2/10 + 5/100 + 4/1000
= 0.2 + 0.05 + 0.004
Thus, 0.254 has 2 tenths, 5 hundredths and 4 thousandths.

Total cost = 5 × ₹9.50
= ₹(5 × 95/10)
= ₹(475/10) = ₹47.50
Multiplying the price of one pen by 5 gives the cost of all five. The final amount is 47 rupees and 50 paise.

Distance = distance per litre × litres used
= 12.5 × 7.5
= (125 × 75)/100
= 9375/100 = 93.75 km
The two factors each have one decimal place, so the product is obtained by dividing the whole-number product by 100.

One-way distance = 827/1000 = 0.827 km
Daily distance = 2 × 0.827 = 1.654 km
Distance in 6 days = 6 × 1.654 = 9.924 km
Both the morning and return journeys are counted each day.

Area = length × breadth
= 5.7 × 13.3
= (57 × 133)/100
= 7581/100 = 75.81 cm²
Multiplication gives area in square centimetres; adding the two side lengths would not give the area.

5.96 = 596/100 and 24.8 = 248/10.
Product = (596 × 248)/(100 × 10)
= 147808/1000 = 147.808
There are 2 + 1 = 3 decimal places to account for in the whole-number product.

0.75 × 0.4 = (75 × 4)/1000
= 300/1000 = 0.3
Now 0.3 < 0.4 and 0.3 < 0.75. Multiplying two positive numbers smaller than 1 makes a product smaller than either number.

Notebook cost = 4 × ₹15.50 = ₹62
Eraser cost = 3 × ₹2.75 = ₹8.25
Total cost = ₹62 + ₹8.25 = ₹70.25
The price of each type is multiplied by its own quantity before the two costs are added.

Height in millimetres = 36 × 1.45 = 52.2 mm
Since 10 mm = 1 cm, height in centimetres = 52.2 ÷ 10
= 5.22 cm
The final division converts millimetres to centimetres; it does not change the actual height.

Profit on one notebook = ₹30 − ₹23.60 = ₹6.40
Profit on 50 notebooks = 50 × ₹6.40
= ₹320
The total sales of ₹1500 are not the profit because the purchase cost must first be accounted for.

0.306 = 306/1000
0.306 × 1000 = (306/1000) × 1000 = 306
Multiplying by 1000 makes the number 1000 times as large. The digits therefore move three place-value positions to the left.

Length of each piece = 3.9 ÷ 100
= (39/10) × (1/100)
= 39/1000 = 0.039 m
Dividing by 100 moves the decimal point two places left. Checking gives 100 × 0.039 = 3.9 m.

Each share = 29/4 m
= (29 × 25)/(4 × 25) m
= 725/100 m = 7.25 m
Multiplying the numerator and denominator by 25 gives an equivalent fraction whose denominator is 100, making the decimal easy to read.

4 × 331 = 1324, leaving 1 to share.
Remaining share = 1/4 = 0.25
1325 ÷ 4 = 331 + 0.25 = 331.25
The remainder becomes tenths and then hundredths in long division, rather than being written directly as a decimal digit.

0.06 = 60 thousandths.
60 thousandths ÷ 5 = 12 thousandths.
12 thousandths = 0.012
Check: 0.012 × 5 = 0.06. The zero in the tenths place is necessary because the quotient is only a little more than one hundredth.

Average speed = distance ÷ time
= 126 ÷ 2.5
= 1260 ÷ 25 = 50.4 km/h
Multiplying both dividend and divisor by 10 removes the decimal from the divisor without changing the quotient.

Multiplying both numbers by 100 makes the divisor a whole number.
4.68 ÷ 0.13 = 468 ÷ 13
= 36
Check: 36 × 0.13 = 4.68. Multiplying only the divisor would change the quotient and give an incorrect result.

Long division gives the repeating digits 142857. The remainders return in a cycle instead of becoming zero.
Therefore, 1 ÷ 7 = 0.142857142857…
Writing only 0.142857 would stop the expansion, so it would not be the exact quotient.

128 ÷ 0.4 = 1280 ÷ 4
= 320
Since 0.4 is a positive number smaller than 1, more than 128 groups of size 0.4 fit into 128. Thus, the quotient is greater than the dividend.

3 litres = 3000 ml
Each share = 3000 ÷ 8
= 375 ml
Equivalently, 3 ÷ 8 = 0.375 litre, and 0.375 × 1000 = 375 ml. The answer must use the requested unit of millilitres.

All sides of a regular polygon are equal.
Side length = perimeter ÷ number of sides
= 208.8 ÷ 12 = 17.4 cm
Check: 17.4 × 12 = 208.8 cm. The perimeter is the sum of all 12 equal sides.

The same difference accumulates each year.
Difference after 100 years = 100 × 0.2422
= 24.22 days
Multiplying by 100 moves the decimal point two places right. This calculation explains why a small yearly difference cannot simply be ignored over many years.

A century year is a leap year only when it is divisible by 400.
2000 ÷ 400 = 5, an integer.
1900, 2100 and 2200 are not divisible by 400. Therefore, 2000 is the leap year among these choices.

Century years to exclude = 1000 ÷ 100 = 10
Multiples of 400 to restore = 2
Leap years = 250 − 10 + 2 = 242
Years 400 and 800 are included because the 400-year rule takes priority.

Total interval = 3.2 − 3.1 = 0.1
Each part = 0.1 ÷ 10 = 0.01
Six parts = 6 × 0.01 = 0.06
Required number = 3.1 + 0.06 = 3.16. It lies between 3.1 and 3.2 as expected.

Number of books = 160 ÷ 2.5
= 1600 ÷ 25 = 64
Length occupied = 64 × 2.5 = 160 cm
Remaining length = 160 − 160 = 0 cm
So exactly 64 books fit with no space left.

The mixed numbers are 6¼ = 6.25 and 2½ = 2.5.
6.25 ÷ 2.5 = 62.5 ÷ 25
= 2.5
Check: 2.5 × 2.5 = 6.25. Converting both mixed numbers to decimals makes the division straightforward.

75.6 is 756 divided by 10, while 360 is 36 multiplied by 10.
The quotient therefore becomes 1/100 of 21.
75.6 ÷ 360 = 21 ÷ 100 = 0.21
Check: 360 × 0.21 = 75.6.