Class 7 Maths Ganita Prakash Part 1 Chapter 3 MCQs – A Peek Beyond the Point

One unit contains 10 tenths, so 3 units contain 30 tenths.
3 units and 4 tenths = 30 tenths + 4 tenths
= 34 tenths
The same length can be written as 34/10 units or 3.4 units.

2.7 + 3.6 = 27/10 + 36/10
= 63/10 = 6.3
The 7 tenths and 6 tenths make 13 tenths, which is 1 whole and 3 tenths. This extra whole combines with the original 5 whole units.

Finger length = 12.4 − 6.7
12.4 = 11 units and 14 tenths
Subtracting 6 units and 7 tenths leaves 5 units and 7 tenths.
Therefore, the finger length is 5.7 units. Regrouping one unit as ten tenths makes the subtraction possible.

8.9 units = 890 hundredths of a unit
Half of 890 hundredths = 445 hundredths
445/100 = 4.45 units
The folded strip lies between 4.4 and 4.5 units. Hundredths are needed to state its length exactly.

One tenth can be written with denominator 100.
1/10 = 10/100
Therefore, 10 hundredths make one tenth. A whole unit contains 100 hundredths, while one tenth is only one of the ten equal parts of that whole.

Seven units contribute 7, and five hundredths contribute 0.05.
7 + 5/100 = 7.05
The zero in the tenths place is necessary. Writing 7.5 would mean five tenths, which is ten times the fractional part required.

The first place after the decimal point is tenths, the second is hundredths and the third is thousandths.
0.274 = 2/10 + 7/100 + 4/1,000
The 7 is in the second decimal place, so its value is 7/100.

234 hundredths = 234/100
= 200/100 + 30/100 + 4/100
= 2 + 0.3 + 0.04
= 2.34
The hundredths can be regrouped as two whole units, three tenths and four hundredths.

12 tens = 12 × 10 = 120
12 tenths = 12/10 = 1.2
Total = 120 + 1.2 = 121.2
The twelve tenths contain one whole and two tenths, so they add more than one to 120.

I write the fraction with denominator 100.
3/4 = (3 × 25)/(4 × 25)
= 75/100
= 0.75
Three quarters therefore means seventy-five hundredths of a whole, which places the decimal between 0.5 and 1.

The number 2 7⁄10 cm means 2 cm and 7 one-tenths of a cm. It can be written as 2.7 cm using decimal notation. This shows how the scale divides each unit into 10 equal parts for accuracy.

A unit divided into 10 equal parts results in ten one-tenths. Each one-tenth is 1⁄10 of a unit. This helps measure small lengths accurately such as a screw or a pencil.

41 one-tenths means 41 × 1⁄10 = 41⁄10. It is equal to 4 1⁄10 in mixed number form or 4.1 in decimal form. All represent the same length using different notations.

6 units and 3 one-tenths means 6 + 3⁄10, which equals 6.3. The place value of 3 is tenths, and it appears after the decimal point. This notation makes it easier to add and subtract.

Since 10 mm = 1 cm, each millimetre is one tenth of a centimetre.
134 mm = 134/10 cm = 13.4 cm
This is also 13 cm and 4 mm. Converting to the larger unit gives a smaller numerical value.

2 m = 200 cm
0.07 m = 7 cm
2.07 m = 200 cm + 7 cm = 207 cm
The zero in the tenths place shows that the extra length is seven hundredths of a metre, not seven tenths.

One kilogram contains 1,000 grams, so each gram is one thousandth of a kilogram.
68 g = 68/1,000 kg = 0.068 kg
The zero after the decimal point keeps the 6 in the hundredths place and the 8 in the thousandths place.

100 paise = ₹1
250 paise = 250/100 rupees = ₹2.50
The amount consists of 200 paise, or ₹2, and another 50 paise, or ₹0.50. Adding these parts gives two rupees and fifty paise.

1 km = 1,000 m and 1 m = 1,000 mm.
1 km = 1,000 × 1,000 mm
= 10,00,000 mm
Both conversions are needed. Stopping after converting kilometres to metres would give a value a thousand times too small.

2 7/10 = 2.7 and 3 2⁄10 = 3.2. Since 3.2 > 2.7, 3 2/10 is longer. Decimal notation helps in easy comparison of such values without converting them into fractions.

Adding two tenths: 27⁄10 + 35⁄10 = (27 + 35)⁄10 = 62⁄10. It can be written as 6 2⁄10 or 6.2. Adding fractional parts using the same denominator.

A unit divided into 100 equal parts gives one-hundredths. So, 100 one-hundredths equal 1 unit. This concept helps in understanding values like 4.45 where 45 is in hundredths.

1 1/10 = 11/10 = 110/100, add 4/100 to get 114/100. It is written as 1.14 in decimal form. This shows conversion between mixed numbers and decimal representation.

Length of the interval = 1.1 − 1 = 0.1
Each part = 0.1 ÷ 10 = 0.01
Fourth mark after 1 = 1 + 4 × 0.01 = 1.04
The small divisions represent hundredths, not tenths.

Both numbers have 6 units and 4 tenths. At the hundredths place, 6.456 has 5 while 6.465 has 6.
5 hundredths < 6 hundredths Therefore, 6.456 < 6.465. The thousandths digits cannot reverse the comparison already decided at the hundredths place.

4.05 means 4 units and 5 hundredths. Writing another zero at the end adds zero thousandths.
4.050 = 4 + 0/10 + 5/100 + 0/1,000 = 4.05
The digits keep their place values, so the number remains unchanged.

The distances from 1.09 are:
1.09 − 0.9 = 0.19
1.1 − 1.09 = 0.01
1.09 − 1.01 = 0.08
1.11 − 1.09 = 0.02
The smallest distance is 0.01, so 1.1 is closest.

A number between 100 and 1,000 needs three digits before the decimal point. The smallest possible hundreds digit is 1, followed by 0 and then 4.
The remaining digits 6 and 8 give the smallest fractional part in that order.
The number is 104.68.

7 ones and 5 hundredths mean 7 + 5⁄100 = 7.05. The 5 appears in the hundredths place in decimal notation. This accurately represents measurements requiring fine precision.

1 cm = 10 mm, so 5 mm = 5/10 = 0.5 cm. This shows how smaller units like millimeters convert into decimal fractions of a centimeter for accurate measurement.

Since 1 rupee = 100 paise, 75 paise is 75/100 rupee, which is 0.75. Decimal notation helps convert paise into rupees easily and allows comparison with other decimal values in financial contexts.

Folding 8 9/10 units in half gives 4 45/100 or 4.45 units. Both represent the same quantity in different forms—one in mixed fraction and the other in decimal notation.

The 6 in 0.6 represents six tenths, or 600 thousandths.
0.934 + 0.6 = 0.934 + 0.600
= 1.534
Writing the extra zeroes makes the matching place values clear. It does not change the value of 0.6.

I express both numbers in thousandths.
17.000 − 16.198 = (17,000 − 16,198)/1,000
= 802/1,000
= 0.802
The difference is less than 1 because 16.198 lies between 16 and 17. This also checks that the decimal point is in the right place.

First three days = 3.79 + 4.20 + 4.25 = 12.24 L
Last three days = 25.00 − 12.24 = 12.76 L
The six-day total contains both parts, so subtracting the first three days gives the combined amount for the remaining three days.

I group quantities that are easy to add.
0.25 + 0.05 = 0.30 kg
0.3 + 0.5 + 0.2 = 1.0 kg
Total = 0.30 + 1.0 = 1.30 kg
All quantities are already in kilograms, so no unit conversion is needed.

The increase is 10.67 − 10.56 = 0.11. The next increase is also 0.11.
10.78 + 0.11 = 10.89
10.89 + 0.11 = 11.00
Ten hundredths regroup as one tenth, and ten tenths regroup as one whole.

Both have 6 units and 4 tenths, but 6.465 has 6 hundredths while 6.456 has only 5 hundredths. Comparing digits from left to right, the larger digit at the hundredths place determines the larger value.

25 9/10 – 6 4/10 7/100 = 19 4/10 3/100 = 19.43 = 19.403 (in extended form). These representations are equivalent and show how decimals, mixed numbers, and hundredths can describe the same value.

Converting all values to hundredths and adding gives 1802/100 = 18 2/100. It demonstrates the importance of aligning place values and understanding that 10 hundredths equal one tenth during addition.

Since 1 kg = 1000 g, 254 g = 254⁄1000 = 0.254 kg. This conversion helps understand small weights in decimal form and relate them to the base kilogram unit.

25 < 25.936 < 26 and 8 < 8.202 < 9. Adding the lower bounds gives 25 + 8 = 33. Adding the upper bounds gives 26 + 9 = 35. Therefore, the sum lies strictly between 33 and 35.

4.5 hours = 4 hours + 0.5 hour
0.5 hour = half of 60 minutes = 30 minutes
Four hours and thirty minutes after noon is 4:30 p.m. The decimal part is a fraction of an hour, not a written number of minutes.

2.5 feet = 2 feet + 0.5 foot
0.5 foot = half of 12 inches = 6 inches
So 2.5 feet means 2 feet 6 inches. The decimal digit 5 represents half a foot, not five inches.

Five complete overs contain 5 × 6 = 30 balls.
Total = 30 + 5 = 35 balls
Here, the part after the dot counts extra balls. It is not a decimal fraction, so 5.5 does not mean five and a half overs in this notation.

45 paise = ₹0.45
Total fee = 1,00,000 × ₹0.45 = ₹45,000
Alternatively, 1,00,000 × 45 = 45,00,000 paise, and dividing by 100 converts this to ₹45,000. The conversion prevents treating paise as rupees.

23 tens means 23 × 10 = 230. This is a whole number with no fractional part. It is essential to distinguish between tens and tenths in such questions.

87 ones + 5 tenths + 60 hundredths = 87 + 0.5 + 0.60 = 88.10. The sum of the fractional parts adds 1, increasing the ones digit by one. Decimal addition handles this carry-over automatically.

Comparing each number’s distance from 1, we find 1.01 is only one hundredth greater than 1. All others are farther away. The smallest absolute difference determines the closest decimal.

1 cm = 10 mm, so 1/10 cm = 0.1 cm. It is important to note that 1 mm = 0.1 cm is incorrect. Decimals should reflect correct place value and conversion.