CLASS 7 · GANITA PRAKASH PART I · CHAPTER 3
Understand tenths, hundredths and decimals through measurement, place value, comparison and everyday calculations.
44 worked answers · short steps first, explanations when you need them
Textbook pages 47–54
Question 1
The first scale only tells the whole centimetre.
Subdividing each centimetre lets us describe the extra part.
Tenths let us record lengths between whole centimetres, such as 2 7/10 cm.
Question 2
Ten tenths make one whole.
Separate whole units from fractional units.
3 4/10=3.4 units; 34/10=3.4 units; 4/10=0.4; 41 1/10=41.1.
Question 3
Convert to decimals: 0.9,1.7,13,13.1,10.5,7.6,6.7,0.4.
Sort from least to greatest.
0.4, 0.9, 1.7, 6.7, 7.6, 10.5, 13, 13.1.
Question 4
Write each as a decimal: 4.1,10,4.1,41.1.
4 1/10 = 41/10 < 10 < 41 1/10.
Question 5
Add whole parts: 2+3=5.
Add tenths: 7/10+6/10=13/10=1 3/10.
Combine.
6 3/10 units, or 6.3 units.
Question 6
Divide 8.9 by 2.
8.9÷2=4.45.
4.45 units = 4 units, 4 tenths and 5 hundredths.
Question 7
Put each count in its place-value position.
Use zeroes to hold empty places.
2.35; 10.5; 4.06; 101.01; 0.98.
Question 8
The denominator tells how many decimal places are needed.
0.05; 0.016; 1.2; 0.254.
Question 9
Expand each digit according to its place.
0.34=3/10+4/100; 1.02=1+2/100; 0.8=8/10; 0.362=3/10+6/100+2/1000.
Question 10
Trailing zeroes do not change a decimal’s value.
Compare the place-value digits.
0.2=0.20=0.200 (greatest); 0.02 is smaller; 0.002 is least.
Question 11
Write zeroes in matching decimal places and compare.
4.5=4.50=04.50; 4.05=4.050. The others are distinct.
Question 12
10 mm=1 cm, so divide mm by 10.
100 cm=1 m, so divide cm by 100.
12 mm=1.2 cm; 56=5.6 cm; 9=0.9 cm; 134=13.4 cm; 70=7 cm. 36 cm=0.36 m; 50=0.5 m; 4=0.04 m; 325=3.25 m.
Question 13
1 kg=1,000 g.
Divide grams by 1,000.
0.465 kg; 0.068 kg; 0.704 kg; 0.56 kg; 1.56 kg; 2.5 kg.
Question 14
100 paise=₹1.
Divide the paise count by 100.
₹0.10; ₹0.05; ₹0.36; ₹0.50; ₹0.99; ₹2.50.
Textbook pages 55–73
Question 1
Divide the interval from 4.3 to 4.4 into ten equal hundredth steps.
Count three steps after 4.30.
4.37 is the seventh hundredth mark after 4.30 (or the third after 4.34); it lies between 4.3 and 4.4.
Question 2
Write the endpoints as 1.00 and 1.10.
Count by hundredths without including endpoints.
1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09.
Question 3
Compare digits from the leftmost place.
Append zeroes if needed to align decimal places.
6.456<6.465; 1.23<1.32; 3.81<13.800; 1.009<1.090.
Question 4
Align decimal places with trailing zeroes.
Compare place values from left to right.
(a) 11.10,11.01,1.101,1.011,1.01. (b) 2.768,2.698,2.675,2.567,2.499. (c) 4.678,4.666,4.656,4.600,4.595 g. (d) 33.331,33.313,33.31,33.133,33.13 m.
Question 5
Find each absolute distance from the target.
Choose the smallest difference.
(a) 1.01; (b) 1.1; (c) 3.65; (d) 1.08.
Question 6
The whole-number part should be as close as possible to 25.
Arrange the remaining digits after the decimal to make the small difference.
Several valid arrangements are possible; the exact optimum depends on where the decimal point is allowed. The printed box layout is needed to determine its restrictions.
Question 7
Count tick marks from 6.40: a is the second tick, c the sixth, and b the seventh.
Each tick adds 0.01.
a=6.42, c=6.46, b=6.47.
Question 8
Count hundredth marks from 5.00.
Compare the hundredths digits.
A=5.09, B=5.13, C=5.20, D=5.31 and A<B<C<D.
Question 9
Each small mark in the first interval is 0.01.
Each small mark in the second interval is 0.05.
d=8.01, e=8.05; f=4.35, g=4.50, h=4.85.
Question 10
First place 1.4 between 1 and 2 using tenths.
For 1.04, divide the 1-to-1.1 interval into hundredths.
For 1.407, divide the 1.4-to-1.5 interval into thousandths.
1.4 is four tenths after 1; 1.04 is four hundredths after 1; 1.407 is seven thousandths after 1.4.
Textbook pages 74–76
Question 1
Line up decimal points.
Add by place value, regrouping ten of a place into one of the next place.
7.9; 26.8; 7.41; 18.11; 39.10; 1.534; 0.78; 6.723.
Question 2
Write missing decimal places as zeroes.
Align decimal points and subtract by place value, regrouping where needed.
3.3; 9.2; 5.9; 0.802; 16.95; 16.405; 0.81; 5.749.
Question 3
Find the constant change between consecutive terms.
Repeat that change three times.
First: 6.4,6.8,7.2. (a) +0.05: 4.55,4.60,4.65. (b) +0.5: 27.25,27.75,28.25. (c) +0.11: 10.89,11.00,11.11. (d) +2.5: 21,23.5,26. (e) +0.9: 11.2,12.1,13.0. (f) −0.05: 4.85,4.80,4.75. (g) −0.5: 10.95,10.45,9.95. (h) −3.5: 26,22.5,19.
Question 4
Each nonnegative decimal part is at least 0 and less than 1.
Their sum is at least 0 and less than 2.
Yes: the sum is 34.138, so 33<34.138<35. In general, for whole parts a,b and nonnegative decimal parts, a+b≤sum<a+b+2.
Question 5
Identify how many smaller units make one larger unit.
Divide or multiply by that conversion factor.
Keep the unit label with the result.
For example, 1 km=1,000 m=1,000,000 mm; 45 paise×100,000 people=₹45,000.
Textbook pages 78–80
Question 1
Write the numerator in the decimal place indicated by the denominator.
0.05; 0.016; 1.2; 0.254.
Question 2
Pad with zeroes to equal decimal lengths, then compare digit by digit.
11.10>11.01>1.101>1.011>1.01; 2.768>2.698>2.675>2.567>2.499; 4.678>4.666>4.656>4.600>4.595; 33.331>33.313>33.310>33.133>33.130.
Question 3
For closeness to 30, test whole-number parts near 30 and arrange remaining digits to minimize the gap.
For the smallest value between 100 and 1,000, choose the smallest allowed hundreds digit and order the rest increasingly.
One closest choice is 40.168 (given the chapter’s decimal-point placement rules); smallest in the requested interval is 104.68.
Question 4
Align decimal places and add: 0.25+0.30+0.50+0.20+0.05.
1.30 kg.
Question 5
First-three-day total=3.79+4.20+4.25=12.24 L.
Subtract from 25 L.
12.76 L.
Question 6
Compare the two weights.
35.75−34.50=1.25.
He lost 1.25 kg.
Question 7
The changes alternate +0.9 and −0.01.
After 7.28, add 0.90 to get 8.18, then subtract 0.01.
Using the answer-section correction: 9.07, 9.06.
Question 8
1 km=1,000 m and each metre=1,000 mm.
Convert 45 paise to ₹0.45, then multiply by 100,000.
1 km=1,000,000 mm. Total=₹45,000.
Question 9
Write each as a decimal.
0.1>0.01; 0.01<0.09; 0.001<0.90.
Question 10
Convert every amount to units.
Add the values.
88.10; 121.2; 111.1; 277.75.
Question 11
Use equivalent fractions with denominator 10, 100 or 1,000.
0.5; 1.5; 0.25; 0.75; 0.2; 0.8.
Question 12
Read each digit by its place.
Leave out places whose digit is zero.
0.34=3/10+4/100; 1.02=1+2/100; 0.8=8/10; 0.362=3/10+6/100+2/1000.
Question 13
Write both fractions in decimal form.
Compare their place values.
10/1000=0.010<0.1; 0.01<0.090; 0.001<0.90.
Question 14
Convert each named place-value amount to units.
Add the parts.
(a) 121.2; (b) 111.1; (c) 277.75.
Question 15
Use 0.643 and 9.857, placing eight different digits in the boxes.
Add the thousandths: 643 thousandths + 857 thousandths = 1,500 thousandths = 1.5.
Then 0+9+1.5=10.5.
One exact filling is 0.643+9.857=10.500. Since the sum reaches 10.5 exactly, it is as close as possible.