3. A Peek Beyond the Point​

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Chapter 3 — A Peek Beyond the Point (Class 7) | 1-Mark Q&A

Chapter 3: A Peek Beyond the Point

Part 1 — 20 Most Important 1-Mark Questions (with Solutions)

1What does the decimal point separate in a number like \(7.05\)?
It separates the whole-number part and the fractional part (tenths, hundredths, …).
2Write \(2\dfrac{7}{10}\) in decimal form.
\(2.7\).
3How many millimetres make \(1\) centimetre?
\(10\) mm \(=1\) cm; hence \(1\text{ mm}=0.1\text{ cm}\).
4Write \(\dfrac{3}{10}\) as a decimal.
\(0.3\).
5Express “34 tenths” as a mixed number and as a decimal.
\(3\dfrac{4}{10}\) and \(3.4\).
6In \(70.5\), the digit \(5\) is in which place?
Tenths place (five-tenths).
7Which is greater: \(1.23\) or \(1.32\)?
\(1.32\) (compare tenths: \(3\gt2\)).
8Which of \(0.9,\,1.01,\,1.1,\,1.11\) is closest to \(1\)?
\(1.01\) (distance \(=0.01\)).
9Convert \(70\) mm to cm.
\(70\text{ mm}=7.0\text{ cm}\).
10Convert ₹\(0.75\) to paise.
\(75\) paise.
11How many hundredths make one tenth?
\(10\) hundredths \(= 1\) tenth.
12Write “234 tenths” in decimal form.
\(234\) tenths \(=\dfrac{234}{10}=23.4\).
13Which is greater: \(6.456\) or \(6.465\)?
\(6.465\) (hundredths \(6\gt5\)).
14Are \(0.2,\;0.20,\;0.200\) equal in value?
Yes — all represent two-tenths.
15Find \(5.3+2.6\).
\(7.9\).
16Convert “234 hundredths” to decimal.
\(234\) hundredths \(=\dfrac{234}{100}=2.34\).
17How many centimetres are there in \(1\) metre?
\(100\) cm.
18What is the hundredths digit in \(7.05\)?
\(5\) (the tenths digit is \(0\)).
19Write \(\dfrac{5}{100}\) as a decimal.
\(0.05\).
20Compute \(0.934+0.6\).
\(1.534\).
Chapter 3 — A Peek Beyond the Point | 2-Mark Q&A

Chapter 3: A Peek Beyond the Point

Part 2 — 20 Most Important 2-Mark Questions (with Solutions)

1Write as decimals and compare: \(2\dfrac{7}{10}\) and \(3\dfrac{2}{10}\). Which is larger?
\(2\dfrac{7}{10}=2.7,\;\;3\dfrac{2}{10}=3.2\Rightarrow 3.2\gt 2.7\).
2Arrange in increasing order: \(\dfrac{9}{10},\;1\dfrac{7}{10},\;\dfrac{130}{10},\;13\dfrac{1}{10}\).
Decimals: \(0.9,\;1.7,\;13.0,\;13.1\). Order: \(\dfrac{9}{10} < 1\dfrac{7}{10} < \dfrac{130}{10} < 13\dfrac{1}{10}\).
3Express \(0.362\) as a sum of tenths, hundredths and thousandths.
\(0.362=\dfrac{3}{10}+\dfrac{6}{100}+\dfrac{2}{1000}\).
4Between \(1\) and \(1.1\) mark the hundredths and list them.
\(1.01,\,1.02,\,1.03,\,1.04,\,1.05,\,1.06,\,1.07,\,1.08,\,1.09\) (each is \(\dfrac{1}{100}\) apart).
5Add using place value: \(2.7+3.5\).
As tenths: \(\dfrac{27}{10}+\dfrac{35}{10}=\dfrac{62}{10}=6.2\).
6Subtract using tenths: \(3.5-2.7\).
\(\dfrac{35}{10}-\dfrac{27}{10}=\dfrac{8}{10}=0.8\).
7Convert \(70\text{ mm}\) to cm and \(12\text{ cm}\) to m.
\(70\text{ mm}=7.0\text{ cm};\quad 12\text{ cm}=0.12\text{ m}\).
8Convert \(465\text{ g},\;68\text{ g},\;1560\text{ g}\) into kilograms.
\(0.465\text{ kg},\;0.068\text{ kg},\;1.560\text{ kg}\).
9Convert money: \(10\text{ p},\;50\text{ p},\;99\text{ p},\;250\text{ p}\) to rupees.
₹\(0.10,\;0.50,\;0.99,\;2.50\) respectively.
10Which is larger: \(\dfrac{10}{1000}\) or \(\dfrac{1}{10}\)?
\(\dfrac{10}{1000}=0.01\lt 0.1=\dfrac{1}{10}\Rightarrow \dfrac{1}{10}\) is larger.
11Find the total length: \(2\dfrac{7}{10}+3\dfrac{6}{10}\).
\(\dfrac{27}{10}+\dfrac{36}{10}=\dfrac{63}{10}=6.3\).
12Find the difference: \(25\dfrac{9}{10}-6\dfrac{47}{100}\).
\(25.9-6.47=19.43\) \(\big(=19\dfrac{43}{100}\big)\).
13Compute by converting to hundredths: \(15\dfrac{3}{10}\dfrac{4}{100}+2\dfrac{6}{10}\dfrac{8}{100}\).
\(15\dfrac{34}{100}+2\dfrac{68}{100}=17\dfrac{102}{100}=18\dfrac{2}{100}=18.02\).
14Convert to decimals: (i) \(234\) hundredths (ii) \(105\) tenths.
(i) \(2.34\);\;\; (ii) \(10.5\).
15Compare by place values: \(6.456\) and \(6.465\).
Units \(6=6\), tenths \(4=4\), hundredths \(5\lt 6\Rightarrow 6.465\gt 6.456\).
16Convert \(0.89\text{ m}\) and \(2.07\text{ m}\) to centimeters.
\(0.89\text{ m}=89\text{ cm};\quad 2.07\text{ m}=207\text{ cm}\).
17“Overs left: \(5.5\)”. How many balls are left?
\(5.5=5\dfrac{5}{6}\) overs \(=5\times 6+5=35\) balls left.
18Which is closest to \(1\): \(0.9,\;1.01,\;1.1,\;1.11\)?
\(1.01\) (distance \(0.01\) from \(1\)).
19How many millimetres make \(1\) kilometre?
\(1\text{ km}=1000\text{ m}=1000\times 1000\text{ mm}=1{,}000{,}000\text{ mm}\).
20Travel insurance costs \(45\) paise per passenger. For \(1\) lakh passengers, find the total fee.
₹\(0.45\times 100{,}000=₹45{,}000\).
Chapter 3 — A Peek Beyond the Point | 3-Mark Q&A

Chapter 3: A Peek Beyond the Point

Part 3 — 20 Most Important 3-Mark Questions (with Solutions)

1Add \(2\dfrac{7}{10}\) and \(3\dfrac{6}{10}\) by two methods (tenths and decimals).
As tenths: \(\dfrac{27}{10}+\dfrac{36}{10}=\dfrac{63}{10}=6\dfrac{3}{10}=6.3\).
As decimals: \(2.7+3.6=6.3\).
2Find \(12\dfrac{4}{10}-6\dfrac{7}{10}\). Show the borrow in tenths.
Convert: \(12.4-6.7\). Borrow \(1\) tenth: \(12.4=12.3+0.1\Rightarrow(12.3+0.1)-6.7\).
\(\dfrac{24}{10}-\dfrac{17}{10}=\dfrac{7}{10}=0.7\), units \(12-6=6\Rightarrow 6-0=6\).
Final: \(5\dfrac{7}{10}=5.7\).
3Evaluate \(15\dfrac{3}{10}\dfrac{4}{100}+2\dfrac{6}{10}\dfrac{8}{100}\) in two ways.
Hundredths: \(15\dfrac{34}{100}+2\dfrac{68}{100}=17\dfrac{102}{100}=18\dfrac{2}{100}=18.02\).
Decimals: \(15.34+2.68=18.02\).
4Compute \(15\dfrac{3}{10}\dfrac{4}{100}-2\dfrac{6}{10}\dfrac{8}{100}\) using hundredths.
\(15\dfrac{34}{100}-2\dfrac{68}{100}=\dfrac{1534-268}{100}=\dfrac{1266}{100}=12\dfrac{66}{100}=12.66\).
5Convert: (i) \(56\text{ mm}\to\text{cm}\) (ii) \(0.9\text{ cm}\to\text{mm}\) (iii) \(203.6\text{ cm}\to\text{m}\).
(i) \(56\text{ mm}=\dfrac{56}{10}\text{ cm}=5.6\text{ cm}\).
(ii) \(0.9\text{ cm}=9\text{ mm}\).
(iii) \(203.6\text{ cm}=\dfrac{203.6}{100}\text{ m}=2.036\text{ m}\).
6Money conversion & sum: Convert \(10\text{ p},50\text{ p},99\text{ p}\) to rupees and find the total.
₹\(0.10, 0.50, 0.99\); sum \(=0.10+0.50+0.99=₹1.59\).
7Write the decimals and arrange in descending order: (i) \(7\) hundreds \(0\) tens \(5\) ones; (ii) \(7\) tens \(5\) tenths; (iii) \(7\) ones \(5\) hundredths.
(i) \(705\);\; (ii) \(70.5\);\; (iii) \(7.05\). Descending: \(705>70.5>7.05\).
8Order and identify shortest/longest: \(\dfrac{3}{10},\;\dfrac{3}{100},\;\dfrac{33}{100}\).
Decimals: \(0.3,\;0.03,\;0.33\). Increasing: \(\dfrac{3}{100}<\dfrac{3}{10}<\dfrac{33}{100}\).
Shortest: \(\dfrac{3}{100}\); Longest: \(\dfrac{33}{100}\).
9Locate \(4.185\) on a number line by successive place-value zoom.
\(4.185=4+\dfrac{1}{10}+\dfrac{8}{100}+\dfrac{5}{1000}\).
First between \(4\) and \(5\), take \(4.1\); in \([4.18,4.19]\), take \(4.18\); split into thousandths: fifth tick after \(4.18\) is \(4.185\).
10Using digits \(2,5,4,1,8\) exactly once, form a decimal closest to \(25\).
Make integer \(25\) and the smallest possible fractional part with remaining digits: \(0.148\).
Best choice: \(25.148\) (distance \(0.148\)); any \(24.\dots\) choice is at least \(0.149\) away.
11Pinto supplies \(3.79\text{ L},\,4.2\text{ L},\,4.25\text{ L}\) in the first three days. If he supplies \(25\text{ L}\) in six days, how much in the last three days?
First three total \(=3.79+4.2+4.25=12.24\text{ L}\). Last three \(=25-12.24=12.76\text{ L}\).
12Mahi buys \(0.25\text{ kg}\) beans, \(0.3\text{ kg}\) carrots, \(0.5\text{ kg}\) potatoes, \(0.2\text{ kg}\) capsicums, \(0.05\text{ kg}\) ginger. Total weight?
Sum \(=0.25+0.30+0.50+0.20+0.05=1.30\text{ kg}\).
13Extend the sequence by three terms: \(10.56,\,10.67,\,10.78,\,\ldots\)
Common difference \(=0.11\). Next terms: \(10.89,\,11.00,\,11.11\).
14Find \(7\dfrac{7}{1000}+\dfrac{4}{10}+2\dfrac{1}{100}\) as a decimal.
\(7.007+0.4+2.01=9.417\).
15On a number line from \(2\) to \(3\) divided into \(10\) equal parts: P is the 7th tick after \(2\). Q is three hundredths after \(2.80\). Find P and Q.
P \(=2.7\). Q \(=2.80+0.03=2.83\).
16A ribbon is \(1\text{ m }25\text{ cm}\) long. (i) Write in cm and mm. (ii) After cutting \(36.5\text{ cm}\), how much remains (in m)?
(i) \(1\text{ m }25\text{ cm}=125\text{ cm}=1250\text{ mm}\).
(ii) Remaining \(=125-36.5=88.5\text{ cm}=0.885\text{ m}\).
17“Zero dilemma”: State which are equal and which are not: \(4.5,\,4.50,\,04.50,\,4.05,\,4.005\).
\(4.5=4.50=04.50\) (same value). \(4.05\neq 4.005\) (hundredths vs thousandths).
18Is a decimal with more digits always greater? Justify with examples.
No. \(1.9=1.90\) (same). Also \(1.09<1.1\) though \(1.09\) has more digits. Place value, not length, decides size.
19Convert to decimals: (a) \(\dfrac{3}{4}\) (b) \(\dfrac{1}{5}\) (c) \(\dfrac{254}{1000}\). Show the idea briefly.
(a) \(\dfrac{3}{4}=\dfrac{75}{100}=0.75\). (b) \(\dfrac{1}{5}=\dfrac{20}{100}=0.20=0.2\). (c) \(\dfrac{254}{1000}=0.254\).
20Estimate then compute exactly: \(84.691-77.345\).
Estimate: whole parts \(84-77=7\Rightarrow\) answer is between \(7\) and \(8\).
Exact: \(84.691-77.345=7.346\).
Chapter 3 — A Peek Beyond the Point | Textbook Exercises (Solved)

Chapter 3: A Peek Beyond the Point

Part 4 — Textbook Exercises (Fully Solved)

3.3 — Figure it Out: Sums & Differences

1Find: \(\dfrac{3}{10}+\dfrac{3}{100}\).
\(0.3+0.03=0.33=\dfrac{33}{100}\).
2Find: \(9\dfrac{5}{10}\dfrac{7}{100}+2\dfrac{1}{10}\dfrac{3}{100}\).
\(9.57+2.13=11.70=11.7=11\dfrac{7}{10}\) (also \(=11\dfrac{70}{100}\)).
3Find: \(15\dfrac{6}{10}\dfrac{4}{100}+14\dfrac{3}{10}\dfrac{6}{100}\).
\(15.64+14.36=30.00=30\).
4Find: \(7\dfrac{7}{100}-4\dfrac{4}{100}\).
\(7.07-4.04=3.03=3\dfrac{3}{100}\).
5Find: \(8\dfrac{6}{100}-5\dfrac{3}{100}\).
\(8.06-5.03=3.03\).
6Find: \(12\dfrac{6}{100}\dfrac{2}{100}-9\dfrac{1}{10}\dfrac{9}{100}\).
\(12.062-9.19=2.872\).

3.4 — Place Value, Notation, Writing & Reading

7Write each quantity in decimal form (and read it):
(a) 2 ones, 3 tenths, 5 hundredths
(a) \(2.35\) — “two point three five”.
8(b) 1 ten and 5 tenths
\(10.5\) — “ten point five”.
9(c) 4 ones and 6 hundredths
\(4.06\) — “four point zero six”.
10(d) 1 hundred, 1 one and 1 hundredth
\(101.01\) — “one hundred one point zero one”.
11(e) \(\dfrac{8}{100}\) and \(\dfrac{9}{10}\)
\(0.08+0.9=0.98\).
12(f) \(\dfrac{5}{100}\)
\(0.05\).
13(g) \(\dfrac{1}{10}\)
\(0.1\).
14(h) \(2\dfrac{1}{100},\;4\dfrac{1}{10},\;7\dfrac{7}{1000}\)
\(2.01,\;4.1,\;7.007\).
15Write in decimal: (a) 234 hundredths (b) 105 tenths.
(a) \(\dfrac{234}{100}=2.34\);\;\; (b) \(\dfrac{105}{10}=10.5\).

3.5 — Unit Conversions (mm↔cm, cm↔m, g↔kg, Rupee↔Paise)

16Fill (mm ↔ cm): \(12\text{ mm}=?\), \(56\text{ mm}=?\), \(70\text{ mm}=?\).
\(12\text{ mm}=1.2\text{ cm};\;56\text{ mm}=5.6\text{ cm};\;70\text{ mm}=7.0\text{ cm}\).
17Fill (mm ↔ cm): \(\_\_\_\_\_\_ = 0.9\text{ cm},\;\;134\text{ mm}=\_\_\_\_\_\_,\;\;\_\_\_\_\_\_ = 203.6\text{ cm}\).
\(9\text{ mm}=0.9\text{ cm};\;134\text{ mm}=13.4\text{ cm};\;2036\text{ mm}=203.6\text{ cm}\).
18Fill (cm ↔ m): \(36\text{ cm}=?\), \(50\text{ cm}=?\), \(\_\_\_\_ = 0.89\text{ m}\).
\(36\text{ cm}=0.36\text{ m};\;50\text{ cm}=0.50\text{ m};\;89\text{ cm}=0.89\text{ m}\).
19Fill (cm ↔ m): \(4\text{ cm}=?\), \(325\text{ cm}=?\), \(\_\_\_\_ = 2.07\text{ m}\).
\(4\text{ cm}=0.04\text{ m};\;325\text{ cm}=3.25\text{ m};\;207\text{ cm}=2.07\text{ m}\).
20Fill (g ↔ kg): \(465\text{ g}=?\), \(68\text{ g}=?\), \(1560\text{ g}=?\).
\(0.465\text{ kg},\;0.068\text{ kg},\;1.560\text{ kg}\) respectively.
21Fill (g ↔ kg): \(704\text{ g}=?\), \(\_\_\_\_ = 0.56\text{ kg}\), \(\_\_\_\_ = 2.5\text{ kg}\).
\(704\text{ g}=0.704\text{ kg};\;560\text{ g}=0.56\text{ kg};\;2500\text{ g}=2.5\text{ kg}\).
22Fill (Rupee ↔ Paise): \(10\text{ p}=\_),\;\_\_\text{p}=₹0.05,\;\_\_\text{p}=₹0.36,\;\_\_=₹0.50,\;99\text{ p}=\_,\;250\text{ p}=\_.\)
₹0.10,\;5 p,\;36 p,\;50 p,\;₹0.99,\;₹2.50 respectively.

3.6 — Locating & Comparing Decimals

23Name all the hundredths between \(1\) and \(1.1\).
\(1.01,\,1.02,\,1.03,\,1.04,\,1.05,\,1.06,\,1.07,\,1.08,\,1.09\).
24“Zero dilemma”: Which are equal among \(0.2,\,0.20,\,0.200,\,0.02,\,0.002\)?
\(0.2=0.20=0.200\). They differ from \(0.02\) and \(0.002\).
25Compare: \(6.456\) and \(6.465\).
Equal units and tenths; hundredths \(5<6\Rightarrow 6.465>6.456\).
26Closest to \(1\) among \(0.9,\,1.01,\,1.1,\,1.11\)?
\(1.01\) (distance \(0.01\)).
27Closest to \(1.09\) among \(0.9,\,1.01,\,1.1,\,1.11\)?
\(1.10\) (distance \(0.01\)).
28Closest to \(4\) among \(3.56,\,3.65,\,3.099\)?
\(3.65\) (distance \(0.35\) vs \(0.44\) and \(0.901\)).
29Closest to \(1\) among \(0.8,\,0.69,\,1.08\)?
\(1.08\) (distance \(0.08\)).
Items that ask for exact labels “A, B, C, …” on a picture-number-line need the original figure.
Method: divide the marked unit into tenths/hundredths as indicated and count the ticks from the left endpoint to get the decimal.

3.7 — Addition & Subtraction; Sequences; Estimation

30Find the sums: (a) \(5.3+2.6\) (b) \(18+8.8\) (c) \(2.15+5.26\) (d) \(9.01+9.10\)
(a) \(7.9\);\; (b) \(26.8\);\; (c) \(7.41\);\; (d) \(18.11\).
31Find the sums: (e) \(29.19+9.91\) (f) \(0.934+0.6\) (g) \(0.75+0.03\) (h) \(6.236+0.487\)
(e) \(39.10\) (=\(39.1\)); (f) \(1.534\); (g) \(0.78\); (h) \(6.723\).
32Find the differences: (a) \(5.6-2.3\) (b) \(18-8.8\) (c) \(10.4-4.5\) (d) \(17-16.198\)
(a) \(3.3\);\; (b) \(9.2\);\; (c) \(5.9\);\; (d) \(0.802\).
33Find the differences: (e) \(17-0.05\) (f) \(34.505-18.1\) (g) \(9.9-9.09\) (h) \(6.236-0.487\)
(e) \(16.95\);\; (f) \(16.405\);\; (g) \(0.81\);\; (h) \(5.749\).
34Extend the sequences (next 3 terms):
(a) \(4.4,\,4.45,\,4.5,\ldots\)\;  (b) \(25.75,\,26.25,\,26.75,\ldots\)\;  (c) \(10.56,\,10.67,\,10.78,\ldots\)\;  (d) \(13.5,\,16,\,18.5,\ldots\)
(a) \(4.55,\,4.60,\,4.65\) (\(+0.05\));
(b) \(27.25,\,27.75,\,28.25\) (\(+0.50\));
(c) \(10.89,\,11.00,\,11.11\) (\(+0.11\));
(d) \(21.0,\,23.5,\,26.0\) (\(+2.5\)).
35Extend the sequences (next 3 terms):
(e) \(8.5,\,9.4,\,10.3,\ldots\)\;  (f) \(5,\,4.95,\,4.90,\ldots\)\;  (g) \(12.45,\,11.95,\,11.45,\ldots\)\;  (h) \(36.5,\,33,\,29.5,\ldots\)
(e) \(11.2,\,12.1,\,13.0\) (\(+0.9\));
(f) \(4.85,\,4.80,\,4.75\) (\(-0.05\));
(g) \(10.95,\,10.45,\,9.95\) (\(-0.50\));
(h) \(26.0,\,22.5,\,19.0\) (\(-3.5\)).
36Estimation check: For \(25.936+8.202\), show the sum is \(>25+8\) and \(<25+1+8+1\).
Whole parts give \(33\). Each decimal part is \(<1\), so \(<35\). Exact sum \(=34.138\in(33,35)\).
37Suggest a range for \(A-B\) using only whole parts of \(A\) and \(B\).
If \(A=a+\alpha,\;B=b+\beta\) with \(a,b\in\\mathbb{Z}\) (whole parts) and \(0\le \alpha,\beta<1\), then
\(a-b-1 \;\le\; A-B \;\le\; a-b+1\).
Tighter: \(a-b-1<A-B<a-b+1\) (strict when both fractional parts are nonzero).

3.8 — Figure it Out

38Convert to decimals: (a) \(\dfrac{5}{100}\) (b) \(\dfrac{16}{1000}\) (c) \(\dfrac{12}{10}\) (d) \(\dfrac{254}{1000}\).
(a) \(0.05\);\; (b) \(0.016\);\; (c) \(1.2\);\; (d) \(0.254\).
39Write as a sum of tenths/hundredths/thousandths: (a) \(0.34\) (b) \(1.02\) (c) \(0.8\) (d) \(0.362\).
(a) \(\dfrac{3}{10}+\dfrac{4}{100}\);
(b) \(\dfrac{10}{10}+\dfrac{2}{100}\) (i.e., \(1+\dfrac{2}{100}\));
(c) \(\dfrac{8}{10}\);
(d) \(\dfrac{3}{10}+\dfrac{6}{100}+\dfrac{2}{1000}\).
40Arrange in descending order:
(a) \(11.01,\,1.011,\,1.101,\,11.10,\,1.01\)
\(11.10 \;>\; 11.01 \;>\; 1.101 \;>\; 1.011 \;>\; 1.01\).
41Arrange in descending order:
(b) \(2.567,\,2.675,\,2.768,\,2.499,\,2.698\)
\(2.768 \;>\; 2.698 \;>\; 2.675 \;>\; 2.567 \;>\; 2.499\).
42Arrange in descending order (grams):
(c) \(4.678,\,4.595,\,4.600,\,4.656,\,4.666\)
\(4.678 \;>\; 4.666 \;>\; 4.656 \;>\; 4.600 \;>\; 4.595\).
43Arrange in descending order (meters):
(d) \(33.13,\,33.31,\,33.133,\,33.331,\,33.313\)
\(33.331 \;>\; 33.313 \;>\; 33.31 \;>\; 33.133 \;>\; 33.13\).
44Using digits \(1,4,0,8,6\): (a) decimal closest to \(30\); (b) smallest decimal between \(100\) and \(1000\).
This task depends on the exact instruction “use each digit once” and whether other digits are allowed. Without digit ‘3’, a number starting with “30…” cannot be formed solely from \(1,4,0,8,6\). If the intent is “use each given digit exactly once”, then a valid answer for (b) is \(104.68\) (smallest \(>\!100\)). For (a), clarify whether additional digits are permitted; otherwise the problem is under-specified.
45Is a decimal with more digits always greater than one with fewer digits?
No. \(1.9=1.90\) (same). Also \(1.09<1.1\) though \(1.09\) has more digits. Place values decide size.
46Mahi buys \(0.25\) kg beans, \(0.3\) kg carrots, \(0.5\) kg potatoes, \(0.2\) kg capsicums, \(0.05\) kg ginger. Total weight?
Total \(=0.25+0.30+0.50+0.20+0.05=1.30\text{ kg}\).
47Pinto supplies \(3.79\) L, \(4.2\) L, \(4.25\) L in 3 days; in 6 days he supplies \(25\) L. Quantity in last 3 days?
First three \(=12.24\) L; last three \(=25-12.24=12.76\) L.
48Tinku weighed \(35.75\) kg in Jan and \(34.50\) kg in Feb. Gained or lost? By how much?
Lost \(35.75-34.50=1.25\) kg.
49Extend the pattern: \(5.5,\,6.4,\,6.39,\,7.29,\,7.28,\,6.18,\,6.17,\,\_\_,\,\_\_\).
The printed sequence appears inconsistent at the term “\(6.18\)”. A consistent rule many texts use here is “\(+0.90,\,-0.01\)” repeating. If we adopt that rule, the correct 6th term should be \(8.18\), and the next two are \(9.07,\,9.06\). If your book’s figure shows otherwise, follow its exact ticks.
50How many millimetres make \(1\) kilometre?
\(1\text{ km}=1000\text{ m}=1000\times 1000\text{ mm}=1{,}000{,}000\text{ mm}\).
51Insurance ₹\(0.45\) per passenger; \(1\) lakh passengers opt in. Total fee?
₹\(0.45\times 100{,}000=₹45{,}000\).
52Which is greater?
(a) \(\dfrac{10}{1000}\) or \(\dfrac{1}{10}\);\;  (b) one-hundredth or \(90\) thousandths;\;  (c) one-thousandth or \(90\) hundredths
(a) \(\dfrac{1}{10}\) (i.e., \(0.1>0.01\));
(b) \(90\) thousandths \(=0.09\) \(>\) \(0.01\);
(c) \(90\) hundredths \(=0.90\) \(>\) \(0.001\).
53Decimal forms:
(a) 87 ones, 5 tenths, 60 hundredths;
(b) 12 tens and 12 tenths;
(c) 10 tens, 10 ones, 10 tenths, 10 hundredths;
(d) 25 tens, 25 ones, 25 tenths, 25 hundredths.
(a) \(87+0.5+0.60=88.10\);\; (b) \(120+1.2=121.2\);
(c) \(100+10+1+0.1=111.1\);\; (d) \(250+25+2.5+0.25=277.75\).
54Write in decimal: (a) \(\dfrac{1}{2}\) (b) \(\dfrac{3}{2}\) (c) \(\dfrac{1}{4}\) (d) \(\dfrac{3}{4}\) (e) \(\dfrac{1}{5}\) (f) \(\dfrac{4}{5}\).
(a) \(0.5\);\; (b) \(1.5\);\; (c) \(0.25\);\; (d) \(0.75\);\; (e) \(0.2\);\; (f) \(0.8\).
Items that require a specific picture (e.g., “fill the boxes to make sum closest to 10.5”, or lettered ticks on a line) need the original diagram. Use the same place-value and tick-counting method shown above to obtain the exact numbers from your figure.

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