Exercise: 4-C
Q1: Multiply:
i. \(0.87 \times 10\)
Step 1: Multiply \(0.87\) by \(10\) (shift decimal 1 place right):
\[
0.87 \times 10 = 8.7
\]
Answer: 8.7
ii. \(2.948 \times 100\)
Step 1: Multiply \(2.948\) by \(100\) (shift decimal 2 places right):
\[
2.948 \times 100 = 294.8
\]
Answer: 294.8
iii. \(6.4 \times 1000\)
Step 1: Multiply \(6.4\) by \(1000\) (shift decimal 3 places right):
\[
6.4 \times 1000 = 6400
\]
Answer: 6400
iv. \(5.8 \times 4\)
Step 1: Multiply \(5.8\) by \(4\):
5.8 × 4 ──── 23.2
Answer: 23.2
v. \(16.32 \times 28\)
Step 1: Multiply \(16.32\) by \(28\):
16.32 × 28 ──────── 130.56 (16.32 × 8) 326.40 (16.32 × 20) ──────── 456.96
Answer: 456.96
vi. \(5.037 \times 8\)
Step 1: Multiply \(5.037\) by \(8\):
5.037 × 8 ─────── 40.296
Answer: 40.296
vii. \(4.6 \times 2.1\)
Step 1: Remove decimals and multiply \(46 \times 21\):
46 × 21 ───── 46 (46 × 1) 920 (46 × 20) ───── 966
Step 2: Place decimal back (1 + 1 = 2 decimal places):
\[
4.6 \times 2.1 = 9.66
\]
Answer: 9.66
viii. \(0.568 \times 6.4\)
Step 1: Remove decimals and multiply \(568 \times 64\):
568 ×64 ────── 2272 (568 × 4) 34080 (568 × 60) ────── 36352
Step 2: Place decimal back (3 + 1 = 4 decimal places):
\[
0.568 \times 6.4 = 3.6352
\]
Answer: 3.6352
Q2: Multiply each number by 10, 100 and 1000:
i. \(0.5\)
\[
0.5 \times 10 = 5.0 \\
0.5 \times 100 = 50.0 \\
0.5 \times 1000 = 500.0
\]
Answer:5, 50, 500
ii. \(0.112\)
\[
0.112 \times 10 = 1.12 \\
0.112 \times 100 = 11.2 \\
0.112 \times 1000 = 112.0
\]
Answer:1.12, 11.2, 112
iii. \(4.8\)
\[
4.8 \times 10 = 48.0 \\
4.8 \times 100 = 480.0 \\
4.8 \times 1000 = 4800.0
\]
Answer:48, 480, 4800
iv. \(0.0359\)
\[
0.0359 \times 10 = 0.359 \\
0.0359 \times 100 = 3.59 \\
0.0359 \times 1000 = 35.9
\]
Answer:0.359, 3.59, 35.9
v. \(16.27\)
\[
16.27 \times 10 = 162.7 \\
16.27 \times 100 = 1627.0 \\
16.27 \times 1000 = 16270.0
\]
Answer:162.7, 1627, 16270
vi. \(234.8\)
\[
234.8 \times 10 = 2348.0 \\
234.8 \times 100 = 23480.0 \\
234.8 \times 1000 = 234800.0
\]
Answer:2348, 23480, 234800
Q3: Evaluate:
i. \(5.897 \times 2.3\)
Step 1: Remove decimals and multiply \(5897 \times 23\):
5897 × 23 ────── 17691 (5897 × 3) 117940 (5897 × 20) ────── 135631
Step 2: Place decimal back (3 + 1 = 4 decimal places):
\[
5.897 \times 2.3 = 13.5631
\]
Answer:13.5631
ii. \(0.894 \times 87\)
Step 1: Remove decimals and multiply \(894 \times 87\):
894 × 87 ───── 6258 (894 × 7) 71520 (894 × 80) ───── 77778
Step 2: Place decimal back (3 decimal places):
\[
0.894 \times 87 = 77.778
\]
Answer:77.778
iii. \(0.01 \times 0.001\)
Step 1: Remove decimals and multiply \(1 \times 1 = 1\):
1 × 1 ─── 1
Step 2: Place decimal back (2 + 3 = 5 decimal places):
\[
0.01 \times 0.001 = 0.00001
\]
Answer:0.00001
iv. \(0.84 \times 2.2 \times 4\)
Step 1: Multiply \(0.84 \times 2.2\) Remove decimals and multiply \(84 \times 22\):
84 × 22 ──── 168 (84 × 2) 1680 (84 × 20) ──── 1848
Place decimal back (2 decimal places total): \[ 0.84 \times 2.2 = 1.848 \]Step 2: Multiply \(1.848 \times 4\)
1848 × 4 ───── 7392
Place decimal back (3 decimal places):
\[
1.848 \times 4 = 7.392
\]
Answer:7.392
v. \(4.75 \times 0.08 \times 3\)
Step 1: Multiply \(4.75 \times 0.08\) Remove decimals and multiply \(475 \times 8\):
475 ×8 ──── 3800
Place decimal back (4 decimal places total):
\[
4.75 \times 0.08 = 0.38
\]Step 2: Multiply \(0.38 \times 3\)
Remove decimals and multiply \(38 \times 3\):
38 × 3 ── 114
Place decimal back (2 decimal places):
\[
0.38 \times 3 = 1.14
\]
Answer:1.14
vi. \(2.4 \times 3.5 \times 4.8\)
Step 1: Multiply \(2.4 \times 3.5\)
Remove decimals and multiply \(24 \times 35\):
24 × 35 ──── 120 (24 × 5) 720 (24 × 30) ──── 840
Place decimal back (2 decimal places):
\[
2.4 \times 3.5 = 8.4
\]Step 2: Multiply \(8.4 \times 4.8\)
Remove decimals and multiply \(84 \times 48\):
84 × 48 ──── 672 (84 × 8) 3360 (84 × 40) ──── 4032
Place decimal back (2 decimal places):
\[
8.4 \times 4.8 = 40.32
\]
Answer:40.32
vii. \(0.8 \times 1.2 \times 0.25\)
Step 1: Multiply \(0.8 \times 1.2\)
Remove decimals and multiply \(8 \times 12\):
12 × 8 ── 96
Place decimal back (2 decimal places):
\[
0.8 \times 1.2 = 0.96
\]Step 2: Multiply \(0.96 \times 0.25\)
Remove decimals and multiply \(96 \times 25\):
96 × 25 ──── 480 (96 × 5) 1920 (96 × 20) ──── 2400
Place decimal back (4 decimal places):
\[
0.96 \times 0.25 = 0.24
\]
Answer:0.24
viii. \(0.3 \times 0.03 \times 0.003\)
Step 1: Multiply \(0.3 \times 0.03\)
Remove decimals and multiply \(3 \times 3\):
3 × 3 ── 9
Place decimal back (3 decimal places):
\[
0.3 \times 0.03 = 0.009
\]Step 2: Multiply \(0.009 \times 0.003\)
Remove decimals and multiply \(9 \times 3\):
9 × 3 ── 27
Place decimal back (6 decimal places):
\[
0.009 \times 0.003 = 0.000027
\]
Answer:0.000027
Q4: Divide:
i. \(54.9 \div 10\)
Step 1: Dividing by 10 shifts decimal point 1 place left:
\[
54.9 \div 10 = 5.49
\]
Answer:5.49
ii. \(7.8 \div 100\)
Step 1: Dividing by 100 shifts decimal point 2 places left:
\[
7.8 \div 100 = 0.078
\]
Answer:0.078
iii. \(324.76 \div 1000\)
Step 1: Dividing by 1000 shifts decimal point 3 places left:
\[
324.76 \div 1000 = 0.32476
\]
Answer:0.32476
iv. \(12.8 \div 4\)
Step 1: Divide 12.8 by 4 using long division:
3.2
_____
4| 12.8
-12
---
08
-8
---
0
Answer:3.2
v. \(27.918 \div 9\)
Step 1: Divide 27.918 by 9 using long division:
3.102
_______
9| 27.918
-27
----
09
-9
---
01
0
---
18
-18
---
0
(Here 9 goes into 27 three times, remainder 0; next digit 9 goes 1 time; etc.)
Answer:3.102
vi. \(4.672 \div 8\)
Step 1: Divide 4.672 by 8 using long division:
0.584
______
8| 4.672
-0
---
46
-40
---
67
-64
---
32
-32
---
0
Answer:0.584
vii. \(4.32 \div 1.2\)
Step 1: Remove decimal from divisor by multiplying numerator and denominator by 10: \[ \frac{4.32}{1.2} = \frac{4.32 \times 10}{1.2 \times 10} = \frac{43.2}{12} \]Step 2: Divide 43.2 by 12 using long division:
3.6
_____
12| 43.2
-36
---
72
-72
---
0
Answer:3.6
viii. \(7.644 \div 1.4\)
Step 1: Remove decimal from divisor by multiplying numerator and denominator by 10: \[ \frac{7.644}{1.4} = \frac{7.644 \times 10}{1.4 \times 10} = \frac{76.44}{14} \]Step 2: Divide 76.44 by 14 using long division:
5.46
______
14| 76.44
-70
---
64
-56
---
84
-84
---
0
Answer:5.46
ix. \(4.8432 \div 0.08\)
Step 1: Remove decimal from divisor by multiplying numerator and denominator by 100: \[ \frac{4.8432}{0.08} = \frac{4.8432 \times 100}{0.08 \times 100} = \frac{484.32}{8} \]Step 2: Divide 484.32 by 8 using long division:
60.54
_______
8| 484.32
-48
----
44
-40
----
43
-40
----
32
-32
----
0
Answer:60.54
Q5: Divide each of given numbers by 10, 100, 1000 and 10000:
i. Number: 2.1
Step 1: Divide by 10 (move decimal 1 place left):
\[
2.1 \div 10 = 0.21
\]
Step 2: Divide by 100 (move decimal 2 places left):
\[
2.1 \div 100 = 0.021
\]
Step 3: Divide by 1000 (move decimal 3 places left):
\[
2.1 \div 1000 = 0.0021
\]
Step 4: Divide by 10000 (move decimal 4 places left):
\[
2.1 \div 10000 = 0.00021
\]
Answer:0.21, 0.021, 0.0021, 0.00021
ii. Number: 8.64
Step 1: Divide by 10:
\[
8.64 \div 10 = 0.864
\]
Step 2: Divide by 100:
\[
8.64 \div 100 = 0.0864
\]
Step 3: Divide by 1000:
\[
8.64 \div 1000 = 0.00864
\]
Step 4: Divide by 10000:
\[
8.64 \div 10000 = 0.000864
\]
Answer:0.864, 0.0864, 0.00864, 0.000864
iii. Number: 5.01
Step 1: Divide by 10:
\[
5.01 \div 10 = 0.501
\]
Step 2: Divide by 100:
\[
5.01 \div 100 = 0.0501
\]
Step 3: Divide by 1000:
\[
5.01 \div 1000 = 0.00501
\]
Step 4: Divide by 10000:
\[
5.01 \div 10000 = 0.000501
\]
Answer:0.501, 0.0501, 0.00501, 0.000501
iv. Number: 0.0906
Step 1: Divide by 10:
\[
0.0906 \div 10 = 0.00906
\]
Step 2: Divide by 100:
\[
0.0906 \div 100 = 0.000906
\]
Step 3: Divide by 1000:
\[
0.0906 \div 1000 = 0.0000906
\]
Step 4: Divide by 10000:
\[
0.0906 \div 10000 = 0.00000906
\]
Answer:0.00906, 0.000906, 0.0000906, 0.00000906
v. Number: 0.125
Step 1: Divide by 10:
\[
0.125 \div 10 = 0.0125
\]
Step 2: Divide by 100:
\[
0.125 \div 100 = 0.00125
\]
Step 3: Divide by 1000:
\[
0.125 \div 1000 = 0.000125
\]
Step 4: Divide by 10000:
\[
0.125 \div 10000 = 0.0000125
\]
Answer:0.0125, 0.00125, 0.000125, 0.0000125
vi. Number: 111.11
Step 1: Divide by 10:
\[
111.11 \div 10 = 11.111
\]
Step 2: Divide by 100:
\[
111.11 \div 100 = 1.1111
\]
Step 3: Divide by 1000:
\[
111.11 \div 1000 = 0.11111
\]
Step 4: Divide by 10000:
\[
111.11 \div 10000 = 0.011111
\]
Answer:11.111, 1.1111, 0.11111, 0.011111
Q6: Evaluate:
i. \(9.75 \div 5\)
Step 1: Divide 9.75 by 5 using long division:
1.95
_______
5 | 9.75
-5
---
47
-45
---
25
-25
---
0
Answer:1.95
ii. \(4.4064 \div 4\)
Step 1: Divide 4.4064 by 4 using long division:
1.1016
_______
4 | 4.4064
-4
---
04
-4
---
00
-0
---
06
-04
---
24
-24
---
0
Answer:1.1016
iii. \(27.69 \div 30\)
Step 1: Multiply numerator and denominator by 10 to remove decimal from divisor:
\[
\frac{27.69}{30} = \frac{276.9}{300}
\]Step 2: Simplify fraction: divide numerator and denominator by 3:
\[
\frac{276.9}{300} = \frac{92.3}{100}
\]Step 3: Divide 92.3 by 100 (shift decimal 2 places left):
\[
92.3 \div 100 = 0.923
\]Answer:0.923
iv. \(19.25 \div 25\)
Step 1: Multiply numerator and denominator by 4 to make denominator 100:
\[
\frac{19.25}{25} = \frac{19.25 \times 4}{100} = \frac{77}{100}
\]Step 2: Divide 77 by 100 (shift decimal 2 places left):
\[
77 \div 100 = 0.77
\]Answer:0.77
v. \(20.64 \div 16\)
Step 1: Divide 20.64 by 16 using long division:
1.29
_______
16| 20.64
-16
---
46
-32
---
144
-144
----
0
Answer:1.29
vi. \(3.204 \div 9\)
Step 1: Divide 3.204 by 9 using long division:
0.356
_______
9 | 3.204
-0
---
32
-27
---
50
-45
---
54
-54
---
0
Answer:0.356
vii. \(0.125 \div 25\)
Step 1: Multiply numerator and denominator by 4 to make denominator 100:
\[
\frac{0.125}{25} = \frac{0.125 \times 4}{100} = \frac{0.5}{100}
\]Step 2: Divide 0.5 by 100 (shift decimal 2 places left):
\[
0.5 \div 100 = 0.005
\]Answer:0.005
viii. \(0.14616 \div 72\)
Step 1: Multiply numerator and denominator by 1000 to remove decimal from numerator: \[ \frac{0.14616}{72} = \frac{146.16}{72000} \]Step 2: Use calculator or simplify fraction to decimal:
0.00203
_______
72 | 0.14616
-0
---
01
-00
---
14
-00
---
146
-144
----
21
-00
----
216
-216
----
0
\[
0.14616 \div 72 = 0.00203
\]Answer:0.00203
ix. \(0.6227 \div 1300\)
Step 1: Multiply numerator and denominator by 10,000 to remove decimal: \[ \frac{0.6227}{1300} = \frac{6227}{13,000,000} \]Step 2: Divide numerator by denominator to get decimal:
0.000479
_______
13000000 | 6227
- 0
------
62270
- 0
-------
622700
- 0
---------
6227000
- 0
---------
62270000
-52000000
------------
102700000
-91000000
------------
117000000
-117000000
-----------
0
\[
0.6227 \div 1300 = 0.000479
\]Answer:0.000479
x. \(257.894 \div 0.169\)
Step 1: Multiply numerator and denominator by 1000 to remove decimal from denominator: \[ \frac{257.894}{0.169} = \frac{257894}{169} \]Step 2: Divide 257894 by 169 (long division or calculator):
1526
_______
169 | 257894
-169
-----
888
-845
------
439
-338
-------
1014
-1014
------
0
\[
257894 \div 169 = 1526
\]Answer:1526
xi. \(6.3 \div (0.3)^2\)
Step 1: Calculate \((0.3)^2 = 0.09\)
\[
0.3 \times 0.3 = 0.09
\]Step 2: Divide 6.3 by 0.09:
\[
6.3 \div 0.09
\]Step 3: Multiply numerator and denominator by 100 to remove decimal from divisor:
\[
\frac{6.3}{0.09} = \frac{630}{9} = 70
\]Answer:70
Q7: Evaluate:
i. \(4.3 \times 0.52 \times 0.3\)
Step 1: Multiply \(4.3 \times 0.52\)
43 × 52 ----- 86 (43 × 2) 2150 (43 × 50) ----- 2236
Step 2: Place decimal (1 + 2 = 3 decimal places):
\[
4.3 \times 0.52 = 2.236
\]Step 3: Multiply \(2.236 \times 0.3\)
\[
2.236 \times 0.3 = 0.6708
\]Answer:0.6708
ii. \(3.2 \times 2.5 \times 0.7\)
Step 1: Multiply \(3.2 \times 2.5\)
\[
3.2 \times 2.5 = 8.0
\]Step 2: Multiply \(8.0 \times 0.7 = 5.6\)
Answer:5.6
iii. \(0.8 \times 1.5 \times 0.6\)
Step 1: Multiply \(0.8 \times 1.5 = 1.2\)
Step 2: Multiply \(1.2 \times 0.6 = 0.72\)
Answer:0.72
iv. \(0.3 \times 0.3 \times 0.3\)
Step 1: Multiply \(0.3 \times 0.3 = 0.09\)
Step 2: Multiply \(0.09 \times 0.3 = 0.027\)
Answer:0.027
v. \(1.2 \times 1.2 \times 4\)
Step 1: Multiply \(1.2 \times 1.2 = 1.44\)
Step 2: Multiply \(1.44 \times 4 = 5.76\)
Answer:5.76
vi. \(0.4 \times 0.04 \times 0.004\)
Step 1: Multiply \(0.4 \times 0.04 = 0.016\)
Step 2: Multiply \(0.016 \times 0.004 = 0.000064\)
Answer:0.000064
vii. \(0.5 \times 0.6 \times 0.7\)
Step 1: Multiply \(0.5 \times 0.6 = 0.3\)
Step 2: Multiply \(0.3 \times 0.7 = 0.21\)
Answer:0.21
viii. \(0.5 \times 0.06 \times 0.007\)
Step 1: Multiply \(0.5 \times 0.06 = 0.03\)
Step 2: Multiply \(0.03 \times 0.007 = 0.00021\)
Answer:0.00021
Q8: Evaluate:
i. \(\left(0.9\right)^2\)
Step 1: Multiply \(0.9 \times 0.9\)
9 × 9 --- 81
Step 2: Place decimal back (1 + 1 = 2 decimal places):
\[
(0.9)^2 = 0.81
\]Answer:0.81
ii. \(\left(0.6\right)^2 \times 0.5\)
Step 1: Calculate \((0.6)^2 = 0.6 \times 0.6 = 0.36\)
Step 2: Multiply \(0.36 \times 0.5\)
\[
0.36 \times 0.5 = 0.18
\]Answer:0.18
iii. \(0.3 \times \left(0.5\right)^2\)
Step 1: Calculate \((0.5)^2 = 0.5 \times 0.5 = 0.25\)
Step 2: Multiply \(0.3 \times 0.25 = 0.075\)
Answer:0.075
iv. \(\left(0.4\right)^3\)
Step 1: Multiply \(0.4 \times 0.4 = 0.16\)
Step 2: Multiply \(0.16 \times 0.4 = 0.064\)
Answer:0.064
v. \(\left(0.2\right)^3 \times 5\)
Step 1: Calculate \((0.2)^3\)
\[
0.2 \times 0.2 = 0.04, \quad 0.04 \times 0.2 = 0.008
\]Step 2: Multiply \(0.008 \times 5 = 0.04\)
Answer:0.04
vi. \(\left(0.2\right)^3 \times 0.05\)
Step 1: Calculate \((0.2)^3 = 0.008\) (from above)
Step 2: Multiply \(0.008 \times 0.05\)
\[
0.008 \times 0.05 = 0.0004
\]Answer:0.0004
Q9: Find the cost of 36.75 kg wheat at rate of ₹12.80 per kg.
Step 1: Write the multiplication expression: \[ \text{Cost} = 36.75 \times 12.80 \]Step 2: Remove decimals and multiply \(3675 \times 1280\):
3675 × 1280 ────────── 0000 (3675 × 0) 294000 (3675 × 80) 735000 (3675 × 200) 3675000 (3675 × 1000) ────────── 4704000
Step 3: Place decimal back:
Total decimal places = 2 (in 36.75) + 2 (in 12.80) = 4
\[
36.75 \times 12.80 = 470.4000 = 470.4
\]Answer:₹470.40
Q10: The cost of a pen is ₹56.15. Find the cost of 16 such pens.
Step 1: Write the multiplication expression: \[ \text{Total cost} = 56.15 \times 16 \]Step 2: Remove decimal and multiply \(5615 \times 16\):
5615 × 16 ─────── 33690 (5615 × 6) 56150 (5615 × 10) ─────── 89840
Step 3: Place decimal back:
Decimal places in 56.15 = 2
\[
56.15 \times 16 = 898.40
\]Answer:₹898.40
Q11: Evaluate
i. \(0.0072 \div 0.06\)
Step 1: Remove decimals by multiplying numerator and denominator by 1000: \[ \frac{0.0072}{0.06} = \frac{7.2}{60} \] Step 2: Divide \(7.2 \div 60\):
0.12
_______
60 | 7.2
-0
----
72
-60
----
120
-120
---
0
Answer:0.12
ii. \(0.621 \div 0.3\)
Step 1: Remove decimals by multiplying numerator and denominator by 10: \[ \frac{0.621}{0.3} = \frac{6.21}{3} \] Step 2: Divide \(6.21 \div 3\):
2.07
_______
3 | 6.21
-6
----
02
-00
----
21
-21
---
0
Answer:2.07
iii. \(0.0532 \div 0.005\)
Step 1: Remove decimals by multiplying numerator and denominator by 1000: \[ \frac{0.0532}{0.005} = \frac{53.2}{5} \] Step 2: Divide \(53.2 \div 5\):
10.64
_______
5 | 53.2
-5
----
3
-0
----
32
-30
---
20
-20
---
0
Answer:10.64
iv. \(0.01162 \div 0.14\)
Step 1: Remove decimals by multiplying numerator and denominator by 100: \[ \frac{0.01162}{0.14} = \frac{1.162}{14} \] Step 2: Divide \(1.162 \div 14\):
0.083
_______
14 | 1.162
-0
----
11
-0
---
116
-112
----
42
-42
---
0
Answer:0.083
v. \(\left(7.5 \times 40.4\right) \div 25\)
Step 1: Multiply \(7.5 \times 40.4\):
404 × 75 ─────── 2020 (404 × 5) 28280 (404 × 70) ─────── 30300
Since \(7.5 \times 40.4 = 303.0\) (decimal places 1 + 1 = 2, so 3030 ÷ 100 = 303.0)
Step 2: Divide \(303.0 \div 25\):
12.12
_______
25 | 303.0
-25
----
53
-50
----
30
-25
---
50
-50
---
0
Answer:12.12
vi. \(2.1 \div (0.1 \times 0.1)\)
Step 1: Multiply \(0.1 \times 0.1 = 0.01\)
Step 2: Divide \(2.1 \div 0.01\):
2.1 ÷ 0.01 = 210
Answer:210
Q12: Fifteen identical articles weigh 31.50 kg. Find the weigh of each article.
Step 1: Total weight of 15 articles = 31.50 kg
Let weight of each article = \(x\) kg.
So, \(15 \times x = 31.50\)
Step 2: Find \(x\) by dividing total weight by number of articles:
\[
x = \frac{31.50}{15}
\]
2.1
_______
15 | 31.50
-30
---
15
-15
---
0
Answer: Each article weighs 2.1 kg.
Q13: The product of two numbers is 211.2. If one of these two numbers is 16.5, find the other number.
Step 1: Let the other number be \(x\).
Given,
\[
16.5 \times x = 211.2
\]Step 2: Find \(x\) by dividing 211.2 by 16.5:
\[
x = \frac{211.2}{16.5}
\]
12.8
_______
165 | 2112
-165
----
462
-330
----
1320
-1320
------
0
Answer: The other number is 12.8.
Q14: One dozen identical articles cost ₹45.96. Find the cost of each article.
Step 1: One dozen means 12 articles. Let the cost of each article be \(x\).
Given,
\[
12 \times x = 45.96
\]Step 2: Find \(x\) by dividing 45.96 by 12:
\[
x = \frac{45.96}{12}
\]
3.83
_______
12 | 45.96
-36
----
99
-96
----
36
-36
---
0
Answer: The cost of each article is ₹3.83.
Q15: Find whether the given division forms a terminating or a non-terminating decimal:
i. \(3\div8\)
Step 1: Prime factorize the denominator 8 = \(2^3\).
Since denominator has only 2 as prime factors, division gives a terminating decimal.
Answer: Terminating decimal.
ii. \(8 \div 3\)
Step 1: Denominator 3 is prime.
Division gives a repeating decimal (non-terminating).
Answer: Non-terminating decimal.
iii. \(6 \div 5\)
Step 1: Denominator 5 is prime.
Division gives a terminating decimal.
Answer: Terminating decimal.
iv. \(5 \div 6\)
Step 1: Denominator 6 = \(2 \times 3\) includes 3, so non-terminating decimal.
Answer: Non-terminating decimal.
v. \(12.5 \div 4\)
Step 1: Denominator 4 = \(2^2\), only 2’s prime factors.
Division gives terminating decimal.
Answer: Terminating decimal.
vi. \(23 \div 0.7 = \frac{23}{0.7} = \frac{230}{7}\)
Step 1: Denominator 7 is prime (other than 2 or 5), so division is non-terminating decimal.
Answer: Non-terminating decimal.
vii. \(42 \div 9\)
Step 1: Denominator 9 = \(3^2\), prime factor is 3, non-terminating decimal.
Answer: Non-terminating decimal.
viii. \(0.56 \div 0.11 = \frac{56}{11}\)
Step 1: Denominator 11 is prime, division is non-terminating decimal.
Answer: Non-terminating decimal.
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