Subjective Questions
Q1:
Convert the decimal number into quinary number.
425
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="83"><tbody><tr><td> 5</td> <td> 425</td> <td> 0</td> </tr><tr><td> 5</td> <td> 85</td> <td> 0</td> </tr><tr><td> 5</td> <td> <p> 17</p> </td> <td> 2</td> </tr><tr><td> 5</td> <td> 3</td> <td> 3</td> </tr><tr><td></td> <td></td> <td></td> </tr></tbody></table><p> 0</p> <p>∴ 425<sub>10</sub> = 3200<sub>5</sub></p>
Q2:
Convert the decimal number into quinary number.
924
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="143"><tbody><tr><td> 5</td> <td> 924</td> <td> 4</td> </tr><tr><td> 5</td> <td> 184</td> <td> 4</td> </tr><tr><td> 5</td> <td> 36</td> <td> 1</td> </tr><tr><td> 5</td> <td> 7</td> <td> 2</td> </tr><tr><td> 5</td> <td> 1</td> <td> 1</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p></p> <p>∴ 924<sub>10</sub> = 12144<sub>5</sub></p>
Q3:
Convert the decimal number into quinary number.
924
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="120"><tbody><tr><td> 5</td> <td> 924</td> <td> 4</td> </tr><tr><td> 5</td> <td> 184</td> <td> 4</td> </tr><tr><td> 5</td> <td> 36</td> <td> 1</td> </tr><tr><td> 5</td> <td> 7</td> <td> 2</td> </tr><tr><td> 5</td> <td> 1</td> <td> 1</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p>∴ 924<sub>10</sub> = 12144<sub>5</sub></p>
Q4:
Convert the decimal number into quinary number.
1574
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="127"><tbody><tr><td> 5</td> <td> 1574</td> <td> 4</td> </tr><tr><td> 5</td> <td> 312</td> <td> 2</td> </tr><tr><td> 5</td> <td> 62</td> <td> 2</td> </tr><tr><td> 5</td> <td> 12</td> <td> 2</td> </tr><tr><td> 5</td> <td> 2</td> <td> 2</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p>∴ 1574<sub>10</sub> = 22224<sub>5</sub></p>
Q5:
Convert the decimal number into quinary number.
2487
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="113"><tbody><tr><td> 5</td> <td> 2487</td> <td> 2</td> </tr><tr><td> 5</td> <td> 497</td> <td> 2</td> </tr><tr><td> 5</td> <td> 99</td> <td> 4</td> </tr><tr><td> 5</td> <td> 19</td> <td> 4</td> </tr><tr><td> 5</td> <td> 3</td> <td> 3</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p>∴ 2487<sub>10</sub> = 34422<sub>5</sub></p>
Q6:
Convert the decimal number into quinary number.
3040
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="95"><tbody><tr><td> 5</td> <td> 3040</td> <td> 0</td> </tr><tr><td> 5</td> <td> 608</td> <td> 3</td> </tr><tr><td> 5</td> <td> 121</td> <td> 1</td> </tr><tr><td> 5</td> <td> 24</td> <td> 4</td> </tr><tr><td> 5</td> <td> 4</td> <td> 4</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p>∴ 3040<sub>10</sub> = 44130<sub>5</sub></p>
Q7:
Convert the decimal number into quinary number.
5864
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="102"><tbody><tr><td> 5</td> <td> 5864</td> <td> 4</td> </tr><tr><td> 5</td> <td> 1172</td> <td> 2</td> </tr><tr><td> 5</td> <td> 234</td> <td> 4</td> </tr><tr><td> 5</td> <td> 46</td> <td> 1</td> </tr><tr><td> 5</td> <td> 9</td> <td> 5</td> </tr><tr><td> 5</td> <td> 1</td> <td> 1</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p>∴ 5864<sub>10</sub> = 151424<sub>5</sub></p>
Q8:
Convert the quinary number into binary number.
1215
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>121<sub>5</sub></p> <p>= 1 × 5<sup>2</sup> + 2× 5<sup>1</sup> + 1 × 5<sup>0</sup></p> <p>= 25 + 10 + 1</p> <p>= 36<sub>10</sub></p> <p>Then,</p> <table width="88"><tbody><tr><td>2</td> <td>36</td> <td>0</td> </tr><tr><td>2</td> <td>18</td> <td>0</td> </tr><tr><td>2</td> <td>9</td> <td>1</td> </tr><tr><td>2</td> <td>4</td> <td>0</td> </tr><tr><td>2</td> <td>2</td> <td>0</td> </tr><tr><td>2</td> <td>1</td> <td>1</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 36<sub>10</sub> = 100100<sub>2</sub></p>
Q9:
Convert the quinary number into binary number.
2035
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>203<sub>5</sub></p> <p>= 2× 5<sup>2</sup> + 0× 5<sup>1</sup> + 3× 5<sup>0</sup></p> <p>= 50 + 0+ 3</p> <p>= 53<sub>10</sub></p> <p>Then,</p> <table width="102"><tbody><tr><td>2</td> <td>53</td> <td>1</td> </tr><tr><td>2</td> <td>26</td> <td>0</td> </tr><tr><td>2</td> <td>13</td> <td>1</td> </tr><tr><td>2</td> <td>6</td> <td>0</td> </tr><tr><td>2</td> <td>3</td> <td>1</td> </tr><tr><td></td> <td>1</td> <td></td> </tr></tbody></table><p>∴ 53<sub>10</sub> = 110101<sub>2</sub></p>
Q10:
Convert the quinary number into binary number.
4325
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>432<sub>5</sub></p> <p>= 4× 5<sup>2</sup> + 3× 5<sup>1</sup> + 2× 5<sup>0</sup></p> <p>= 100 + 15 + 2</p> <p>= 152<sub>10</sub></p> <p>Then,</p> <p></p> <table width="104"><tbody><tr><td>2</td> <td>152</td> <td>0</td> </tr><tr><td>2</td> <td>76</td> <td>0</td> </tr><tr><td>2</td> <td>38</td> <td>0</td> </tr><tr><td>2</td> <td>19</td> <td>1</td> </tr><tr><td>2</td> <td>9</td> <td>1</td> </tr><tr><td>2</td> <td>4</td> <td>0</td> </tr><tr><td>2</td> <td>2</td> <td>0</td> </tr><tr><td></td> <td>1</td> <td></td> </tr></tbody></table><p>∴ 152<sub>10</sub> = 10011000<sub>2</sub></p> <p></p> <p></p>
Q11:
Convert the binary number into quinary number.
1101102
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>110110<sub>2</sub></p> <p>= 1× 2<sup>5</sup> +1× 2<sup>4</sup>+0× 2<sup>3</sup>+1× 2<sup>2</sup>+1× 2<sup>1</sup>+0× 2<sup>0</sup></p> <p>= 32 +16 +0 +4 +2 +0</p> <p>= 54<sub>10</sub></p> <p>Now,</p> <table width="75"><tbody><tr><td>5</td> <td>54</td> <td>4</td> </tr><tr><td>5</td> <td>10</td> <td>0</td> </tr><tr><td>5</td> <td>2</td> <td>2</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 110110<sub>2</sub> = 54<sub>10</sub> = 204<sub>5</sub></p>
Q12:
Convert the binary number into quinary number.
11101102
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>1110110<sub>2</sub></p> <p>= 1× 2<sup>6</sup> + 1× 2<sup>5</sup> + 1 × 2<sup>4</sup> + 0× 2<sup>3</sup> + 1× 2<sup>2</sup> + 1× 2<sup>1</sup> + 0× 2<sup>0</sup></p> <p>= 64 + 32 + 16 +0 + 4 + 2 +0</p> <p>= 118<sub>10</sub></p> <p>Now,</p> <table width="88"><tbody><tr><td>5</td> <td>118</td> <td>3</td> </tr><tr><td>5</td> <td>23</td> <td>3</td> </tr><tr><td>5</td> <td>4</td> <td>4</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 1110110<sub>2</sub> = 118<sub>10</sub> = 433<sub>5</sub></p>
Q13:
convert the binary number into quinary number.
111011012
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>11101101<sub>2</sub></p> <p>= 1× 2<sup>7</sup> + 1× 2<sup>6</sup> + 1× 2<sup>5</sup> + 0× 2<sup>4</sup> + 1× 2<sup>3</sup> + 1×2<sup>2</sup> + 0× 2<sup>1</sup> + 1× 2<sup>0</sup></p> <p>= 128 + 64 + 32 + 0+ 8 +4 +0 + 1</p> <p>= 237<sub>10</sub></p> <p>Now,</p> <table width="80"><tbody><tr><td>5</td> <td>237</td> <td>2</td> </tr><tr><td>5</td> <td>47</td> <td>2</td> </tr><tr><td>5</td> <td>9</td> <td>4</td> </tr><tr><td>5</td> <td>1</td> <td>1</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 11101101<sub>2</sub> = 237<sub>10</sub> = 1422<sub>5</sub></p>
Q14:
What is the smallest possible number with 5 digits? Convert your answer to base 5 and base 10.
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Smallest possible number = 10000<sub>2</sub></p> <p>Now,</p> <p>10000<sub>2</sub> = (?)<sub>10</sub></p> <p>= 1× 2<sup>4</sup></p> <p>= 16<sub>10</sub></p> <p>Then,</p> <p>base<sub>5</sub> =</p> <table width="73"><tbody><tr><td>5</td> <td>16</td> <td>1</td> </tr><tr><td>5</td> <td>3</td> <td>3</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>= 31<sub>5</sub></p> <p>∴ 10000<sub>2</sub> = 16<sub>10</sub> = 31<sub>5</sub></p> <p>So, base10 = 16<sub>10</sub></p> <p>base 5 = 31<sub>5</sub></p>
Q15:
Convert the quinary number into binary number.
43215
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>4321<sub>5</sub></p> <p>= 4× 5<sup>3</sup> + 3× 5<sup>2</sup> + 2× 5<sup>1</sup> + 1× 5<sup>0</sup></p> <p>= 500 + 75 + 10 + 1</p> <p>= 586<sub>10</sub></p> <p>Then,</p> <table width="87"><tbody><tr><td>2</td> <td>586</td> <td>0</td> </tr><tr><td>2</td> <td>293</td> <td>1</td> </tr><tr><td>2</td> <td>146</td> <td>0</td> </tr><tr><td>2</td> <td>73</td> <td>1</td> </tr><tr><td>2</td> <td>36</td> <td>0</td> </tr><tr><td>2</td> <td>18</td> <td>0</td> </tr><tr><td>2</td> <td>9</td> <td>1</td> </tr><tr><td>2</td> <td>4</td> <td>1</td> </tr><tr><td>2</td> <td>2</td> <td>0</td> </tr><tr><td></td> <td>1</td> <td></td> </tr></tbody></table><p>∴ 586<sub>10</sub> = 1011001010<sub>2</sub></p>
Q16:
Convert the quinary number into decimal number.
33045
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>3304<sub>5</sub></p> <p>= 3× 5<sup>3</sup> + 3× 5<sup>2</sup> + 0× 5<sup>1</sup> + 4× 5<sup>0</sup></p> <p>= 375 + 75 +0 + 4</p> <p>= 454<sub>10</sub></p> <p>Then,</p> <table width="78"><tbody><tr><td>2</td> <td>454</td> <td>0</td> </tr><tr><td>2</td> <td>227</td> <td>1</td> </tr><tr><td>2</td> <td>113</td> <td>1</td> </tr><tr><td>2</td> <td>56</td> <td>0</td> </tr><tr><td>2</td> <td>28</td> <td>0</td> </tr><tr><td>2</td> <td>14</td> <td>0</td> </tr><tr><td>2</td> <td>7</td> <td>1</td> </tr><tr><td>2</td> <td>3</td> <td>1</td> </tr><tr><td></td> <td>1</td> <td></td> </tr></tbody></table><p>∴ 454<sub>10</sub> = 111000110<sub>2</sub></p>
Q17:
Convert the decimal number into quinary number.
1574
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <table width="111"><tbody><tr><td> 5</td> <td> 1574</td> <td> 4</td> </tr><tr><td> 5</td> <td> 312</td> <td> 2</td> </tr><tr><td> 5</td> <td> 62</td> <td> 2</td> </tr><tr><td> 5</td> <td> 12</td> <td> 2</td> </tr><tr><td> 5</td> <td> 2</td> <td> 2</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p>∴ 1574<sub>10</sub> = 22224<sub>5</sub></p>
Q18:
Convert the decimal number into quinary number.
5864
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <table width="107"><tbody><tr><td> 5</td> <td> 5864</td> <td> 4</td> </tr><tr><td> 5</td> <td> 1172</td> <td> 2</td> </tr><tr><td> 5</td> <td> 234</td> <td> 4</td> </tr><tr><td> 5</td> <td> 46</td> <td> 1</td> </tr><tr><td> 5</td> <td> 9</td> <td> 4</td> </tr><tr><td> 5</td> <td> 1</td> <td> 1</td> </tr><tr><td></td> <td> 0</td> <td></td> </tr></tbody></table><p></p> <p>∴ 5864<sub>10</sub> = 141424<sub>5</sub></p>
Q19:
Convert the quinary number into decimal number.
2125
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>212<sub>5</sub></p> <p>= 2× 5<sup>2</sup> + 1× 5<sup>1</sup> + 2× 5<sup>0</sup></p> <p>= 2× 25 + 1× 5 + 2× 1</p> <p>= 50 + 5 + 2</p> <p>= 57<sub>10</sub></p>
Q20:
Convert the quinary number into decimal number.
23045
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>2304<sub>5</sub></p> <p>= 2× 5<sup>3</sup> + 3× 5<sup>2</sup> + 0× 4<sup>1</sup> + 4× 5<sup>0</sup></p> <p>= 2× 125 + 3× 25 + 0×4 + 4×1</p> <p>= 250 + 75 +0 +4</p> <p>= 329<sub>10</sub></p>
Q21:
Convert the quinary number into decimal number.
31045
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>3104<sub>5</sub></p> <p>= 3× 5<sup>3</sup> + 1× 5<sup>2</sup> + 0×5<sup>1</sup> + 4× 5<sup>0</sup></p> <p>= 3× 125 + 1× 25 + 0×5 + 4×1</p> <p>= 375 + 25 + 0+ 4</p> <p>= 404<sub>10</sub></p>
Q22:
Convert the binary number into quinary number.
11102
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>1110<sub>2</sub></p> <p>= 1× 2<sup>3</sup> + 1× 2<sup>2</sup> + 1× 2<sup>1</sup>+ 0×2<sup>0</sup></p> <p>= 8 + 4 + 2 +0</p> <p>= 14<sub>10</sub></p> <p>Now,</p> <table width="76"><tbody><tr><td>5</td> <td>14</td> <td>4</td> </tr><tr><td>5</td> <td>2</td> <td>2</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 1110<sub>2</sub> = 14<sub>10</sub> = 24<sub>5</sub></p>
Q23:
Convert the binary number into quinary number.
10112
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>1011<sub>2</sub></p> <p>= 1 × 2<sup>3</sup> + 0× 2<sup>2</sup> + 1× 2<sup>1</sup> + 1× 5<sup>0</sup></p> <p>= 8 + 0 + 2 + 1</p> <p>= 11<sub>10</sub></p> <p>Then,</p> <table width="95"><tbody><tr><td>5</td> <td>11</td> <td>1</td> </tr><tr><td>5</td> <td>2</td> <td>2</td> </tr><tr><td></td> <td>0</td> <td></td> </tr><tr><td></td> <td></td> <td></td> </tr></tbody></table><p>∴ 1011<sub>2</sub> = 11<sub>10</sub> = 21<sub>5</sub></p>
Q24:
Convert the binary number into quinary number.
11112
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>1111<sub>2</sub></p> <p>= 1× 2<sup>3</sup> + 1× 2<sup>2</sup> + 1× 2<sup>1</sup> + 1×2<sup>0</sup></p> <p>= 8 + 4 + 2 + 1</p> <p>= 15<sub>10</sub></p> <p>Then,</p> <table width="108"><tbody><tr><td>5</td> <td>15</td> <td>0</td> </tr><tr><td>5</td> <td>3</td> <td>3</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 1111<sub>2</sub> = 15<sub>10</sub> = 30<sub>5</sub></p>
Q25:
Convert the quinary number into binary number.
4415
Type: Long
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>441<sub>5</sub></p> <p>= 4× 5<sup>2</sup>+ 4× 5<sup>1</sup> + 1× 5<sup>0</sup></p> <p>= 4× 25 + 4× 5 + 1</p> <p>= 100 + 20 + 1</p> <p>= 121<sub>10</sub></p> <p>Then,</p> <table width="100"><tbody><tr><td>2</td> <td>121</td> <td>1</td> </tr><tr><td>2</td> <td>60</td> <td>0</td> </tr><tr><td>2</td> <td>30</td> <td>0</td> </tr><tr><td>2</td> <td>15</td> <td>1</td> </tr><tr><td>2</td> <td>7</td> <td>1</td> </tr><tr><td>2</td> <td>3</td> <td>1</td> </tr><tr><td>2</td> <td>1</td> <td>1</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 441<sub>5</sub> = 121<sub>10</sub> = 1111001<sub>2</sub></p>
Q26:
Convert the quinary number into binary number.
21345
Type: Short
Difficulty: Easy
Show/Hide Answer
Answer: <p>Solution:</p> <p>2134<sub>5</sub></p> <p>= 2× 5<sup>3</sup> + 1× 5<sup>2</sup> + 3× 5<sup>1</sup> + 4× 5<sup>0</sup></p> <p>= 250 + 25 + 15 + 4</p> <p>= 294</p> <p>Then,</p> <table width="134"><tbody><tr><td>2</td> <td>244</td> <td>0</td> </tr><tr><td>2</td> <td>122</td> <td>0</td> </tr><tr><td>2</td> <td>61</td> <td>1</td> </tr><tr><td>2</td> <td>30</td> <td>0</td> </tr><tr><td>2</td> <td>15</td> <td>1</td> </tr><tr><td>2</td> <td>7</td> <td>1</td> </tr><tr><td>2</td> <td>3</td> <td>1</td> </tr><tr><td>2</td> <td>1</td> <td>1</td> </tr><tr><td></td> <td>0</td> <td></td> </tr></tbody></table><p>∴ 294<sub>10</sub> = 11110100<sub>2</sub></p>