Question 1192159
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The student should understand the method shown by the other tutor for doing these conversions, because it helps the student learn about place values in different bases.<br>
However, the method shown is inefficient, especially for numbers with many digits, since it requires knowing all the powers of the given base.  There is a much more efficient method for doing these conversions.<br>
Here is the algorithm:
start from the leftmost digit and
(1) multiply by the base and add the next digit;
(2) repeat (1) until all digits have been used<br>
Here are the calculations for your 3rd example, 1023 base 5:<br>
1*5=5; 5+0=5
5*5=25; 25+2=27
27*5=135; 135+3=138<br>
And for your 4th example, 10053 base 7:<br>
1*7=7; 7+0=7
7*7=49; 49+0=49
49*7=343; 343+5=348
348*7=2436;2436+3=2439<br>
And your last, 32102 base 4:<br>
3*4=12; 12+2=14
14*4=56; 56+1=57
57*4=228; 228+0=228
228*4=912; 912+2=914<br>