The following number is base-10 number.
Convert this number to base-60 and then write it
in modern sexagesimal form.
Place the appropriate numbers in the boxes below.
We are given 120,760 base-10 and asked to
write this in base-60.
Just like in base-10, the place value are powers of 10,
in base-60, the place value are powers of 60.
Starting on the far right and working left,
we add the 60 to zero power or one's place value,
60 to the first or 60's place value,
60 to the second or 3,600's place value,
60 to the third or 216,000's place value and so on.
When converting a number in base-10 to a new base,
the first step is to determine the highest power
of the new base that will divide
into the number at least once.
Notice in this case, the highest power of 60
that will divide the given number at least once
is 60 squared or 3,600.
We know this because 60 to the third or 216,000
is greater than the given number in base-10.
So now we know in base-60, the number will have
one, two, three place values.
It'll have a whole number in the 60 squared place value,
which is a 3,600's place value.
It will have a whole number in the 60 to the first
or 60's place value, as well as the 60 raised to the
zero power place value, which is the one's place value.
We begin by determine the whole number in the 60's
squared or 3,600 place value by dividing 120,760 by 3,600.
We begin by determining how many 3,600's are in 12,076,
which is three.
Three times 3,600 is 10,800.
Now we subtract.
Bring down the last digit of zero and now determine
how many 3,600's are in 12,760,
which I believe is also three.
We already know three times 3,600 is 10,800
with this difference is less than 3,600,
this three is correct.
So now we subtract.
1,960 is less than 3,600 and therefore, the quotient of 33
is correct and this is a remainder.
33 is the whole number in the 60's squared
or 3,600's place value.
To find the whole number in the 60's place value,
we now divide the remainder by 60.
So now we divide 1,960 by 60.
There are three 60's in 196.
Three times 60 is 180, subtract, the difference is 16.
Bring down the last digit of zero
and there are two 60's in 160.
Two times 60 is 120, subtract.
The difference is 40.
40 is the remainder.
32 is the whole number in the 60's place value
and then finally we have the 60 to the zero
one's place value and we know there are 40 one's in 40
and therefore, the whole number in the one's
place value is 40.
The number in base-60 is 33, 32, 40.
Let's quickly check this on the calculator.
Let's verify that 33 times 3,600
plus 32 times 60,
plus 40 times one is 40,
does equal the base-10 number of 120,760,
which is does, verifying our answer is correct.
I hope you found this helpful.