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Find the base five numeral expanded to give (3 x 5 x 5) + (4 x 1) and workout 212three - 121three.
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8 stepsHere are the solutions to the problems:
: Find the base five numeral expanded to give
Rewrite the expanded form using powers of 5.
The given expression is .
This can be written as:Identify the coefficients for each power of 5.
In base five, a number is represented as .
Comparing this to our expression:
The coefficient for is 3.
There is no term, so its coefficient is 0.
The coefficient for (which is 1) is 4.Construct the base five numeral.
The digits are 3 (for ), 0 (for ), and 4 (for ).
Therefore, the base five numeral is .The base five numeral is .
: Workout:
Set up the subtraction in base three.
We subtract column by column from right to left.
Subtract the rightmost digits (units place).
.
Subtract the middle digits (3s place).
We need to calculate . Since , we must borrow from the next place value (the place).
Borrow 1 from the in the place. This borrowed 1 is equivalent to in the place.
So, the in the place becomes .
Now, subtract: .
The in the place becomes after borrowing.Subtract the leftmost digits ( place).
We now have .
Combine the results.
The result is , which is written as .
The result of the workout is .
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