Flashcards · 6 cards

Number bases

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Rule
How do you change $3021_{\text{five}}$ to base ten?
Answer
Multiply each digit by its place value and add: $3 \times 5^3 + 0 \times 5^2 + 2 \times 5 + 1 = 386$ .
Place values in base fiveEach place is 5 times the one to its right
From the lesson: Number bases
Rule
How do you change a base-ten number to base five?
Answer
Divide by 5 again and again, writing down the remainders. Read them upwards: the first remainder is the units digit.
Divide, then read upwardsThe first remainder is the units digit
From the lesson: Number bases
Know it
How do you change a number from base three to base five?
Answer
Go through base ten: base three → base ten → base five.
From the lesson: Number bases
Know it
Which digits can a number in base $n$ use?
Answer
$0$ up to $n - 1$ . Base five uses 0 to 4, so any digit of 5 or more tells you the base is bigger.
From the lesson: Number bases
Rule
Adding in base five: when do you carry?
Answer
Each time a column reaches 5. For $4 + 3 = 7 = 1 \times 5 + 2$ : write 2 and carry 1.
Carrying in base fiveCarry 1 each time a column reaches 5
From the lesson: Number bases
Which method?
WAEC 2014 · Paper 2 · Q2 (b)
If $124_n = 232_{\text{five}}$ , find $n$ .
How do you find $n$ ?
Answer
Change both sides to base ten: $124_n = n^2 + 2n + 4$ . That gives a quadratic in $n$ . Keep only a whole number bigger than every digit.
From the lesson: Number bases Try the question