(0 x 10^0) + (0/10^1) + (0/10^2) + (7/10^3)
7 × 101 + 2 × 100 + 0 × 10-1 + 0 × 10-2 + 1 × 10-3 + 6 × 10-4
1,024 = (1 x 10^3) + (0 x 10^2) + (2 x 10^1) + (4 x 10^0)
(1*100) + (0*10-1) + (0*10-2) + (7*10-3) + (6*10-4)
81.402 = (8 x 10^1) + (1 x 10^0) + (4/10^1) + (0/10^2) + (2/10^3)
100,203 in expanded form is (1 x 100000) + (0 x 10000) + (0 x 1000) + (2 x 100) + (0 x 10) + (3 x 1)(1x1,000)+(2x3) or (1 x 10^5) + (0 x 10^4) + (0 x 10^3) + (2 x 10^2) + (0 x 10^1) + (3 x 10^0)100000 + 200 + 3
A huge number. 0 + 1 + 2 = 3 0 + 2 + 1 = 3 1 + 0 + 2 = 3 1 + 2 + 0 = 3 2 + 0 + 1 = 3 2 + 1 + 0 = 3 -0 + 1 + 2 = 3 -0 + 2 + 1 = 3 1 - 0 + 2 = 31 + 2 - 0 = 32 - 0 + 1 = 32 + 1 - 0 = 3 0 - 1 + 3 = 2 0 + 3 - 1 = 2 -1 + 0 + 3 = 2 -1 + 3 + 0 = 2 3 + 0 - 1 = 2 3 - 1 + 0 = 2 -0 - 1 + 3 = 2-0 + 3 - 1 = 2-1 - 0 + 3 = 2-1 + 3 - 0 = 23 - 0 - 1 = 23 - 1 - 0 = 2 0 - 2 + 3 = 1 0 + 3 - 2 = 1 -2 + 0 + 3 = 1 -2 + 3 + 0 = 1 3 + 0 - 2 = 1 3 - 2 + 0 = 1 -0 - 2 + 3 = 1-0 + 3 - 2 = 1-2 - 0 + 3 = 1-2 + 3 - 0 = 13 - 0 - 2 = 13 - 2 - 0 = 1 1 + 2 - 3 = 0 1 - 3 + 2 = 0 2 + 1 - 3 = 0 2 - 3 + 1 = 0 -3 + 1 + 2 = 0 -3 + 2 + 1 = 0 For each of these equations there is a counterpart in which all signs have been switched. For example 0 + 1 + 2 = 3 gives -0 - 1 - 2 = -3and so on. Now, all of the above equations has three numbers on the left and one on the right. Each can be converted to others with two numbers on each side. For example:the equation 0 + 1 + 2 = 3 gives rise to0 + 1 = 3 - 20 + 1 = -2 + 30 + 2 = 3 - 10 + 2 = -1 + 31 + 2 = 3 - 01 + 2 = -0 + 3-0 + 1 = 3 - 2-0 + 1 = -2 + 3-0 + 2 = 3 - 1-0 + 2 = -1 + 31 + 2 = 3 + 01 + 2 = +0 + 3 As you can see, the number of equations is huge!
1 (0+1) 3 (0+1+2) 6 (0+1+2+3) 10 (0+1+2+3+4) 15 (0+1+2+3+4+5) 21 (0+1+2+3+4+5+6) Notice these are the numbers you can arrange into equalateral triangles.
21000 = (2 x 10000) + (1 x 1000) + (0 x 100) + (0 x 10) + (0 x 1) OR (2 x 10^4) + (1 x 10^3) + (0 x 10^2) + (0 x 10^1) + (0 x 10^0)
7 × 101 + 2 × 100 + 0 × 10-1 + 0 × 10-2 + 1 × 10-3 + 6 × 10-4
0=0 in binary 1=1 2=10 3=11 . . . Got it?
243,090 = (2 x 100000) + (4 x 10000) + (3 x 1000) + (0 x 100) + (9 x 10) + (0 x 1) OR (2 x 10^5) + (4 x 10^4) + (3 x 10^3) + (0 x 10^2) + (9 x 10^1) + (0 x 10^0)
There are 12 ways to make change for a 50 dollar bill using 5, 10's and 20's. $20's $10's $5's 2 1 0 2 0 2 1 3 0 1 2 2 1 1 4 1 0 6 0 5 0 0 4 2 0 3 4 0 2 6 0 1 8 0 0 10
There are 50 ways to make $1 using Australian coins: Tries Coins 100 50 20 10 5 1 1 2 2 3 1 2 1 4 1 2 0 2 5 1 1 3 6 1 1 2 2 7 1 1 1 4 8 1 1 0 6 9 1 0 5 10 1 0 4 2 11 1 0 3 4 12 1 0 2 6 13 1 0 1 8 14 1 0 0 10 15 5 16 4 2 17 4 1 2 18 4 0 4 19 3 4 20 3 3 2 21 3 2 4 22 3 1 6 23 3 0 8 24 2 6 25 2 5 2 26 2 4 4 27 2 3 6 28 2 2 8 29 2 1 10 30 2 0 12 31 1 8 32 1 7 2 33 1 6 4 34 1 5 6 35 1 4 8 36 1 3 10 37 1 2 12 38 1 1 14 39 1 0 16 40 10 0 41 9 2 42 8 4 43 7 6 44 6 8 45 5 10 46 4 12 47 3 14 48 2 16 49 1 18 50 20
(1*100) + (0*10-1) + (0*10-2) + (7*10-3) + (6*10-4)
4309 * 10^-3 4*10^0 + 3*10^-1 + 0*10^-2 + 9*10^-3
(6 x 10^7) + (7 x 10^6) + (1 x 10^5) + (0 x 10^4) + (2 x 10^3) + (2 x 10^2) + (0 x 10^1) + (0 x 10^0)