Convert 1000000 from decimal to Base 7
(base 7) notation:
Raise our base of 7 to a power
Start at 0 and increasing by 1 until it is >= 1000000
70 = 1
71 = 7
72 = 49
73 = 343
74 = 2401
75 = 16807
76 = 117649
77 = 823543
78 = 5764801 <--- Stop: This is greater than 1000000
Since 5764801 is greater than 1000000, we use 1 power less as our starting point which equals 7
Work backwards from a power of 7
We start with a total sum of 0:
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 1
Multiplying this coefficient by our original value, we get: 1 * 823543 = 823543
Add our new value to our running total, we get:
0 + 823543 = 823543
This is <= 1000000, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 823543
Our Base 7 notation is now equal to 1
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 1
Multiplying this coefficient by our original value, we get: 1 * 117649 = 117649
Add our new value to our running total, we get:
823543 + 117649 = 941192
This is <= 1000000, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 941192
Our Base 7 notation is now equal to 11
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 3
Multiplying this coefficient by our original value, we get: 3 * 16807 = 50421
Add our new value to our running total, we get:
941192 + 50421 = 991613
This is <= 1000000, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 991613
Our Base 7 notation is now equal to 113
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 3
Multiplying this coefficient by our original value, we get: 3 * 2401 = 7203
Add our new value to our running total, we get:
991613 + 7203 = 998816
This is <= 1000000, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 998816
Our Base 7 notation is now equal to 1133
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 3
Multiplying this coefficient by our original value, we get: 3 * 343 = 1029
Add our new value to our running total, we get:
998816 + 1029 = 999845
This is <= 1000000, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 999845
Our Base 7 notation is now equal to 11333
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 3
Multiplying this coefficient by our original value, we get: 3 * 49 = 147
Add our new value to our running total, we get:
999845 + 147 = 999992
This is <= 1000000, so we assign our outside coefficient of 3 for this digit.
Our new sum becomes 999992
Our Base 7 notation is now equal to 113333
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 1
Multiplying this coefficient by our original value, we get: 1 * 7 = 7
Add our new value to our running total, we get:
999992 + 7 = 999999
This is <= 1000000, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 999999
Our Base 7 notation is now equal to 1133331
The highest coefficient less than 6 we can multiply this by to stay under 1000000 is 1
Multiplying this coefficient by our original value, we get: 1 * 1 = 1
Add our new value to our running total, we get:
999999 + 1 = 1000000
This = 1000000, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 1000000
Our Base 7 notation is now equal to 11333311