This problem solving activity has a number focus.
Think of the number 71999.
Now think of it after it has been multiplied out.
What digit is in the ones place?
In this problem students work with powers of numbers and come to understand what is happening to the numbers.
Students also see how an apparently enormous and difficult calculation can be broken down into manageable parts. The students should come to realise that there are only a limited number of unit digits obtained when 7 is raised to a power. Further, these specific digits 'cycle round' as the power of 7 increases. This cycle is 7, 9, 3, 1, 7, 9, …
The same is true of the digit in the tens place.
Think of the number 71999. Now think of it after it has been multiplied out. What digit is in the ones place?
How about its tens digit?
Can you find out the general pattern here. No matter what number you raise 7 to, can you tell with as little calculation as possible, what its unit digit is?
Repeat this problem with numbers other than 7.
The answer is found when you look for patterns in the powers of 7.
71 = 7
72 = 49
73 = 343
74 = 2401
75 = 16807
76 = 117649
77 = 823543
78 = 5764801
79 = 44353607
710 = 282475249
The cycle for the units digit is 7, 9, 3, 1, 7, 9...
71999 Units digit = 3
The cycle for the tens digit is 4, 4, 0, 0, 4, 4, 0...
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/powers-seven at 8:58pm on the 26th February 2024