Find out the units digit in the value of 2^224 ÷ 4^32? [Hint: 4 = 2²] Class 8

Find out the units digit in the value of 2²²⁴ ÷ 4³²? [Hint: 4 = 2²] Class 8

Question 1.

Find out the units digit in the value of 2²²⁴ ÷ 4³²? [Hint: 4 = 2²] Class 8

Solution:

2²²⁴ ÷ 4³² = 2²²⁴ ÷ (2²)³²

= 2²²⁴ ÷ 2⁶⁴ = 2^224-64 = 2¹⁶⁰.

Now, 2¹, 2⁵, 2⁹, ..., 2^4n-3 ends in the digit 2,

2², 2⁶, 2¹⁰, ..., 2^4n-2 ends in the digit 4,

2³, 2⁷, 2¹¹,..., 24^4n-1 ends in the digit 8,

and 2⁴, 2⁸, 2¹², ..., 2⁴ⁿ ends in the digit 6.

Further, 2¹⁶⁰ is of the form 2⁴⁽⁴⁰⁾ (i.e., of the form 2⁴ⁿ),

Hence, 2¹⁶⁰ will end in the digit 6.

So, unit digit will be 6.

Question 2.

There are 5 bottles in a container. Every day, a new container is brought in. How many bottles would be there after 40 days? Class 8

Solution:

Number of bottles = 5 + 5 + 5 + ... 40 times = 5 × 40 = 200.