Question

How many 4 digit numbers in all are there in 10 base system

Answer 1

Answer:

9000

Step-by-step explanation:

lets do it in a different way.

Say we have a four digit number abcd

_a_ _b_ _c_ _d_ .

Now in our number system we have numbers from 0 to 9 and we need to replace a b c and d from by these numbers .

Lets first replace a . As no number can start with zero so we can replace a in nine ways i.e by 1 2 3 4 5 6 7 8 9

When it comes to replace b , we can replace it in ten ways i.e 0 1 2 3 4 5 6 7 8 9.

In similar way we can replace c and d in ten ten ways.

So we get

_9_ _10_ _10_ _10_.

Thus the total four digit number in decimal system is = 9 x 10 x 10 x 10 = 9000.

Another simple way to answer this is given below.

Smallest four digit number = 1000

Largest four digit number = 9999

So total four digit number =(9999- 1000) +1 = 9000

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