Question

What is the hundredths digit of the decimal z ? (1) The tenths digit of 100z is 2. (2) The units digit of 1,000z is 2.

Answer 1

The information is not enough to determine the hundredths of z.

Explanation:

We can label the number z as a.bcd, where c represents the hundredths, the goal is to determine if any of those statements will help us find the value of c.

Working with the first statement.

The tenths digit of 100z is 2, so we can start writing 100z

`100z = 100(a.bcd)`

By multiplying by 100 we move the decimal point 2 places to the right so we will have

`100z=abc.d`

Now if the tenths of 100z is 2, that means we will have d = 2.

So far we have

`z= a.bc2`

Working with the second statement.

The units digit of 1000z is 2, we can start writing 1000z

`1000z = 1000a.bc2`

In order to multiply by 1000, we need to move the decimal point 3 places to the right so we have

`1000z =abc2`

So we have verified that the units digit is indeed 2.

However we have the number as

`z= a.bc2`

Thus we can conclude that those statements do not give us enough information about the hundredths.