Question

what is the greatest integer k for which 32.45*10^k is less than 1

Answer 1

I think it will be yes.

Answer 2

Answer:

k = 2

$0.3245\times 10^{2}<1$

Step-by-step explanation:

 Given : expression $32.45\cdot 10^{k}$

We have to find the greatest integer k for which $32.45\cdot 10^{k}$ is less than 1

Since, we have write   $32.45\cdot 10^{k}$  less than 1

we can write  $32.45\cdot 10^{k}$ in scientific notation

Scientific notation is a way of writing large numbers less than 1 using notation by dividing by power of 10 to shift the decimals toward left.

$a\cdot 10^{n}$ , where 0< a < 10 and n is integer.

Thus, to make $32.45\cdot 10^{k}$  less than 1

Divide and multiply 32.45 by 100 , we get

$\frac{32.45\times 100}{100}=0.3245\times 10^{2}$

Thus, on comparing k = 2

$0.3245\times 10^{2}<1$