Question

without actual calculation state which of the following rational numbers are terminating decimals and non terminating decimals: 1. 13 / 8 , 2. -19 / 9 ,3. 16/25 ,4. 132 /64​

Answer 1

Answer:

answer is 9

Step-by-step explanation:

The characteristics of particles of matter are:

All matter is composed of very small particles which can exist independently.

Particles of matter have spaces between them.

Particles of matter are continuously moving.

Particles of matter attract each other.

Answer 2

The first few terms are –6, 12, –24:

a1 = 3(–2)1 = (3)(–2) = –6

a2 = 3(–2)2 = (3)(4) = 12

a3 = 3(–2)3 = (3)(–8) = –24

So this is a geometric series with common ratio r = –2. (I can also tell that this must be a geometric series because of the form given for each term: as the index increases, each term will be multiplied by an additional factor of –2.)

The first term of the sequence is a = –6. Plugging into the summation formula, I get:

So the value of the summation is:

2,097,150

Evaluate S10 for 250, 100, 40, 16,....

The notation "S10" means that I need to find the sum of the first ten terms. The first term is a = 250. Dividing pairs of terms, I get:

...and so forth, so the terms being added form a geometric sequence with common ratio .

Unlike the formula for the n-th partial sum of an arithmetic series, I don't need the value of the last term when finding the n-th partial sum of a geometric series. So I have everything I need to proceed. When I plug in the values of the first term and the common ratio, the summation formula gives me:

I will not "simplify" this to get the decimal form, because that would almost-certainly be counted as a "wrong" answer. Instead, my answer is: