Question

Which number would make the sentence true?


2/11< ________ < 1.42

Question 2 options:


1 2/3


0.153



22%



1.3 × 10 ^1

Answer 1

Answer:

22% = 0.22

Step-by-step explanation:

Lat'e express all the given numbers in decimal form so we understand how they are located on the number line.

We start with 2/11 , since the number we are looking for has to be larger than this \, and smaller than 1.42:

$\frac{2}{11} = 0.181818181818...$

So we understand that we are looking for a number that can be placed between the lower boundary (0.181818...) and the upper boundary (1.42) on the number line. That is: we are looking for a number greater than 0.18181818... and less than 1.42.

Now let's look at each of the given options (also writing them in decimal form to facilitate the comparison with the lower and upper boundaries we just found):

$1\frac{2}{3} = 1.66666666...$ This number is grater than the upper boundary given to us (1.42), it would be placed to the right of 1.42 on the number line. Therefore we discard it for not being in the requested interval (section) of the number line.

0.153 is already in decimal form, and clearly less than (thus to be placed on the left of) the lower boundary (0.181818...) of the requested interval. Therefore we discard it for not being in the requested interval (section) of the number line.

22% in decimal form is written as: $\frac{22}{100} = 0.22$. This number is greater than the lower boundary (0.181818...) and also less than the upper boundary (1.42). Therefore it is a choice that would make the sentence true.

$1.3*10^1=1.3*10=13$ which is clearly greater than the upper boundary of the interval, so we discard it.

Answer 2

Answer: C    22%

explanation: 22% is equivalent to 0.22 which is greater than 2/11 and less than 1.42