Question

2
Consider these numbers. Which of these would lie on the number line
i)before 1 ii) between 1 and 2
17 / 8​

Answer 1

The complete question is as follows.

Consider these numbers. Which of these would lie on the number line

i)before 1 ii) between 1 and 2

$\frac{17}{8}, \frac{11}{4}, \frac{1}{3}, \frac{7}{9}, \frac{7}{5}, \frac{6}{11}, \frac{9}{2}, \frac{9}{5}$

Final Answer:

Among the considered numbers $\frac{17}{8}, \frac{11}{4}, \frac{1}{3}, \frac{7}{9}, \frac{7}{5}, \frac{6}{11}, \frac{9}{2}, \frac{9}{5}$ , the numbers that will lie before $1$ are  $\frac{1}{3}, \frac{6}{11}, \frac{7}{9}$.

The  numbers among the considered ones $\frac{17}{8}, \frac{11}{4}, \frac{1}{3}, \frac{7}{9}, \frac{7}{5}, \frac{6}{11}, \frac{9}{2}, \frac{9}{5}$ , that will lie between $1$ and $2$ are $\frac{7}{5}, \frac{9}{5}$.

Given:

These numbers are considered $\frac{17}{8}, \frac{11}{4}, \frac{1}{3}, \frac{7}{9}, \frac{7}{5}, \frac{6}{11}, \frac{9}{2}, \frac{9}{5}$.

To Find:

i) The numbers among the given numbers that will lie before $1$

ii) The numbers selected from the given numbers that will  lie between $1$ and $2$.

Explanation:

The numbers  $\frac{17}{8}, \frac{11}{4}, \frac{1}{3}, \frac{7}{9}, \frac{7}{5}, \frac{6}{11}, \frac{9}{2}, \frac{9}{5}$ are in fractional form. To spot their positions in the number line, convert these fractions into their respective decimal forms.

To change a number from its fractional form to its corresponding decimal form, simply perform a division operation where the numerator of the fraction will be the dividend, and the denominator of the fraction will be the divisor. The resulting quotient is the equivalent decimal form of the considered fraction.

Step 1 of 3

Convert each of these fractions  $\frac{17}{8}, \frac{11}{4}, \frac{1}{3}, \frac{7}{9}, \frac{7}{5}, \frac{6}{11}, \frac{9}{2}, \frac{9}{5}$ into their corresponding decimal form to get the following results.

$\frac{17}{8}=2.10,\\\frac{11}{4}=2.75,\\\frac{1}{3}=0.33,\\\frac{7}{9}=0.77,\\\frac{7}{5}=1.40,\\\frac{6}{11}=0.54,\\\frac{9}{2}=4.50,\\\frac{9}{5}=1.80$

Step 2 of 3

Now, rearrange these calculated decimal numbers in the following ascending order.

$0.33 < 0.54 < 0.77 < 1.40 < 1.80 < 2.10 < 2.75 < 4.50$.

So, it is clear that there are total eight numbers.

Maintaining the above ascending order, replace the decimal numbers with their corresponding fractional forms in the following way.

$\frac{1}{3} < \frac{6}{11} < \frac{7}{9} < \frac{7}{5} < \frac{9}{5} < \frac{17}{8} < \frac{11}{4} < \frac{9}{2}$

Step 3 of 3

Mark the decimal numbers sequentially, which are lying before $1$ in the number line and write their fractional forms.

Since,  $0.33 < 0.54 < 0.77 < 1$, the  numbers which are lying before $1$ are $0.33, 0.54, 0.77$ or  $\frac{1}{3}, \frac{6}{11}, \frac{7}{9}$.

Next, observe the decimal numbers sequentially, which are lying between $1$ and $2$ in the number line and write them in the fractional forms.

As $1 < 1.40 < 1.80 < 2$, the numbers which are lying between $1$ and $2$ are $1.40, 1.80$ or $\frac{7}{5}, \frac{9}{5}$.

Therefore, among the considered numbers $\frac{17}{8}, \frac{11}{4}, \frac{1}{3}, \frac{7}{9}, \frac{7}{5}, \frac{6}{11}, \frac{9}{2}, \frac{9}{5}$ ,

i) The numbers that will lie before $1$ are  $\frac{1}{3}, \frac{6}{11}, \frac{7}{9}$.

ii) The  numbers will lie between $1$ and $2$ are $\frac{7}{5}, \frac{9}{5}$.

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https://brainly.in/question/20755883

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