Question

the number line shows -1, x, and -\frac{5}{8}. which of the following could be the value of x?
-\frac{3}{5}
9.21×10^{-1}
-0.05
-\frac{7}{9}

Explanation:

Step1: Convert fractions and scientific - notation to decimals

• $\frac{3}{5}=0.6$, so $-\frac{3}{5}=- 0.6$;
• $9.21\times10^{-1}=0.921$;
• $\frac{5}{8}=0.625$, so $-\frac{5}{8}=-0.625$;
• $\frac{7}{9}\approx0.778$, so $-\frac{7}{9}\approx - 0.778$.

Step2: Analyze the position on the number - line

The number $x$ is between $-1$ and $-\frac{5}{8}(-0.625)$.

• For $-\frac{3}{5}=-0.6$, $-0.625<-0.6$, so $-\frac{3}{5}$ is not in the range.
• For $9.21\times10^{-1}=0.921$, it is positive, so it is not in the range.
• For $-0.05$, $-0.05>-0.625$, so it is not in the range.
• For $-\frac{7}{9}\approx - 0.778$, and $-1<-0.778<-0.625$.

Answer:

$-\frac{7}{9}$