(21) Arrange the following numbers in ascending order. (a) $$ \frac{1}{9}, \frac{1}{99}, \frac{1}{999} $$ (b) $$ -\frac{1}{9},-\frac{1}{99},-\frac{1}{999} $$

Question

UpStudy AI · Accepted Answer

Let's arrange the given fractions in ascending order for both parts (a) and (b).

### Part (a)
**Numbers:** $$ \frac{1}{9}, \frac{1}{99}, \frac{1}{999} $$

**Observation:**
- All fractions are positive.
- A larger denominator means a smaller fraction when the numerator is the same.

**Arrangement:**
- $$ \frac{1}{999} $$ is the smallest because 999 is the largest denominator.
- $$ \frac{1}{99} $$ is next.
- $$ \frac{1}{9} $$ is the largest because 9 is the smallest denominator.

**Ascending Order:**
$$
\frac{1}{999}, \frac{1}{99}, \frac{1}{9}
$$

### Part (b)
**Numbers:** $$ -\frac{1}{9}, -\frac{1}{99}, -\frac{1}{999} $$

**Observation:**
- All fractions are negative.
- A larger denominator (in absolute terms) means the fraction is closer to zero (i.e., less negative).

**Arrangement:**
- $$ -\frac{1}{9} $$ is the smallest because it's the most negative.
- $$ -\frac{1}{99} $$ is next.
- $$ -\frac{1}{999} $$ is the largest because it's the least negative.

**Ascending Order:**
$$
-\frac{1}{9}, -\frac{1}{99}, -\frac{1}{999}
$$

---

**Final Answer:**

(a) $$ \dfrac{1}{999}, \dfrac{1}{99}, \dfrac{1}{9} $$

(b) $$ -\dfrac{1}{9},\; -\dfrac{1}{99},\; -\dfrac{1}{999} $$
(a) $$ \frac{1}{999}, \frac{1}{99}, \frac{1}{9} $$ (b) $$ -\frac{1}{9}, -\frac{1}{99}, -\frac{1}{999} $$

(21) Arrange the following numbers in ascending order. (a) \( \frac{1}{9}, \frac{1}{99}, \frac{1}{999} \) (b) \( -\frac{1}{9},-\frac{1}{99},-\frac{1}{999} \)

Real Tutor Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions