The problem asks us to express the number $0.016$ in three different forms: as a common fraction in its lowest terms, correct to 1 significant figure, and in standard form.

1. Problem Description

The problem asks us to express the number $0.016$ in three different forms: as a common fraction in its lowest terms, correct to 1 significant figure, and in standard form.

2. Solution Steps

(a) To express $0.016$ as a common fraction in its lowest terms, we first write it as a fraction:

$0.016 = \frac{16}{1000}$.

Now we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 16 and 1000 is

8. $\frac{16}{1000} = \frac{16 \div 8}{1000 \div 8} = \frac{2}{125}$.

(b) To express $0.016$ correct to 1 significant figure, we look at the first non-zero digit, which is

1. The digit to its right is 6, which is greater than or equal to

5. Therefore, we round up the 1 to

2. So, $0.016$ rounded to 1 significant figure is $0.02$.

(c) To express $0.016$ in standard form (scientific notation), we write it as $a \times 10^n$, where $1 \le a < 10$ and $n$ is an integer. We can rewrite $0.016$ as $1.6 \times 10^{-2}$.

3. Final Answer

(a) $\frac{2}{125}$

(b) $0.02$

(c) $1.6 \times 10^{-2}$