Solve the Proportion: Finding the Missing Term in 1.66:?=0.166

To solve this problem, we'll use the equation $1.66 \div x = 0.166$. This can be rewritten in terms of multiplication as:

• $x = \frac{1.66}{0.166}$

Now, let's perform the division:

First, recognize that dividing by a decimal is equivalent to dividing their fractions:

• $1.66 = \frac{166}{100}$
• $0.166 = \frac{166}{1000}$

Therefore, we have:

$x = \frac{1.66}{0.166} = \frac{\frac{166}{100}}{\frac{166}{1000}}$

Dividing these fractions is equivalent to multiplying by the reciprocal:

$x = \frac{166}{100} \times \frac{1000}{166}$

Cancel out $166$ in the numerator and denominator:

$x = \frac{1000}{100} = 10$

Therefore, the missing number $x$ is $\boxed{10}$.