2. Leann says $$ 18 \div 6=3 $$, so $$ 1.8 \div 0.6=0.3 $$ and $$ 0.18 \div 0.06=0.03 $$. Is Leann correct? Explain how to solve these division problems.

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We start by writing the division problems in fraction form:

$$
\text{For } 1.8 \div 0.6, \quad \frac{1.8}{0.6}
$$

$$
\text{For } 0.18 \div 0.06, \quad \frac{0.18}{0.06}
$$

To eliminate the decimals, multiply the numerator and the denominator by the same power of 10 so that the denominator becomes a whole number.

1. For $$\frac{1.8}{0.6}$$, multiply by 10 (since there is 1 decimal place):

$$
\frac{1.8 \times 10}{0.6 \times 10} = \frac{18}{6}
$$

Now, $$\frac{18}{6} = 3$$.

2. For $$\frac{0.18}{0.06}$$, multiply by 100 (since there are 2 decimal places):

$$
\frac{0.18 \times 100}{0.06 \times 100} = \frac{18}{6}
$$

Again, $$\frac{18}{6} = 3$$.

Leann’s method correctly shows that $$18 \div 6 = 3$$, but she made an error when she assumed that dividing the decimal numbers would simply halve the result from $$18 \div 6$$. In fact, after adjusting for the decimals properly as shown, we see that:

$$
1.8 \div 0.6 = 3 \quad \text{and} \quad 0.18 \div 0.06 = 3.
$$

Thus, Leann is not correct. The key idea is to shift the decimal point by multiplying the numerator and the denominator by the same power of 10 so that the problem is converted into a division with whole numbers.
Leann is not correct. When dividing decimals, you should multiply both the numerator and the denominator by the same power of 10 to eliminate the decimals. For $$1.8 \div 0.6$$: $$ \frac{1.8 \times 10}{0.6 \times 10} = \frac{18}{6} = 3 $$ For $$0.18 \div 0.06$$: $$ \frac{0.18 \times 100}{0.06 \times 100} = \frac{18}{6} = 3 $$ So, both divisions equal 3, not 0.3 or 0.03 as Leann thought.

2. Leann says \( 18 \div 6=3 \), so \( 1.8 \div 0.6=0.3 \) and \( 0.18 \div 0.06=0.03 \). Is Leann correct? Explain how to solve these division problems.

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