Solve Decimal Division: 0.49 ÷ 0.7 Step-by-Step Solution

To solve the division of two decimal numbers $0.49$ and $0.7$, we will follow these steps:

• Step 1: Convert the decimals to fractions. Since $0.49$ has two decimal places, it can be written as $\frac{49}{100}$. Similarly, $0.7$, which has one decimal place, can be written as $\frac{7}{10}$.
• Step 2: Set up the division of fractions: $\frac{49}{100} \div \frac{7}{10}$.
• Step 3: Recall that division by a fraction is the same as multiplication by its reciprocal. Thus, we rewrite the division as multiplication by the reciprocal of $\frac{7}{10}$:

$\frac{49}{100} \times \frac{10}{7}$.

• Step 4: Multiply the numerators and the denominators:

$\frac{49 \times 10}{100 \times 7} = \frac{490}{700}$.

• Step 5: Simplify the fraction by finding the greatest common divisor (GCD) of $490$ and $700$. The GCD is $70$.

After dividing both the numerator and the denominator by $70$, we have:

$\frac{490 \div 70}{700 \div 70} = \frac{7}{10}$.

Thus, the result of $0.49 \div 0.7$ is $\frac{7}{10}$, which is $0.7$.

Therefore, the solution to the problem is $0.7$.