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

Converting to fractions eliminates decimal placement errors and makes the division clearer. You can see exactly what you're working with: $\frac{49}{100} \div \frac{7}{10}$ is much clearer than trying to line up 0.49 ÷ 0.7.

Count the decimal places! 0.49 has 2 places so it becomes $\frac{49}{100}$, and 0.7 has 1 place so it becomes $\frac{7}{10}$. The denominator is always 10, 100, 1000, etc.

The reciprocal flips the fraction: $\frac{7}{10}$ becomes $\frac{10}{7}$. Dividing by a fraction is the same as multiplying by its reciprocal - it's a fundamental rule that makes division much easier!

Find the Greatest Common Divisor (GCD) of the numerator and denominator. For $\frac{490}{700}$, the GCD is 70. Divide both parts: $\frac{490 \div 70}{700 \div 70} = \frac{7}{10} = 0.7$

Yes! Use multiplication to verify: 0.7 × 0.7 should equal 0.49. Since 0.7 × 0.7 = 0.49 ✓, our answer is correct. Division and multiplication are opposite operations.

Double-check your factoring! List the factors of both numbers to find the largest one they share. For 490 and 700, both are divisible by 10, 14, 35, and 70 is the largest.