0.9 divided by 3=
A.
3
B.
0.3
C.
0.9
D.
30
The Correct answer and Explanation is:
To solve the division problem 0.9÷30.9 \div 30.9÷3, follow these steps:
- Understanding Division: Division is the process of determining how many times one number (the divisor) fits into another number (the dividend). In this case, the dividend is 0.90.90.9 and the divisor is 333.
- Conversion of Decimal: First, let’s convert 0.90.90.9 into a fraction for easier division. 0.90.90.9 can be written as 910\frac{9}{10}109.
- Performing Division with Fractions: Dividing by a number is equivalent to multiplying by its reciprocal. The reciprocal of 333 (or 31\frac{3}{1}13) is 13\frac{1}{3}31. So, 0.9÷30.9 \div 30.9÷3 is the same as 910×13\frac{9}{10} \times \frac{1}{3}109×31.
- Multiplying Fractions: To multiply these fractions, multiply the numerators and the denominators:910×13=9×110×3=930\frac{9}{10} \times \frac{1}{3} = \frac{9 \times 1}{10 \times 3} = \frac{9}{30}109×31=10×39×1=309
- Simplifying the Fraction: To simplify 930\frac{9}{30}309, find the greatest common divisor (GCD) of 9 and 30, which is 3. Divide both the numerator and the denominator by 3:9÷330÷3=310\frac{9 \div 3}{30 \div 3} = \frac{3}{10}30÷39÷3=103
- Decimal Conversion: Convert 310\frac{3}{10}103 back to a decimal. 310\frac{3}{10}103 is equivalent to 0.30.30.3.
Thus, 0.9÷3=0.30.9 \div 3 = 0.30.9÷3=0.3.
Explanation: The process of dividing 0.90.90.9 by 333 involves understanding the relationship between division and fractions. By converting the decimal to a fraction, we simplify the division process. Using the reciprocal method for division, we convert the division problem into a multiplication problem, which is often easier to solve. After finding the product, simplifying the fraction helps in converting it back to a decimal, confirming that the result is 0.30.30.3. This method demonstrates how division of decimals can be approached through fraction multiplication, offering a clear, step-by-step solution.