Question

0.33333......×0.66666........

i want clear explanation too pls​

Answer 1

Explanation:

To multiply 0.33333... by 0.66666..., we can use the concept of long division.

step-by-step:

Step 1: Recognize the repeating decimals

0.33333... and 0.66666... are both repeating decimals. The three-digit repeating pattern in 0.33333... is 3, and the six-digit repeating pattern in 0.66666... is 6.

Step 2: Rewrite the repeating decimals as fractions

To convert 0.33333... into a fraction, we'll use the fact that the repeating pattern of 3s continues infinitely. Let's call the repeating decimal x:

x = 0.33333...

10x = 3.33333...

Now, subtract the equation 10x = 3.33333... - x = 0.33333...:

10x - x = 3.33333... - 0.33333...

9x = 3

x = 3/9

x = 1/3

Similarly, for 0.66666..., let's call the repeating decimal y:

y = 0.66666...

10y = 6.66666...

Subtracting the equation 10y = 6.66666... - y = 0.66666...:

10y - y = 6.66666... - 0.66666...

9y = 6

y = 6/9

y = 2/3

Step 3: Multiply the fractions

Now that we have converted the repeating decimals into fractions, we can multiply them together:

(1/3) × (2/3) = (1 × 2) / (3 × 3) = 2/9

Therefore, the product of 0.33333... and 0.66666... is 2/9.

Answer 2

answer

To calculate the product of 0.33333... and 0.66666..., we can follow these steps:

Step 1: Let's represent 0.33333... as x and 0.66666... as y. This means that x = 0.33333... and y = 0.66666....

Step 2: To eliminate the repeating decimal, we can multiply both sides of x = 0.33333... by 10, and both sides of y = 0.66666... by 10 as well. This gives us 10x = 3.33333... and 10y = 6.66666....

Step 3: Now, let's subtract x = 0.33333... from 10x = 3.33333... to eliminate the repeating part. We have 10x - x = 3.33333... - 0.33333..., which simplifies to 9x = 3.

Step 4: Dividing both sides of 9x = 3 by 9, we find that x = 3/9, which simplifies to 1/3. Therefore, x = 1/3.

Step 5: Similarly, subtracting y = 0.66666... from 10y = 6.66666..., we get 10y - y = 6.66666... - 0.66666..., which simplifies to 9y = 6.

Step 6: Dividing both sides of 9y = 6 by 9, we find that y = 6/9, which simplifies to 2/3. Hence, y = 2/3.

Step 7: Finally, we can multiply x = 1/3 and y = 2/3 to find the product. When multiplying fractions, we multiply the numerators together and the denominators together. Thus, (1/3) × (2/3) = (1 × 2) / (3 × 3) = 2/9.

Therefore, the product of 0.33333... and 0.66666... is 2/9.

Explanation: