Question
(0.333...) x (0.444...) = ?
Answer: Option D
In order to solve this question, we first need to understand the concept of repeating decimals. Repeating decimals are decimals that have a pattern in their digits that repeats itself infinitely. The pattern repeats itself after a certain number of digits. The repeating sequence of digits is sometimes referred to as the repeating block.
For example, in the decimal 0.444..., the repeating sequence is 444 and the repeating block is 4.
Now, to solve this question, we need to multiply the two repeating decimals. The key to multiplying repeating decimals is to multiply the repeating blocks first, then multiply the non-repeating digits.
0.333... x 0.444...
= (3 x 4) x (0.00... x 0.00...)
= 12 x 0.00...
= 0.148148148....
Therefore, the correct answer is Option D – 0.148148148….
Explanation with relevant definitions and formulas:
• Repeating Decimal: A decimal with a pattern of digits that repeats itself infinitely is known as a repeating decimal.
• Multiplying Repeating Decimals: The key to multiplying repeating decimals is to multiply the repeating blocks first, then multiply the non-repeating digits.
Formula:
0.333... x 0.444...
= (3 x 4) x (0.00... x 0.00...)
= 12 x 0.00...
= 0.148148148....
Was this answer helpful ?
In order to solve this question, we first need to understand the concept of repeating decimals. Repeating decimals are decimals that have a pattern in their digits that repeats itself infinitely. The pattern repeats itself after a certain number of digits. The repeating sequence of digits is sometimes referred to as the repeating block.
For example, in the decimal 0.444..., the repeating sequence is 444 and the repeating block is 4.
Now, to solve this question, we need to multiply the two repeating decimals. The key to multiplying repeating decimals is to multiply the repeating blocks first, then multiply the non-repeating digits.
0.333... x 0.444...
= (3 x 4) x (0.00... x 0.00...)
= 12 x 0.00...
= 0.148148148....
Therefore, the correct answer is Option D – 0.148148148….
Explanation with relevant definitions and formulas:
• Repeating Decimal: A decimal with a pattern of digits that repeats itself infinitely is known as a repeating decimal.
• Multiplying Repeating Decimals: The key to multiplying repeating decimals is to multiply the repeating blocks first, then multiply the non-repeating digits.
Formula:
0.333... x 0.444...
= (3 x 4) x (0.00... x 0.00...)
= 12 x 0.00...
= 0.148148148....
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0.444......=4/9
Now,
multiple os 3/9 and 4/9, we get
(3/9)*(4/9) = 12/81
12/81 = 0.148148148
0.444=4/9
(1/3)*(4/9)=4/27
4/27=0.148148148