Write the following infinite decimal expansion as a fraction. You do not need to simplify. [Click for Help Video](10 points)
0.366¯¯¯¯¯¯¯¯=
Let's represent the given infinite decimal expansion as "x."
To convert this decimal to a fraction, we can follow these steps:
Step 1: Multiply both sides of the equation by a power of 10 to eliminate the repeating decimal.
10x = 3.66¯¯¯¯¯¯¯¯
Step 2: Subtract the original equation from the new equation to eliminate the repeating decimal.
10x - x = 3.66¯¯¯¯¯¯¯¯ - 0.366¯¯¯¯¯¯¯¯
9x = 3.294
Step 3: Divide both sides of the equation by 9 to solve for x.
9x/9 = 3.294/9
x = 3.294/9
Therefore, the given infinite decimal expansion 0.366¯¯¯¯¯¯¯¯ can be written as a fraction, 3.294/9.
0.366
To convert the decimal 0.366 to a fraction, we can use the following steps:
Step 1: Let x = 0.366.
Step 2: Since there is only one digit after the decimal point, we can multiply both sides of the equation by a power of 10 to move the decimal point to the right. In this case, we'll multiply by 1000 (10^3) to eliminate the decimal.
1000x = 366.
Step 3: Divide both sides of the equation by 1000 to solve for x.
x = 366/1000.
Step 4: Simplify the fraction if possible.
The fraction 366/1000 can be simplified by dividing both the numerator and denominator by their greatest common divisor (in this case, it is 2), which gives us:
x = 183/500.
Therefore, the decimal 0.366 can be written as the fraction 183/500.
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0.336
To convert the decimal 0.336 to a fraction, we can follow these steps:
Step 1: Let x = 0.336.
Step 2: Since there are three digits after the decimal point, we can multiply both sides of the equation by a power of 10 to move the decimal point to the right. In this case, we'll multiply by 1000 (10^3) to eliminate the decimal.
1000x = 336.
Step 3: Divide both sides of the equation by 1000 to solve for x.
x = 336/1000.
Step 4: Simplify the fraction if possible.
The fraction 336/1000 can be simplified by dividing both the numerator and denominator by their greatest common divisor (in this case, it is 8), which gives us:
x = 42/125.
Therefore, the decimal 0.336 can be written as the fraction 42/125.