0.147 Repeating as a Fraction
The decimal number 0.147 repeating is a repeating decimal, where the sequence "147" repeats indefinitely. To convert this number to a fraction, we can use a few different methods.
Method 1: Converting Repeating Decimals to Fractions
One way to convert a repeating decimal to a fraction is to use the following formula:
x = decimal number y = number of decimal places
Then, we can set up the following equation:
10^y * x = integer part + fractional part
In this case, we have:
x = 0.147 y = 3 (since the sequence "147" has 3 decimal places)
So, we set up the equation:
10^3 * x = integer part + fractional part 1000x = 147 + x
Subtracting x from both sides gives us:
999x = 147
Dividing both sides by 999 gives us:
x = 147/999
x = 49/333
So, 0.147 repeating as a fraction is equal to 49/333.
Method 2: Converting Repeating Decimals to Fractions using Algebra
Another way to convert a repeating decimal to a fraction is to use algebra. Let's say we have a repeating decimal 0.abcd, where abcd is the repeating sequence.
We can set up the following equation:
let x = 0.abcd
Then, we can multiply both sides of the equation by 10^4 (since the sequence has 4 digits):
10^4x = abcd.abcd
Subtracting x from both sides gives us:
10^4x - x = abcd.abcd - 0.abcd
9999x = 9999abcd / 10^4
x = abcd / 10^4 - abcd / 10^4
x = abcd / (10^4 - 1)
In this case, we have abcd = 147, so:
x = 147 / (10^3 - 1) x = 147 / 999 x = 49 / 333
So, again, we get 49/333 as the fraction equivalent to 0.147 repeating.
Conclusion
In conclusion, we have shown two methods for converting the repeating decimal 0.147 to a fraction. Both methods yield the same result: 49/333. This fraction can be used in mathematical calculations and other applications where a precise representation of the decimal number is required.
