0.16 Repeating 7 as a Fraction
Introduction
In this article, we will explore how to convert the repeating decimal 0.16*7 into a fraction. Repeating decimals can be difficult to work with, but they can be converted into fractions, which are often easier to understand and manipulate.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. In the case of 0.16*7, the sequence "167" repeats indefinitely. Repeating decimals can be found in many mathematical operations, such as dividing two numbers.
Converting 0.16*7 into a Fraction
To convert 0.16*7 into a fraction, we can use the following steps:
Step 1: Let x = 0.16*7
Let's start by letting x equal 0.16*7.
Step 2: Multiply Both Sides by 100
Next, we'll multiply both sides of the equation by 100, which is the number of times the sequence "167" repeats.
100x = 16.67*7
Step 3: Subtract x from Both Sides
Now, we'll subtract x from both sides of the equation to get rid of the repeating decimal.
99x = 16.51
Step 4: Divide Both Sides by 99
Finally, we'll divide both sides of the equation by 99 to solve for x.
x = 16.51/99
Step 5: Simplify the Fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 1.
x = 16.51/99 = 50/303
And that's it! We have successfully converted the repeating decimal 0.16*7 into a fraction: 50/303.
Conclusion
In conclusion, converting a repeating decimal into a fraction can be a bit challenging, but it's definitely possible. By following the steps outlined above, we can convert any repeating decimal into a fraction, making it easier to work with and understand.
