What is the recurring decimal 0.8 as a fraction?

0.8 as a recurring decimal can be expressed as a fraction by considering the pattern of the recurring digits. In this case, the decimal 0.8 features a single digit that repeats infinitely, which is the number 8. To convert this recurring decimal to a fraction, we can assign variables to break down the decimal into two parts: the non-recurring part and the recurring part.

Let's assume that x represents the recurring part, which in this case is 8. To find the fraction equivalent of 0.8 as a recurring decimal, we need to multiply the decimal by 10, which will shift the recurring part to the left of the decimal point: 10x = 8.8888...

Now, we can subtract the original decimal from the shifted decimal to get rid of the repeating part: 10x - x = 8.8888... - 0.8888...

Simplifying the equation gives us: 9x = 8

To find the value of x, the recurring part, we divide both sides of the equation by 9: x = 8/9

Therefore, the fraction equivalent of the recurring decimal 0.8 is 8/9. It's important to note that this fraction is in its simplest form and can't be further reduced. So, if you come across the decimal 0.8 in a recurring form, remember that it can be represented as the fraction 8/9.

What is the decimal 0.8 as a fraction?

To find the decimal 0.8 as a fraction, we first need to determine the place value of the decimal. In this case, the digit 8 is in the tenths place, which means that the decimal can be written as 8/10. However, this fraction can be simplified further by dividing both the numerator and denominator by their greatest common divisor, which is 2. After simplifying, the fraction becomes 4/5. Therefore, the decimal 0.8 can be written as the fraction 4/5.

When 0.88888 is converted into a fraction?

Converting decimals to fractions can seem challenging at first, but with a little practice, it becomes easier to understand and apply. In the case of the decimal 0.88888, we can convert it into a fraction in a few simple steps.

To begin, let's consider the decimal as x and write it as an equation:

x = 0.88888

Next, we need to eliminate the decimal point, and to do so, we can multiply both sides of the equation by a power of 10 that will move the decimal point to the rightmost digit. Since we have five repeating digits after the decimal point, we can multiply both sides by 10,000:

10,000x = 8,888.88

The next step is to subtract the original equation from the equation we just obtained to eliminate the decimal part. This can be done by subtracting the equation x = 0.88888 from the equation 10,000x = 8,888.88:

10,000x - x = 8,888.88 - 0.88888

9,999x = 8,888

Finally, we can simplify the equation by dividing both sides by 9,999:

x = 8,888 ÷ 9,999

This fraction can be further simplified by finding the greatest common divisor (GCD) of the numerator and denominator:

x = 8,888 ÷ GCD(8,888, 9,999) / 9,999 ÷ GCD(8,888, 9,999)

After simplifying, you will find the fraction representation of the decimal 0.88888.

Is 0.8 repeating a terminating decimal?

No, 0.8 repeating is not a terminating decimal. To understand why, let's break down the concept of a terminating decimal.

A terminating decimal is a decimal number that ends or terminates after a certain number of digits. For example, the number 0.5 is a terminating decimal because it ends after the digit 5.

On the other hand, 0.8 repeating belongs to a different category called a repeating decimal. A repeating decimal is a decimal number that has a pattern of digits that repeats indefinitely. In the case of 0.8 repeating, the digit 8 repeats infinitely.

Mathematically, 0.8 repeating can be represented as 0.8888... with a bar placed above the digit 8 to indicate the repetition. This pattern of repeating 8s will continue forever.

It's important to note that terminating decimals can be converted into fractions. For example, 0.5 can be written as the fraction 1/2. However, repeating decimals like 0.8 repeating require a different approach.

To convert a repeating decimal into a fraction, we can use the concept of infinite geometric series. In the case of 0.8 repeating, we can represent it as the sum of an infinite series:

Using the formula for the sum of an infinite geometric series, we can determine that 0.8 repeating is equal to the fraction 8/9. This means that 0.8 repeating is equivalent to 8 divided by 9.

In conclusion, 0.8 repeating is not a terminating decimal but a repeating decimal. It can be expressed as the fraction 8/9 using the concept of infinite geometric series.

How do you convert 0.8 into a rational number?

Converting 0.8 into a rational number can be done by representing it as a fraction. To do so, we need to understand that a rational number is any number that can be expressed as the ratio of two integers.

In order to convert 0.8 into a rational number, we first need to rewrite it as a fraction. Since 0.8 can be written as 8/10, we can simplify it further by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 8 and 10 is 2, so dividing both by 2 gives us 4/5.

Once we have simplified the fraction, 0.8 can be expressed as the rational number 4/5. This means that if we divide the numerator (4) by the denominator (5), we will get 0.8 as the result.

By converting 0.8 into a rational number like 4/5, we are able to represent it in a form that shows its relationship to other integers. This h1elps in mathematical calculations and comparisons, making it easier to work with in various scenarios.