When it comes to mathematics, converting decimals into fractions is a fundamental skill. One common conversion is transforming eighteen and two-tenths into a fraction. This seemingly complex task can be simplified by understanding the relationship between decimals and fractions. By exploring the steps involved, we can effectively convert this decimal to a reduced fraction.
To initiate the conversion process, we need to recognize that eighteen and two-tenths can be written as 18.2. The number 18 represents the whole number portion, while the digit 2 in the tenths place denotes two-tenths. To convert this into a fraction, we can place the whole number 18 over the denominator of 10 (since there is one digit in the tenths place) and add the numerator representing the tenths (which is 2). This gives us the fraction 182/10.
However, the fraction 182/10 is not in its simplest form. To reduce the fraction, we need to find the greatest common factor (GCF) of the numerator and denominator. The GCF of 182 and 10 is 2, which means we can divide both the numerator and denominator by 2 to obtain the simplified fraction: 182/10 = 91/5. Therefore, eighteen and two-tenths as a fraction is 91/5.
In conclusion, converting eighteen and two-tenths into a fraction requires an understanding of the relationship between decimals and fractions. By placing the whole number over the appropriate denominator and adding the numerator representing the decimal part, we arrive at the fraction 182/10. However, to obtain the simplest form, we need to identify and divide both the numerator and denominator by their greatest common factor, which in this case is 2, resulting in the reduced fraction of 91/5.
Simplifying the Fraction
Once you have found the greatest common factor (GCF) of the numerator and denominator, you can divide both of them by the GCF to simplify the fraction. In this case, the GCF of 180 and 210 is 30, so we can divide both of them by 30 to get 6 and 7. Therefore, the simplified fraction is 6/7.
Checking Your Answer: Converting the Fraction Back to a Decimal
To check your answer, you can convert the fraction back to a decimal. To do this, divide the numerator by the denominator. In this case, 6 divided by 7 is 0.857142857142… This is a non-terminating, repeating decimal, which means that it will go on forever. However, we can round it to a certain number of decimal places, depending on the desired accuracy. For example, we can round it to two decimal places to get 0.86.
To verify that this is the correct answer, we can compare it to the original decimal number, 18.2. We can see that 0.86 is very close to 18.2, so we can be confident that our answer is correct.
| Decimal | Fraction |
|---|---|
| 18.2 | 180/10 |
| 0.86 | 6/7 |
As you can see, the decimal and fraction representations of 18.2 are equivalent, which confirms that our answer is correct.
Convert 18.2 to a Fraction
1. Multiply the decimal by 10 to move the decimal point one place to the right. This gives us 182.
2. Add a zero to the right of the decimal point. This gives us 182.0.
3. Write the decimal as a fraction with the numerator equal to the number without the decimal point and the denominator equal to 10 followed by the number of zeros added to the right of the decimal point. In this case, the numerator is 1820 and the denominator is 100.
4. Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2. This gives us the final fraction of 910/50.
| Steps | Example |
|---|---|
| Multiply by 10 | 18.2 x 10 = 182 |
| Add zero | 182 + 0 = 182.0 |
| Write as fraction | 1820/100 |
| Simplify | 910/50 |
Troubleshooting: Common Mistakes and Solutions
Mistake 1: Not multiplying the decimal by 10
If you forget to multiply the decimal by 10 before adding the zero, your fraction will be incorrect. To fix this, simply multiply the decimal by 10 and start over.
Mistake 2: Not adding a zero to the right of the decimal point
If you forget to add a zero to the right of the decimal point, your fraction will also be incorrect. To fix this, simply add a zero to the right of the decimal point and start over.
Mistake 3: Dividing the fraction by the wrong common factor
If you divide the fraction by the wrong common factor, your simplified fraction will be incorrect. To fix this, make sure to divide the fraction by the greatest common factor, which can be found using techniques such as prime factorization or the Euclidean algorithm.
How To Make Eighteen And Two Tenths Into A Fraction
To convert a mixed number like eighteen and two tenths into a fraction, follow these steps:
- Multiply the whole number (18) by the denominator of the fraction (10).
- Add the numerator of the fraction (2) to the result from step 1.
- Place the sum from step 2 over the denominator of the fraction.
Using these steps, we can convert 18 and 2/10 into a fraction as follows:
- 18 x 10 = 180
- 180 + 2 = 182
- 182/10
Therefore, eighteen and two tenths can be expressed as the fraction 182/10.
People Also Ask
What is a mixed number?
A mixed number is a number that is made up of a whole number and a fraction.
How do you convert a mixed number to a fraction?
To convert a mixed number to a fraction, follow the steps outlined in the main article above.
What is the fraction equivalent of eighteen and two tenths?
The fraction equivalent of eighteen and two tenths is 182/10.
How do you simplify a fraction?
To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF).
