On the subject of arithmetic, changing decimals into fractions is a basic talent. One frequent conversion is remodeling eighteen and two-tenths right into a fraction. This seemingly advanced activity may be simplified by understanding the connection between decimals and fractions. By exploring the steps concerned, we will successfully convert this decimal to a decreased fraction.
To provoke the conversion course of, we have to acknowledge that eighteen and two-tenths may be written as 18.2. The quantity 18 represents the entire quantity portion, whereas the digit 2 within the tenths place denotes two-tenths. To transform this right into a fraction, we will place the entire quantity 18 over the denominator of 10 (since there’s one digit within the tenths place) and add the numerator representing the tenths (which is 2). This provides us the fraction 182/10.
Nevertheless, the fraction 182/10 shouldn’t be in its easiest kind. To scale back the fraction, we have to discover the best frequent issue (GCF) of the numerator and denominator. The GCF of 182 and 10 is 2, which suggests we will divide each the numerator and denominator by 2 to acquire the simplified fraction: 182/10 = 91/5. Due to this fact, eighteen and two-tenths as a fraction is 91/5.
In conclusion, changing eighteen and two-tenths right into a fraction requires an understanding of the connection between decimals and fractions. By putting the entire quantity over the suitable denominator and including the numerator representing the decimal half, we arrive on the fraction 182/10. Nevertheless, to acquire the only kind, we have to determine and divide each the numerator and denominator by their best frequent issue, which on this case is 2, ensuing within the decreased fraction of 91/5.
Simplifying the Fraction
After you have discovered the best frequent issue (GCF) of the numerator and denominator, you possibly can divide each of them by the GCF to simplify the fraction. On this case, the GCF of 180 and 210 is 30, so we will divide each of them by 30 to get 6 and seven. Due to this fact, the simplified fraction is 6/7.
Checking Your Reply: Changing the Fraction Again to a Decimal
To test your reply, you possibly can convert the fraction again to a decimal. To do that, divide the numerator by the denominator. On this case, 6 divided by 7 is 0.857142857142… This can be a non-terminating, repeating decimal, which suggests that it’s going to go on endlessly. Nevertheless, we will spherical it to a sure variety of decimal locations, relying on the specified accuracy. For instance, we will spherical it to 2 decimal locations to get 0.86.
To confirm that that is the right reply, we will examine it to the unique decimal quantity, 18.2. We are able to see that 0.86 could be very near 18.2, so we may be assured that our reply is right.
| Decimal | Fraction |
|---|---|
| 18.2 | 180/10 |
| 0.86 | 6/7 |
As you possibly can see, the decimal and fraction representations of 18.2 are equal, which confirms that our reply is right.
Convert 18.2 to a Fraction
1. Multiply the decimal by 10 to maneuver the decimal level one place to the correct. This provides us 182.
2. Add a zero to the correct of the decimal level. This provides us 182.0.
3. Write the decimal as a fraction with the numerator equal to the quantity with out the decimal level and the denominator equal to 10 adopted by the variety of zeros added to the correct of the decimal level. On this case, the numerator is 1820 and the denominator is 100.
4. Simplify the fraction by dividing each the numerator and the denominator by their best frequent issue, which is 2. This provides us the ultimate fraction of 910/50.
| Steps | Instance |
|---|---|
| Multiply by 10 | 18.2 x 10 = 182 |
| Add zero | 182 + 0 = 182.0 |
| Write as fraction | 1820/100 |
| Simplify | 910/50 |
Troubleshooting: Widespread Errors and Options
Mistake 1: Not multiplying the decimal by 10
Should you overlook to multiply the decimal by 10 earlier than including the zero, your fraction can be incorrect. To repair this, merely multiply the decimal by 10 and begin over.
Mistake 2: Not including a zero to the correct of the decimal level
Should you overlook so as to add a zero to the correct of the decimal level, your fraction may also be incorrect. To repair this, merely add a zero to the correct of the decimal level and begin over.
Mistake 3: Dividing the fraction by the fallacious frequent issue
Should you divide the fraction by the fallacious frequent issue, your simplified fraction can be incorrect. To repair this, be sure that to divide the fraction by the best frequent issue, which may be discovered utilizing methods akin to prime factorization or the Euclidean algorithm.
How To Make Eighteen And Two Tenths Into A Fraction
To transform a blended quantity like eighteen and two tenths right into a fraction, comply with these steps:
- Multiply the entire quantity (18) by the denominator of the fraction (10).
- Add the numerator of the fraction (2) to the end result from step 1.
- Place the sum from step 2 over the denominator of the fraction.
Utilizing these steps, we will convert 18 and a pair of/10 right into a fraction as follows:
- 18 x 10 = 180
- 180 + 2 = 182
- 182/10
Due to this fact, eighteen and two tenths may be expressed because the fraction 182/10.
Folks Additionally Ask
What’s a blended quantity?
A blended quantity is a quantity that’s made up of a complete quantity and a fraction.
How do you exchange a blended quantity to a fraction?
To transform a blended quantity to a fraction, comply with the steps outlined in the principle article above.
What’s the fraction equal of eighteen and two tenths?
The fraction equal of eighteen and two tenths is 182/10.
How do you simplify a fraction?
To simplify a fraction, divide each the numerator and denominator by their best frequent issue (GCF).
