With regards to arithmetic, changing decimals into fractions is a basic ability. One frequent conversion is reworking eighteen and two-tenths right into a fraction. This seemingly advanced job will be simplified by understanding the connection between decimals and fractions. By exploring the steps concerned, we are able to successfully convert this decimal to a lowered fraction.
To provoke the conversion course of, we have to acknowledge that eighteen and two-tenths will 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 are able to place the entire quantity 18 over the denominator of 10 (since there may be 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 isn’t in its easiest type. 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 implies we are able to 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 inserting 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 best type, we have to establish and divide each the numerator and denominator by their biggest frequent issue, which on this case is 2, ensuing within the lowered fraction of 91/5.
Simplifying the Fraction
Upon getting discovered the best frequent issue (GCF) of the numerator and denominator, you’ll be able to divide each of them by the GCF to simplify the fraction. On this case, the GCF of 180 and 210 is 30, so we are able to 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 verify your reply, you’ll be able to 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… It is a non-terminating, repeating decimal, which implies that it’ll go on endlessly. Nevertheless, we are able to spherical it to a sure variety of decimal locations, relying on the specified accuracy. For instance, we are able to spherical it to 2 decimal locations to get 0.86.
To confirm that that is the proper reply, we are able to examine it to the unique decimal quantity, 18.2. We will see that 0.86 could be very near 18.2, so we will be assured that our reply is right.
| Decimal | Fraction |
|---|---|
| 18.2 | 180/10 |
| 0.86 | 6/7 |
As you’ll be able to 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 biggest 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: Frequent Errors and Options
Mistake 1: Not multiplying the decimal by 10
When you overlook to multiply the decimal by 10 earlier than including the zero, your fraction will likely 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
When you overlook so as to add a zero to the correct of the decimal level, your fraction will even 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 unsuitable frequent issue
When you divide the fraction by the unsuitable frequent issue, your simplified fraction will likely be incorrect. To repair this, make certain to divide the fraction by the best frequent issue, which will be discovered utilizing methods equivalent to prime factorization or the Euclidean algorithm.
How To Make Eighteen And Two Tenths Into A Fraction
To transform a combined quantity like eighteen and two tenths right into a fraction, observe 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 are able to convert 18 and a couple 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 will be expressed because the fraction 182/10.
Folks Additionally Ask
What’s a combined quantity?
A combined quantity is a quantity that’s made up of a complete quantity and a fraction.
How do you exchange a combined quantity to a fraction?
To transform a combined quantity to a fraction, observe the steps outlined in the primary 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 biggest frequent issue (GCF).
