In the case of arithmetic, changing decimals into fractions is a elementary talent. One widespread conversion is reworking eighteen and two-tenths right into a fraction. This seemingly complicated 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.
Nonetheless, the fraction 182/10 will not be in its easiest type. To scale back the fraction, we have to discover the best widespread issue (GCF) of the numerator and denominator. The GCF of 182 and 10 is 2, which implies 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. Nonetheless, to acquire the only type, we have to determine and divide each the numerator and denominator by their best widespread issue, which on this case is 2, ensuing within the decreased fraction of 91/5.
Simplifying the Fraction
After getting discovered the best widespread 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 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’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… This can be a non-terminating, repeating decimal, which implies that it’s going to go on eternally. Nonetheless, 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’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 appropriate. This provides us 182.
2. Add a zero to the appropriate 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 appropriate 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 widespread 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
Should you overlook to multiply the decimal by 10 earlier than including the zero, your fraction might be incorrect. To repair this, merely multiply the decimal by 10 and begin over.
Mistake 2: Not including a zero to the appropriate of the decimal level
Should you overlook so as to add a zero to the appropriate of the decimal level, your fraction may even be incorrect. To repair this, merely add a zero to the appropriate of the decimal level and begin over.
Mistake 3: Dividing the fraction by the unsuitable widespread issue
Should you divide the fraction by the unsuitable widespread issue, your simplified fraction might be incorrect. To repair this, be sure that to divide the fraction by the best widespread issue, which may be discovered utilizing methods corresponding 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 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 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 change a blended quantity to a fraction?
To transform a blended quantity to a fraction, comply with 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 best widespread issue (GCF).
