What is 1.667 as a fraction
The Correct Answer and Explanation is :
To convert the decimal 1.667 into a fraction, follow these steps:
Step 1: Separate the Whole Number
The decimal 1.667 can be broken down into its whole number and decimal parts. Here, the whole number is 1, and the decimal part is 0.667.
Step 2: Convert the Decimal to a Fraction
Next, we need to convert the decimal 0.667 into a fraction.
- Identify the Decimal Places:
- The decimal 0.667 has three decimal places.
- Express as a Fraction:
- To convert 0.667 into a fraction, write it as (\frac{667}{1000}) because there are three digits after the decimal point, which means we use 1000 as the denominator.
Step 3: Combine the Whole Number and Fraction
Now, we combine the whole number with the fraction:
[
1.667 = 1 + 0.667 = 1 + \frac{667}{1000} = \frac{1000}{1000} + \frac{667}{1000} = \frac{1000 + 667}{1000} = \frac{1667}{1000}
]
Step 4: Simplify the Fraction
Next, we check if (\frac{1667}{1000}) can be simplified. To do this, we need to find the greatest common divisor (GCD) of 1667 and 1000.
- Prime Factorization:
- The number 1000 can be factored as (2^3 \times 5^3).
- For 1667, we can check if it’s divisible by small prime numbers. Upon testing, we find that 1667 is a prime number, meaning it has no divisors other than 1 and itself.
Since the GCD of 1667 and 1000 is 1, the fraction (\frac{1667}{1000}) is already in its simplest form.
Conclusion
Therefore, the decimal 1.667 can be expressed as the fraction (\frac{1667}{1000}). This process illustrates how to convert a decimal into a fraction, showing the steps of separating whole numbers, converting decimals, and simplifying fractions.