Convert 1.625 into fraction into simplest form.
The Correct Answer and Explanation is :
The correct answer is: {13}{8}
To convert the decimal 1.625 into a fraction, we can follow these steps:
Step 1: Separate the Whole Number and Decimal
The number 1.625 consists of a whole number part, which is 1, and a decimal part, which is 0.625.
Step 2: Convert the Decimal to a Fraction
To convert 0.625 into a fraction, we can recognize it as:
- The decimal 0.625 can be expressed as (\frac{625}{1000}) because there are three digits after the decimal point (hundredths place).
Step 3: Simplify the Fraction
Next, we need to simplify (\frac{625}{1000}). To do this, we find the greatest common divisor (GCD) of 625 and 1000.
The prime factorization of:
- 625 is (5^4).
- 1000 is (10^3 = 2^3 \cdot 5^3).
The common factors are (5^3), so the GCD is (125).
Now, we can simplify:
[
\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
]
Step 4: Combine the Whole Number with the Fraction
Now, we can combine the whole number part (1) with the simplified fraction:
[
1.625 = 1 + 0.625 = 1 + \frac{5}{8}
]
To express this as a single fraction, convert the whole number into a fraction:
[
1 = \frac{8}{8}
]
Now, add the two fractions:
[
\frac{8}{8} + \frac{5}{8} = \frac{8 + 5}{8} = \frac{13}{8}
]
Conclusion
Thus, the decimal 1.625 converted into a fraction in its simplest form is:
[
\frac{13}{8}
]
This method illustrates the process of converting a decimal to a fraction through separation of the whole number and decimal parts, simplifying the fraction, and then recombining them to obtain the final result.