Write 1.875 as a mixed number.
The Correct answer and Explanation is:
To convert the decimal 1.875 into a mixed number, we start by identifying its whole number and fractional parts.
- Identify the Whole Number:
- The whole number part of 1.875 is 1.
- Convert the Decimal to a Fraction:
- Next, we focus on the decimal part, which is 0.875. To convert this decimal to a fraction, we recognize that it has three decimal places. Therefore, we can express it as: 0.875=87510000.875 = \frac{875}{1000}0.875=1000875
- Simplify the Fraction:
- To simplify 8751000\frac{875}{1000}1000875, we need to find the greatest common divisor (GCD) of 875 and 1000. The GCD of 875 and 1000 is 125.
- We divide both the numerator and the denominator by their GCD: 875÷1251000÷125=78\frac{875 \div 125}{1000 \div 125} = \frac{7}{8}1000÷125875÷125=87
- Thus, 0.8750.8750.875 can be written as 78\frac{7}{8}87.
- Combine the Whole Number and the Fraction:
- Now, we can combine the whole number part and the simplified fraction: 1.875=1+0.875=1+78=1781.875 = 1 + 0.875 = 1 + \frac{7}{8} = 1 \frac{7}{8}1.875=1+0.875=1+87=187
- Final Answer:
- Therefore, the decimal 1.875 as a mixed number is: 1781 \frac{7}{8}187
Summary
The conversion process involves separating the whole number from the decimal, converting the decimal into a fraction, simplifying it, and finally combining it back with the whole number. This method is applicable to any decimal number, facilitating its representation as a mixed number. The mixed number 1781 \frac{7}{8}187 conveys both the whole part (1) and the fractional part (78\frac{7}{8}87), which effectively captures the value of the original decimal 1.875.