Convert the decimal to a fraction.
The Correct Answer and Explanation is:
Decimal: 0.875
Fraction: 7/8
To convert a decimal to a fraction, follow a step-by-step process to understand the relationship between the decimal and its fractional form.
Step 1: Understand the place value of the decimal.
The number 0.875 has three digits after the decimal point, which means it is in the thousandths place. Therefore, write it as a fraction with 875 as the numerator and 1000 as the denominator:0.875=87510000.875 = \frac{875}{1000}0.875=1000875
Step 2: Simplify the fraction.
To simplify the fraction, find the greatest common divisor (GCD) of 875 and 1000.
- 875 and 1000 are both divisible by 125.
- Divide the numerator and denominator by 125:
875÷1251000÷125=78\frac{875 \div 125}{1000 \div 125} = \frac{7}{8}1000÷125875÷125=87
Thus, 0.875 is equivalent to the fraction 7/8.
Explanation:
Decimals and fractions are two different ways to represent the same part of a whole. When a decimal is terminating (i.e., it ends), it can always be written as a fraction. The digits after the decimal point determine the denominator of the fraction based on place value. For 0.875, the digits lie in the thousandths place, so the fraction becomes 875 over 1000. However, this is not in its simplest form.
To reduce a fraction, divide both the numerator and the denominator by their greatest common divisor. Simplifying helps present the number in the cleanest and most understandable way. In mathematical contexts, simplified fractions are preferred for ease of communication and further computation.
Using this approach ensures accuracy and builds a strong foundation for understanding the equivalence between decimals and fractions in various mathematical problems.
