What fraction is equivalent to the decimal 1.375
The correct answer and explanation is:
The decimal 1.375 is equivalent to the fraction 11/8.
Explanation (300 words):
To convert the decimal 1.375 into a fraction, we follow a step-by-step process:
Step 1: Separate the whole number and the decimal part
- The number 1.375 consists of:
- A whole number part: 1
- A decimal part: 0.375
We can write this as: 1.375=1+0.3751.375 = 1 + 0.375
Step 2: Convert the decimal part to a fraction
Let’s focus on converting 0.375 to a fraction.
Since 0.375 has three decimal places, we can express it as: 0.375=37510000.375 = \frac{375}{1000}
Step 3: Simplify the fraction
We now simplify 375/1000 by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 125: 375÷1251000÷125=38\frac{375 \div 125}{1000 \div 125} = \frac{3}{8}
So, 0.375=380.375 = \frac{3}{8}
Step 4: Add the whole number back
Now add the whole number 1 to the fraction 3/8: 1+38=88+38=1181 + \frac{3}{8} = \frac{8}{8} + \frac{3}{8} = \frac{11}{8}
So, the decimal 1.375 is equivalent to the fraction 11/8.
Why This Matters:
Understanding how to convert decimals to fractions is a key math skill. It helps in:
- Solving real-world problems involving measurements and money.
- Working in science, engineering, and cooking where fractions are common.
- Comparing numbers more precisely (e.g., knowing that 1.375 is more than 1¼ or 10/8).
This example also shows how place value (tenths, hundredths, thousandths) helps convert decimals into exact fractions, rather than just estimating.