Given two decimal numbers 0.5 and -0.4375. (a) Multiply the numbers. (b) Converting to decimal to check the results. Show your workings.
The Correct Answer and Explanation is:
To solve this, we will first multiply the two decimal numbers, and then we will convert the result to check the accuracy.
Part (a): Multiplying the Numbers
We are given the two decimal numbers:
- 0.50.50.5
- −0.4375-0.4375−0.4375
Step 1: Multiply the absolute values
We start by multiplying the absolute values of the numbers:0.5×0.4375=0.218750.5 \times 0.4375 = 0.218750.5×0.4375=0.21875
Step 2: Apply the sign
Since one number is positive and the other is negative, the product will be negative. So, the result of the multiplication is:0.5×(−0.4375)=−0.218750.5 \times (-0.4375) = -0.218750.5×(−0.4375)=−0.21875
So, the result of multiplying the numbers is −0.21875-0.21875−0.21875.
Part (b): Converting to Decimal to Check the Result
Now, let’s convert the decimal result −0.21875-0.21875−0.21875 back to decimal form to verify.
We can check the multiplication by converting the fraction −0.21875-0.21875−0.21875 into its fraction form. Here’s how:
Step 1: Express −0.21875-0.21875−0.21875 as a fraction
We can express 0.218750.218750.21875 as a fraction. Since there are 5 decimal places, we write it as:0.21875=218751000000.21875 = \frac{21875}{100000}0.21875=10000021875
Simplifying the fraction:21875100000=732\frac{21875}{100000} = \frac{7}{32}10000021875=327
So:−0.21875=−732-0.21875 = -\frac{7}{32}−0.21875=−327
Step 2: Convert the product of 0.50.50.5 and −0.4375-0.4375−0.4375 to a fraction
Next, let’s convert both of the original decimal numbers into fractions:0.5=12,−0.4375=−7160.5 = \frac{1}{2}, \quad -0.4375 = -\frac{7}{16}0.5=21,−0.4375=−167
Now, multiply the fractions:12×−716=−732\frac{1}{2} \times -\frac{7}{16} = -\frac{7}{32}21×−167=−327
Thus, the product is indeed −732-\frac{7}{32}−327, which is equivalent to −0.21875-0.21875−0.21875, confirming our multiplication result.
Conclusion
The product of 0.50.50.5 and −0.4375-0.4375−0.4375 is −0.21875-0.21875−0.21875, and by converting it back to a fraction, we verified the result.
