What is 7.868 divided by 1.4 and what is 78.013 times 0.45

The Correct Answer and Explanation is

Let’s solve the two problems step by step and then provide a detailed explanation:

1. 7.868 ÷ 1.4 = 5.62

2. 78.013 × 0.45 = 35.106

Explanation (Approximately 300 Words):

In mathematics, operations involving decimals follow the same rules as whole numbers but require special attention to the placement of the decimal point. Let’s break down each problem.

Division: 7.868 ÷ 1.4

To divide decimals, we aim to make the divisor (the number we’re dividing by) a whole number. We can do this by moving the decimal point in both numbers the same number of places to the right.

In this case, 1.4 becomes 14 when we move the decimal one place to the right. Likewise, 7.868 becomes 78.68:

Now we divide:
78.68 ÷ 14 = 5.62

We perform long division or use a calculator to get this precise answer. The result tells us how many times 1.4 fits into 7.868, and that value is 5.62.

Multiplication: 78.013 × 0.45

In multiplying decimals, we multiply as if the numbers are whole numbers, then count the total number of decimal places in both factors and place the decimal in the result accordingly.

Ignore decimals:
78.013 × 0.45 → Multiply 78013 × 45 = 3,510,585
Count decimal places:
78.013 has 3 decimal places, 0.45 has 2, so total = 5 decimal places.
Place the decimal in the result:
3,510,585 → 35.10685 → Rounded (if needed) = 35.106

So, 78.013 multiplied by 0.45 is 35.106.

Conclusion:

Understanding these processes helps build numerical literacy and confidence when dealing with real-world applications like finance, dosage calculations in nursing, or measurements. Precision with decimal placement is critical; a small mistake can lead to large errors in outcomes, especially in fields like healthcare or engineering.