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Chapter 4: Problem 47

Divide. $$ \frac{42.561}{0.01} $$

Short Answer

Expert verified
4256.1

Step by step solution

01

Understand the Division

The task requires dividing 42.561 by 0.01. Dividing by a decimal can be simplified by converting it into a whole number.
02

Convert the Divisor

To make the calculation simpler, convert 0.01 to a whole number by multiplying both the numerator and the denominator by 100.
03

Perform Multiplication

Multiplying 42.561 by 100 gives 4256.1, and multiplying 0.01 by 100 gives 1.
04

Simplify the Division

Now, rewrite the division: \( \frac{42.561}{0.01} = \frac{4256.1}{1} \)
05

Calculate the Result

Dividing 4256.1 by 1 gives 4256.1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Decimal Multiplication
When we multiply decimals, it's crucial to move the decimal point in both numbers. This ensures we correctly calculate the product. For instance, in the problem above, we converted the decimal divisor (0.01) into a whole number by multiplying it by 100. Similarly, the dividend (42.561) is also multiplied by 100. This conversion simplifies the division problem. Multiplying decimals might seem tricky, but by shifting decimal points, we can easily handle the calculations.
Simplifying Division
When dealing with decimal division, converting the divisor to a whole number is one of the best strategies. This simplifies calculations. For example, in our division question, we converted 0.01 to 1 by multiplying by 100. We followed this multipication with the numerator as well, turning 42.561 into 4256.1. Simplifying the division in this way makes it straightforward to get the answer, as shown in the exercise: dividing by 1 is much easier than dividing by a decimal.
Basic Arithmetic Operations
Basic arithmetic includes addition, subtraction, multiplication, and division. These operations form the foundation of all math problems. The division problem above is a good example. We used multiplication to simplify the division process, converting a tricky decimal problem into an easy whole number division. By understanding and applying these basic operations correctly, we solve more complex problems easily. Remember to always follow these steps to ensure accuracy and simplicity in calculations.

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