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Chapter 5: Problem 573

In the following exercises, divide. $$ 9 \div 0.045 $$

Short Answer

Expert verified
200

Step by step solution

01

Convert the Division into a Fraction

First, express the division problem as a fraction. The problem is $$ 9 \ 梅 \ 0.045 $$ can be written as $$ \frac{9}{0.045} $$.
02

Simplify the Decimal

To make it easier to solve, we will simplify the fraction by eliminating the decimal. Multiply both the numerator and the denominator by 1,000 to move the decimal point three places to the right: $$ \frac{9 \times 1000}{0.045 \times 1000} = \frac{9000}{45} $$.
03

Divide the Numerator by the Denominator

Now, simply divide 9,000 by 45 to find the value of the fraction: $$ \frac{9000}{45} = 200 $$.

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Key Concepts

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

Fraction Simplification
Fraction simplification is a fundamental concept in mathematics. Simplifying fractions makes them easier to work with and understand. Most fractions can be expressed in simpler terms by finding common factors between the numerator and the denominator and reducing them accordingly.
In the exercise, we start with the fraction $$\frac{9}{0.045}$$. To simplify, we aim to eliminate the decimal by multiplying both parts of the fraction by a common factor, in this case, 1,000. Once that is done, the fraction becomes $$\frac{9000}{45}$$. The simplification step reduces the complexity and allows for straightforward division.
Decimal Elimination
Decimals in fractions can complicate calculations, so it's common practice to eliminate them. This is done by multiplying both the numerator and the denominator by the same power of 10, shifting the decimal point to the right until you have whole numbers.
In the given exercise, we started with $$0.045$$ in the denominator. By multiplying both the numerator and the denominator by $$1,000$$, we shift the decimal point three places to the right, transforming the fraction into $$\frac{9000}{45}$$.
This makes subsequent calculations more straightforward and allows for easier simplification, as seen when we divided 9,000 by 45 to get the final result of 200.
Numerator and Denominator
Understanding the roles of the numerator and denominator is essential for grasping division problems involving fractions.
The numerator is the top number in a fraction; it represents how many parts of the whole you have. The denominator is the bottom number; it indicates into how many parts the whole is divided.
In the problem $$\frac{9}{0.045}$$, 9 is the numerator and 0.045 is the denominator. Multiplying both by the same factor, such as 1,000, keeps the value of the fraction the same while removing the decimal: $$\frac{9000}{45}$$.
This lets us focus on the simplified fraction, making it easier to divide the numerator by the denominator and arrive at the answer of 200.

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Most popular questions from this chapter

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