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Chapter 5: Problem 50

Divide. $$0.31 \div 0.1$$

Short Answer

Expert verified
3.1

Step by step solution

01

- Understand the Problem

The problem asks to divide 0.31 by 0.1. This can be written as a fraction: \ \( \frac{0.31}{0.1} \ \).
02

- Eliminate the Decimals

To simplify the division, multiply both the numerator and the denominator by 10 to eliminate the decimal points. This gives: \ \( \frac{0.31 \times 10}{0.1 \times 10} = \frac{3.1}{1} \ \).
03

- Perform the Division

Now divide 3.1 by 1, which is straightforward: \ \( 3.1 \ \).

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Key Concepts

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

decimal division
Dividing decimals might seem tricky at first, but it's a straightforward process once you break it down. Let's consider an example: \ \(0.31 \div 0.1 \). The first step is recognizing that you can represent this division as a fraction: \ \( \frac{0.31}{0.1} \). \
\To simplify this fraction, we need to eliminate the decimals. This makes the operation much easier to handle. Multiply both the numerator and the denominator by 10. Why 10? Because it's the smallest power of 10 that transforms both decimals into whole numbers. So we get: \ \( \frac{31}{1} \). \
\Now, dividing by 1 is straightforward, leading us to the answer 3.1.
fraction simplification
Fraction simplification can make many mathematical operations easier. In our example, we started with \ \(\frac{0.31}{0.1}\). This fraction can be simplified by eliminating the decimal points.
\To do this, multiply both the numerator and the denominator by the same number. In this case, we chose 10, because it moves the decimal point one place to the right: \ \( 0.31 \times 10 = 3.1\) and \ \(0.1 \times 10 = 1\).
\The simplified fraction is then \ \( \frac{3.1}{1} \). This action doesn't change the value of the fraction, it just makes the numbers easier to work with, particularly for division.
mathematical operations
Mathematical operations involve basic functions like addition, subtraction, multiplication, and division. In all these operations, understanding the properties of numbers and how they interact is key. Let's consider our example: \ \( 0.31 \div 0.1 \).
\First, we turned this into a simpler fraction \ \(\frac{0.31}{0.1}\). By multiplying both parts by 10, we then got \( \frac{3.1}{1}\), which is hugely easier to deal with.
\Next, we considered the division of 3.1 by 1. Dividing any number by 1 returns the same number. Thus, \ \( 3.1 \div 1 = 3.1 \). This shows how knowing basic operations can simplify seemingly complex problems.

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