Problem 225 Order each pair of numbers, usin... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 225

Order each pair of numbers, using $<$ or $>$ $\frac{2}{5}$ ____ $0.25$

Short Answer

Expert verified

$\frac{2}{5} > 0.25$

Step by step solution

Convert the fraction to a decimal

Convert the fraction $\frac{2}{5}$ to a decimal. Divide 2 by 5, which gives 0.4.

Compare the numbers

Now, compare the decimal values. We have 0.4 and 0.25.

Determine the relationship

Since 0.4 is greater than 0.25, we use the $>$ symbol.

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Key Concepts

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

converting fractions to decimals

Converting fractions to decimals is an essential skill in math. It helps in comparing different types of numbers more easily. A fraction like $\frac{2}{5}$ can be converted to a decimal by performing a simple division.
To convert $\frac{2}{5}$, just divide the numerator (2) by the denominator (5). This can be done as: 2 梅 5 = 0.4. Now, we have the decimal form of the fraction, which makes comparing it to other decimals much easier.

decimal comparison

Comparing decimals involves looking at the digits from left to right, starting with the ones place. In our exercise, we compare 0.4 and 0.25. First, observe the digits before the decimal point. Since neither number has digits before the decimal point, we move to the next position.
Look at the tenths place: 0.4 has 4 in the tenths place, and 0.25 has 2. Because 4 is greater than 2, we know that 0.4 is larger than 0.25. This is a clear and straightforward comparison.

inequalities

Inequalities help show the relationship between two values. The symbols < and > are commonly used to denote 'less than' and 'greater than', respectively. In the given problem, once we've converted $\frac{2}{5}$ to 0.4 and confirmed that 0.4 is greater than 0.25, we can use the appropriate inequality symbol.
We conclude that: 0.4 > 0.25. Hence, \frac{2}{5} > 0.25, showing that $\frac{2}{5}$ (or 0.4) is indeed greater than 0.25.
Using inequalities can efficiently communicate relationships in math and help better understand how numbers compare to each other.

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91影视

Order each pair of numbers, using \(<\) or \(>\) \(\frac{2}{5}\) ____ \(0.25\)

Short Answer

Step by step solution

Convert the fraction to a decimal

Compare the numbers

Determine the relationship

Key Concepts

converting fractions to decimals

decimal comparison

inequalities

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