Problem 108 Is the number 0.0087 less than o... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 7: Problem 108

Is the number 0.0087 less than or greater than $1 \% ?$

Short Answer

Expert verified

0.0087 is less than 1%.

Step by step solution

- Understand the Problem

We need to determine if the number 0.0087 is less than or greater than 1%.

- Convert 1% to a Decimal

Recall that percentage can be converted to decimal by dividing by 100.\[ 1\text{\textpercent} = \frac{1}{100} = 0.01 \]

- Compare the Two Decimals

Now compare the decimal forms of the two numbers: 0.0087 and 0.01. Since 0.0087 is less than 0.01, we can decide the inequality.\[ 0.0087 < 0.01 \]

- Write the Conclusion

From the comparison, conclude that 0.0087 is less than 1%.

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Key Concepts

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

percentage to decimal conversion

When converting a percentage to a decimal, you simply divide by 100. For example, to convert 1% to a decimal, you divide 1 by 100. This calculation can be written as: $1\text{\textpercent} = \frac{1}{100} = 0.01$.

This is a straightforward process where you move the decimal point two places to the left. So, 52% becomes 0.52 and 0.5% becomes 0.005.

Always remember: move the decimal two places to the left for accurate conversion. This conversion is crucial for comparing percentages with decimals easily.

inequality

Inequality is a mathematical statement that shows the relationship between two values that are not equal. It often uses symbols like \<, >, 鈮�, and 鈮�.

In our problem, we use the \< symbol to compare numbers. For instance, if you have numbers 0.0087 and 0.01, you check which is smaller.

$<0.0087 < 0.01 $ shows that 0.0087 is less than 0.01. Understanding inequalities helps in many areas of math, including solving and graphing equations.

comparing decimals

When comparing decimals, line up the decimal points first to make the comparison easier. Compare digit by digit from left to right. This helps to see which number is greater or smaller.

In our exercise, we compare 0.0087 and 0.01. First, line up their decimal points:

0.0087
0.0100

Comparing digit by digit:

At the tenths place: 0 = 0
At the hundredths place: 0 = 0
At the thousandths place: 0 < 1

This shows that 0.0087 is less than 0.01.

Practicing this technique with more examples can help solidify your understanding of comparing decimals.

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91影视

Is the number 0.0087 less than or greater than \(1 \% ?\)

Short Answer

Step by step solution

- Understand the Problem

- Convert 1% to a Decimal

- Compare the Two Decimals

- Write the Conclusion

Key Concepts

percentage to decimal conversion

inequality

comparing decimals

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