Problem 101 Explain the difference between \... [FREE SOLUTION]

91影视

Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 7: Problem 101

Explain the difference between $25 \%$ and $0.25 \%$

Short Answer

Expert verified

25% (0.25) is larger than 0.25% (0.0025).

Step by step solution

- Understand the Percentages

First, recall that a percentage is a way of expressing a number as a fraction of 100. For example, 25% means 25 out of 100, and 0.25% means 0.25 out of 100.

- Convert Percentages to Decimal Form

Convert the percentages to decimal form by dividing by 100. For 25%, calculate $25 \div 100 = 0.25$. For 0.25%, calculate $0.25 \div 100 = 0.0025$.

- Compare the Decimal Values

Now compare the decimal values. 25% converted to a decimal is 0.25, while 0.25% converted to a decimal is 0.0025. Clearly, 0.25 is much larger than 0.0025.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

percentage conversion

When working with percentages, remember that they are a way of expressing numbers as parts of a whole. This whole is always 100. To convert a percentage to a decimal, divide the percentage by 100. This step is crucial as it helps in performing arithmetic operations and comparing different values. For example, let's convert 25% and 0.25% to their decimal forms. For 25%, we have: 25 梅 100 = 0.25.
For 0.25%, we have: 0.25 梅 100 = 0.0025.
This conversion simplifies manipulation and comparison of percentages.

decimal form

Understanding decimal form is essential in mathematics. A decimal number is a way of representing fractions based on the powers of 10. To grasp decimal form, think of it as a number divided into tenths, hundredths, thousandths, etc. For percentages, converting to decimal form means simplifying them for easy comparison. Recall:

25% converted to decimal is 0.25

0.25% converted to decimal is 0.0025

This method breaks down the percentage into smaller, easily comparable numbers. Paying close attention to decimal places can help understand and distinguish between numbers like 0.25 and 0.0025, where one is significantly smaller than the other.

comparing decimals

Once percentages have been converted to decimal form, comparing them becomes straightforward. You can visually compare and determine which one is larger or smaller. For example, let鈥檚 compare 0.25 and 0.0025. The value of 0.25 is much larger than 0.0025 because the position of the digits is far more to the left in the number line.
This position indicates higher value. Comparing decimals:

0.25 (has two decimal places)

0.0025 (has four decimal places)

Clearly, 0.25 is closer to 1 than 0.0025. This clarity in comparison aids in understanding the significant difference in their values post conversion.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Explain the difference between \(25 \%\) and \(0.25 \%\)

Short Answer

Step by step solution

- Understand the Percentages

- Convert Percentages to Decimal Form

- Compare the Decimal Values

Key Concepts

percentage conversion

decimal form

comparing decimals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Applied Mathematics

Mechanics Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.