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Chapter 0: Problem 120

What is \(5 \%\) of \(70 ?\)

Short Answer

Expert verified
3.5

Step by step solution

01

Understand the Problem

First, understand that finding 5% of 70 is asking for what number represents 5 out of every 100 parts of 70.
02

Convert Percentage to Decimal

Convert the percentage to a decimal by dividing by 100. So, 5% becomes 0.05.
03

Multiply by the Given Number

Multiply the decimal by the given number to find the part that represents 5%. Here, multiply 0.05 by 70: \(0.05 \times 70 = 3.5\)
04

Write the Final Answer

The calculation shows that 5% of 70 is 3.5.

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Key Concepts

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

Converting Percentages to Decimals
Understanding how to convert percentages to decimals is crucial for percentage calculations. A percentage is simply a fraction out of 100. To convert a percentage to a decimal, you divide by 100. For example, to convert 5% to a decimal, you divide 5 by 100, resulting in 0.05. This conversion allows you to more easily handle multiplication operations.

Remember:
  • Divide the percentage by 100
  • Move the decimal point two places to the left
For instance, 45% becomes 0.45, and 75% becomes 0.75. With this method, percentages become something you can easily multiply with other numbers.
Basic Multiplication
Multiplication is a straightforward but essential operation in mathematics, especially in percentage calculations. When you multiply a decimal (converted from a percentage) by another number, you are essentially finding a part of that number. For the problem at hand, we were asked to find what 5% of 70 is. After converting 5% into 0.05, you multiply this decimal by 70: \(0.05 \times 70 = 3.5\).

Here's a quick guide:
  • First, perform the standard multiplication ignoring the decimals
  • Count the total decimal places in the factors
  • Place the decimal in the product accordingly
This simplifies fractional problem-solving and approaches to real-world applications like financial estimations.
Understanding Percentages
Percentages represent a ratio or fraction of 100. Understanding this concept helps in interpreting and solving many real-world problems. When we talk about 5%, we are discussing 5 parts out of 100. Comprehending percentages helps you assess proportions easily. For example, in the given problem of finding 5% of 70, you can break it down:
  • 5% means 5 per 100
  • You are seeking 5 parts of every 100 parts of 70
  • This inherently implies a need for multiplication
Breaking down complex ideas into simpler steps can greatly enhance your understanding and ease of calculation, making percentage-based operations simpler and more intuitive.

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Most popular questions from this chapter

Find each sum or difference, and write it in lowest terms as needed. $$ 5 \frac{3}{4}+1 \frac{1}{3} $$

A board is \(15 \frac{5}{8}\) in. long. If it must be divided into three pieces of equal length, how long must each piece be?

What is \(6 \%\) of \(80 ?\)

Write each fraction in lowest terms. $$ \frac{16}{64} $$

Find each product or quotient, and write it in lowest terms as needed. $$ 2 \frac{1}{2} \div 1 \frac{5}{7} $$
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