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Chapter 1: Problem 20

Convert the decimal numbers to whole number percentages. $$0.844$$

Short Answer

Expert verified
The decimal 0.844 is equivalent to 84% when converted to a whole number percentage.

Step by step solution

01

Understand the Conversion

To convert a decimal to a percentage, you multiply the decimal by 100. This is because a percentage is a fraction out of 100. Therefore, each decimal number can be expressed as a percentage by moving the decimal point two places to the right.
02

Multiply Decimal by 100

Take the decimal number 0.844 and multiply it by 100. This calculation will convert the decimal number into a percentage.
03

Perform the Multiplication Calcul

Calculate:\[0.844 \times 100 = 84.4\]So, 0.844 as a percentage is 84.4%.
04

Finalize the Percentage

Since we are converting to a whole number percentage, we need to round the result to the nearest whole number. In this case, 84.4 rounds to 84.

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Key Concepts

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

Multiplying by 100
When converting a decimal number to a percentage, the key step is multiplying by 100. This transformation stems from what a percentage represents: a part out of 100. When you take a decimal鈥攕uch as 0.844鈥攁nd multiply by 100, you're essentially finding how much out of 100 that decimal represents.
This multiplication process is straightforward:
  • Move the decimal point two places to the right. For 0.844, this becomes 84.4.
  • Why two places? Because multiplying by 100 increases the value by 100 times, which translates mathematically to two places right for the decimal point.
Understanding this concept ensures you'll always be able to convert any decimal to a percentage accurately.
Rounding Numbers
Rounding numbers is crucial when you need a clean, whole number percentage. Given the example where multiplying 0.844 by 100 gives you 84.4, it's necessary to round this to the nearest whole number鈥�84.
Here鈥檚 a brief guide on rounding:
  • Identify the digit right after the decimal point (tenths place). For 84.4, it's 4.
  • If this digit is 5 or greater, round up the whole number (e.g., 84.6 rounds to 85).
  • If it's less than 5, the whole number stays the same. Thus, 84.4 becomes 84.
This technique helps simplify numbers, especially in percentage form, making them easier to grasp and compare.
Understanding Percentages
A percentage offers a way to express a number as a fraction of 100. It's a universal language for comparing different values on a common scale. Here's how percentages work and why they matter:
  • Think of a percentage as a way to understand portions: 84% means 84 out of every 100 parts.
  • Percentages are especially useful in contexts like statistics, finance, and everyday comparisons. For example, when you say 50% off, it鈥檚 cutting the number in half.
  • To master percentages, always remember that they are numerical expressions of portions and parts, which is why converting decimals to percentages involves placing them in this context of "per hundred".
Grasping percentages can aid in interpreting data and understanding real-world applications effectively.

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Most popular questions from this chapter

The estimated and actual values are given. Compute the relative error. $$v_{e}=5.28 \text { and } v=5.5$$

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