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Chapter 6: Problem 47

Write each list of numbers in order from least to greatest. $$\frac{2}{3}, 61 \%, 0.69$$

Short Answer

Expert verified
The numbers in order from least to greatest are: \( 61\% \), \( \frac{2}{3} \), \( 0.69 \).

Step by step solution

01

Convert Each Number to Decimal

First, convert each number given in different forms (fraction, percentage, and decimal) to a common form (decimals) to easily compare them.- The number \( \frac{2}{3} \) as a decimal is approximately \( 0.6667 \) (rounded to four decimal places).- The percentage \( 61\% \) can be converted to a decimal by dividing by 100, which equals \( 0.61 \).- The decimal \( 0.69 \) is already in decimal form.
02

Compare the Decimal Values

Now, with all numbers converted to decimal form, compare the values:- \( \frac{2}{3} \approx 0.6667 \)- \( 61\% = 0.61 \)- \( 0.69 \)The order from least to greatest based on these decimal values is \( 0.61, 0.6667, 0.69 \).
03

Write the Numbers in Original Form

Convert the numbers back from decimal form to their original forms while maintaining the same order from least to greatest:- First is \( 61\% \)- Then \( \frac{2}{3} \)- Lastly \( 0.69 \)The sorted order from least to greatest is \( 61\% \), \( \frac{2}{3} \), \( 0.69 \).

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Key Concepts

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

Fractions to Decimals
Converting fractions like \( \frac{2}{3} \) into decimals simplifies the comparison of numbers. It involves a simple division of the numerator by the denominator. In this case, dividing 2 by 3 gives the repeating decimal \( 0.6667 \). When dealing with repeating decimals, it's common to use rounding for easier handling. Here, we rounded to four decimal places for consistency.
  • To convert a fraction to a decimal, divide the top number (numerator) by the bottom number (denominator).
  • For non-terminating decimals, rounding is often necessary for simpler calculations.
Understanding how to convert fractions to decimals is crucial for comparing numbers in different formats accurately.
Percentages to Decimals
Transforming percentages into decimals is another essential step if we want to compare different number forms easily. Doing this conversion is straightforward鈥攁ll you need to do is move the decimal point two places to the left, or, in simpler terms, divide by 100. For instance, converting \( 61\% \) to a decimal involves performing the calculation \( 61 \div 100 = 0.61 \).
  • Move the decimal point two places to the left when converting a percentage to a decimal.
  • If needed, complement tiny percentages with zero-padding (e.g., \( 61\% \) becomes \( 0.61 \), not \( .61 \)).
This process simplifies number comparisons, ensuring precision and ease in calculations.
Number Comparison
When all numbers are presented in decimal form, comparing them becomes much simpler. You can now quickly assess which values are larger or smaller by seeing their placement on the number line. In our example, the decimal equivalents \( 0.61 \), \( 0.6667 \), and \( 0.69 \) were easy to sort from least to greatest.
  • Transform all numbers into a common format (decimals) for straightforward comparison.
  • Order numbers by comparing decimal places, ensuring accuracy in the sequence.
Remember, consistent conversion and comparison are key to making sure you're ordering numbers correctly, regardless of their original form.

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Most popular questions from this chapter

Solve each proportion. $$\frac{86.4}{k}=\frac{27}{100}$$

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