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Chapter 5: Problem 61

Write the numbers in order from smallest to largest. $$ \frac{5}{8}, 0.612,0.649 $$

Short Answer

Expert verified
The order is: \( 0.612, \frac{5}{8}, 0.649 \).

Step by step solution

01

Convert Fractions to Decimals

First, we need to convert the fraction \( \frac{5}{8} \) into a decimal to easily compare it with the other numbers. Divide 5 by 8 to convert the fraction: \[ \frac{5}{8} = 0.625 \].
02

List All Decimals

We now have the following decimals to compare: - \( 0.625 \) - \( 0.612 \) - \( 0.649 \).
03

Compare and Order the Decimals

Compare the decimal numbers from Step 2. Start with the tenths place and if necessary, move to the hundredths place:1. \( 0.612 \) (smallest in the tenths place)2. \( 0.625 \) (smaller than \( 0.649 \) in the hundredths place)3. \( 0.649 \) (largest).
04

Write the Numbers in Order

Finally, write the numbers in order from smallest to largest based on the comparison: \( 0.612, \frac{5}{8} (0.625), 0.649 \).

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Key Concepts

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

Converting Fractions to Decimals
When faced with a mix of fractions and decimals, the first step is to convert fractions into decimals. This makes it easier to compare the numbers directly. To convert a fraction to a decimal, divide the numerator by the denominator. For example, with the fraction \( \frac{5}{8} \), you divide 5 by 8. By doing this, you get the decimal 0.625. This simple division allows you to place the fraction on the same scale as the other decimal numbers.
  • Example: \( \frac{5}{8} \rightarrow 0.625 \)
  • Helps in direct comparison with other decimals
Remember, this process involves basic division, and having a calculator handy can make the conversion quick and error-free. Being comfortable with this concept will streamline your ability to tackle problems involving mixed number formats.
Comparing Decimals
Once all numbers are in decimal form, the next step is to compare them. This is easier because now, we're dealing with numbers in the same format. Start comparing from the leftmost digit, which is the tenths place in our decimals.
If the digits in the tenths place are the same, move to the next digit to the right鈥攖he hundredths place.
  • Compare left to right, starting at the tenths place.
  • If the tenths are equal, check the hundredths place.
Think of it like lining them up and comparing each spot step by step.
It's like sorting things out visually. The smaller the digit, the lesser the value in that specific place. This method helps us identify the order properly.
Number Comparison and Ordering
Now that you have decimals, the task of ordering becomes simpler. The smallest number gets recorded first, followed by the next largest, and so on. In our example:
- First, we have 0.612, the smallest decimal.- Next is 0.625, which we got from \( \frac{5}{8} \).- Finally, 0.649 is the largest.To ensure your ordering is accurate, always double-check each decimal place and read directly from left to right.
  • Smallest to largest: follow the same order you have ''lined up''.
  • Reconfirm each ordering, especially in close calls.
The goal is to see decimals as simply a format that helps clarify comparisons. Mastering this concept makes sorting numbers straightforward, allowing you to confidently write them from smallest to largest.

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