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Chapter 5: Problem 59

Write the numbers in order from smallest to largest. $$ 5.23, \frac{42}{8}, 5.34 $$

Short Answer

Expert verified
The numbers in order are: 5.23, 5.25, 5.34.

Step by step solution

01

Convert Fraction to Decimal

Start by converting the fraction \(\frac{42}{8}\) into a decimal. To do this, divide 42 by 8. The result is 5.25. Now we have the numbers as decimals: 5.23, 5.25, and 5.34.
02

Compare the Numbers

Next, compare the three decimal numbers: 5.23, 5.25, and 5.34. Begin by looking at the integer part. All numbers have the integer part 5. Therefore, proceed to compare the decimal parts.
03

Order the Numbers

Among the decimal parts, 0.23 (from 5.23) is the smallest, 0.25 (from 5.25) is the next smallest, and 0.34 (from 5.34) is the largest. Thus, the numbers in order from smallest to largest are: 5.23, 5.25, 5.34.

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Key Concepts

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

Converting Fractions to Decimals
Converting a fraction into a decimal is a crucial skill. It helps us to compare and order numbers more easily. To convert a fraction such as \( \frac{42}{8} \) into a decimal, we must divide the numerator by the denominator. In this case, divide 42 by 8. This gives us the decimal 5.25. When you are converting fractions to decimals:
  • Perform the division using a calculator or manually.
  • Make sure to carry out the division up to the required decimal places for accuracy.
Having numbers in a consistent format, such as decimals, makes it easier to handle subsequent comparison tasks. Once converted, the numbers become simpler to visualize and analyze.
Comparing Decimals
Once numbers are in decimal form, comparing them is straightforward. Start by examining each digit from left to right.
  • First, look at the whole number part (the number to the left of the decimal point).
  • If they are the same, move to the digits after the decimal point.
For example, take the numbers 5.23, 5.25, and 5.34. Since all of them have 5 as the whole number, check the decimal part next.
  • Compare 0.23, 0.25, and 0.34.
  • In this sequence, 0.23 is the smallest, followed by 0.25, then 0.34.
By systematically comparing decimal places, you ensure accuracy in ordering.
Number Order
Arranging numbers in order from smallest to largest is a fundamental math skill. After converting and comparing, you can sequence the numbers easily. Keeping decimals aligned assists in accurate comparison. To put the numbers in order:
  • Start with the smallest decimal number.
  • Follow on by listing the next greater number.
  • Continue until all numbers are arranged sequentially.
In our earlier problem, we sequenced 5.23, 5.25, and 5.34 in ascending order. This structured approach improves your ability to organize data and simplify calculations in both academic and real-world contexts. Understanding how to order numbers properly is a stepping stone to mastering more complex mathematical concepts.

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