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Chapter 5: Problem 589

In the following exercises, order each pair of numbers, using < or >. 0.33___\(\frac{5}{16}\)

Short Answer

Expert verified
0.33 > \(\frac{5}{16}\).

Step by step solution

01

Convert Fraction to Decimal

Convert the fraction \(\frac{5}{16}\) to a decimal by dividing the numerator by the denominator. \(\frac{5}{16} = 0.3125\).
02

Compare the Decimals

Compare the decimal forms of the numbers. We have 0.33 and 0.3125. Since 0.33 is greater than 0.3125, determine that 0.33 > 0.3125.
03

Write the Result Using > or

Use the comparison from the previous step to write the result: 0.33 > 0.3125 or 0.33 > \(\frac{5}{16}\).

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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 fractions to decimals is an essential skill in comparing and ordering numbers. This process makes it simpler to compare values because decimals are easier to handle. Here's how you do it:
First, take the fraction's numerator (the top number) and divide it by the denominator (the bottom number).
For example, in the exercise \( \frac{5}{16} \), you need to divide 5 by 16.

Performing the division gives us: \[ \frac{5}{16} = 0.3125 \].
Now, you have converted the fraction into a decimal: 0.3125.

Keep in mind, this method works for any fraction. With practice, you鈥檒l find converting fractions to decimals becomes a quick task.
Decimal Comparison
Comparing decimals involves checking their value place by place. Start by comparing the digits from left to right:

1. Begin with the digits in the tenths place.
2. If they are equal, move to the hundredths place, and so on.
3. Continue until you find a difference.

In our example, we compare 0.33 and 0.3125:
- The tenths place for both is the same: 3.
- Move to the hundredths place, where 0.33 has 3 and 0.3125 has 1.

Since 3 > 1, we determine that 0.33 is greater than 0.3125.

Therefore, \[ 0.33 > 0.3125 \]. Understanding this systematic place-by-place comparison helps you to accurately compare any pair of decimal numbers.
Ordering Numbers
Ordering numbers means arranging them from smallest to largest (ascending) or largest to smallest (descending). Here鈥檚 a simple method to do that:

1. If dealing with fractions, convert them to decimals first.
2. Compare each pair of numbers to determine their relative order.
3. Arrange the numbers based on your comparison results.

In the given exercise, we had two numbers to order: 0.33 and \[ \frac{5}{16} \].
- Convert \[ \frac{5}{16} \] to 0.3125.
- Compare 0.33 and 0.3125.

Since 0.33 > 0.3125, 0.33 is placed before 0.3125 in descending order.

Practicing these steps will give you confidence in ordering any set of numbers accurately.

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