Problem 49 - Prealgebra

Question

Write each list of numbers in order from least to greatest. $$18 \%, \frac{1}{8}, 0.08$$

Step-by-Step Solution

Answer

0.08, \(\frac{1}{8}\), 18\%.

Step 1: Convert Percents and Fractions to Decimals

Begin by converting all the numbers to decimals.- For 18\%, move the decimal point two places to the left, resulting in 0.18.- For the fraction \(\frac{1}{8}\), divide 1 by 8 to get the decimal equivalent, which is 0.125.

Step 2: List All Decimals

Now that we have converted all numbers to decimals, list them as follows:- 0.08 remains the same.- 0.125 for \(\frac{1}{8}\).- 0.18 for 18\%.

Step 3: Arrange Decimals in Order

To arrange in order from least to greatest, compare the decimal values:- 0.08- 0.125- 0.18Thus, the numbers ordered from least to greatest are: 0.08, \(\frac{1}{8}\), 18\%.

Key Concepts

Percents to Decimals

Understanding how to convert percents into decimals is crucial for comparing different numerical formats. A percent represents a number out of 100. To transform a percent into a decimal, divide by 100. Turn the percent sign into a decimal by moving the decimal point two places to the left. For instance, if you have 18 gfpercent, you convert it to a decimal like this:

• Remove the percent sign, giving you 18.
• Then, divide by 100 or shift the decimal two places left to get 0.18.

This method applies universally to all percent values, making it easier to handle and compare numbers in decimal form.

Fractions to Decimals

Fractions and decimals are simply different ways to represent the same part of a whole. Converting a fraction to a decimal involves division. This means dividing the numerator (the top number) by the denominator (the bottom number). To convert the fraction \( \frac{1}{8} \):

• Perform the division 1 divided by 8.
• Doing this calculation on a calculator or by hand will give you a decimal result of approximately 0.125.

This conversion facilitates easy comparison with other numbers that are already in decimal form.

Comparing Decimals

Once you have all numbers in the decimal format, you can effortlessly compare them. Begin by lining up the numbers according to their decimal values. The key is to compare the digits starting from the left side. For example, comparing these decimals:

• 0.08
• 0.125
• 0.18

Start with the first decimal place:

• 0.08 has a zero, 0.125 has a one, and 0.18 has a one, making 0.08 the smallest because zero is less than one.

Then focus on the next decimals (if needed):

• Between 0.125 and 0.18, compare 0.125 and 0.18 at the second decimal place. Five is less than eight, so 0.125 precedes 0.18.

These steps help in ordering numbers from least to greatest based on their decimal values.