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Chapter 7: Problem 107

Is the number 1.4 less than or greater than \(100 \% ?\)

Short Answer

Expert verified
1.4 is greater than 100%.

Step by step solution

01

- Understand the question

Determine whether the number 1.4 is less than or greater than 100%.
02

- Convert percentage to a decimal

Convert 100% to a decimal to simplify the comparison. We know that 100% equals 1.0 in decimal form.
03

- Compare the numbers

Compare 1.4 to the decimal equivalent of 100%, which is 1.0. Since 1.4 is greater than 1.0, we conclude that 1.4 is greater than 100%.

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Key Concepts

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

Converting Percentages to Decimals
To make comparisons between numbers and percentages easier, it's helpful to convert percentages to decimals. A percentage is simply a number out of 100. For example, 100% means '100 out of 100' and can be written as 100/100. This equals 1.0 in decimal form. So, 100% is the same as 1.0 when converted to a decimal. Converting percentages to decimals involves a simple step: divide the percentage by 100. Here's a quick way to remember this:
- To convert a percentage to a decimal, move the decimal point two places to the left.
For example:
- 75% becomes 0.75
- 25% becomes 0.25
- 10% becomes 0.1
This way, comparing percentages and decimals becomes straightforward.
Number Comparison
Comparing numbers involves determining which number is larger, smaller, or if they are equal. After converting percentages to decimals, it's easy to compare them with whole numbers. In our example, we were asked to compare 1.4 with 100%. We converted 100% to 1.0. Now, it's clear that we just need to see which is larger: 1.4 or 1.0. This process is critical when dealing with real-world problems such as discounts, interest rates, or growth percentages. Here are a few tips:
- Write both numbers in decimal form.
- Compare the whole number part first.
- If the whole number parts are the same, compare the decimal places one by one.
Understanding Percentages
Percentages are a way of expressing numbers as parts of a whole. The word 'percent' means 'per hundred,鈥� so 50% means 50 out of 100. Percentages are often used in everyday situations like sales, statistics, and data analysis. Here are some key points:
- 100% represents the whole or total.
- More than 100% means an amount greater than the total.
- Less than 100% means an amount less than the total.
Understanding how to convert percentages to decimals and compare them provides a strong foundation for solving many math problems and real-life situations.

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Most popular questions from this chapter

A salesperson receives a weekly salary of \(\$ 100,\) plus a \(5.5 \%\) commission on sales. Her salary last week was \(\$ 1090 .\) What were her sales that week?

Anne borrowed 4500 dollar from a bank that charges \(10 \%\) simple interest. If she repays the loan in \(2 \frac{1}{2}\) years, how much will she have to pay back?

It is customary to leave a \(15-20 \%\) tip for the server in a restaurant. However, when you are at a restaurant in a social setting, you probably do not want to take out a pencil and piece of paper to figure out the tip. It is more socially acceptable to compute the tip mentally. Try this method. Step 1: First, if the bill is not a whole dollar amount, simplify the calculations by rounding the bill to the next-higher whole dollar. Step 2: Take \(10 \%\) of the bill. This is the same as taking one-tenth of the bill. Move the decimal point to the left 1 place. Step 3: If you want to leave a 20\% tip, double the value found in step 2. Step 4: If you want to leave a \(15 \%\) tip, first note that \(15 \%\) is \(5 \%+10 \% .\) Therefore, add one-half of the value found in step 2 to the number in step 2 . Estimate a \(20 \%\) tip on a bill of \(\$ 57.65\) (Hint: Round up to \$58 first.)

Gloria borrowed 400 dollar for 18 months at \(8 \%\) simple interest. a. How much interest will Gloria have to pay? b. What will be the total amount that she has to pay back?

The amount of 12,000 dollar is invested at \(8 \%\) for 1 year. a. Compute the ending balance if the bank calculates simple interest b. Compute the ending balance if the bank calculates interest compounded quarterly. c. How much more interest is earned in the account with compound interest? (TABLE CAN NOT COPY)
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