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Chapter 5: Problem 73

In the following exercises, round each number to the nearest tenth. $$2.84$$

Short Answer

Expert verified
2.8

Step by step solution

01

Identify the Tenths Place

Look at the number 2.84. The tenths place is the first digit to the right of the decimal point, which is 8.
02

Identify the Hundredths Place

Look at the digit to the right of the tenths place to determine rounding. In this case, the hundredths place is 4.
03

Check the Rounding Rule

If the digit in the hundredths place is 5 or greater, round the tenths place up by one. If it is less than 5, keep the tenths place the same. Here, 4 is less than 5.
04

Round to the Nearest Tenth

Since 4 is less than 5, the tenths place will remain as 8. Thus, 2.84 rounded to the nearest tenth is 2.8.

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Key Concepts

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

nearest tenth
When you are asked to round a number to the nearest tenth, you need to focus on the first digit to the right of the decimal point. This digit is known as the tenths place. For example, in the number 2.84, the digit 8 is in the tenths place.
Rounding to the nearest tenth is especially useful in simplifying numbers, making them easier to work with in day-to-day scenarios like quick mental calculations or estimating costs.
decimal places
Decimal places are the digits that come after the decimal point in a number. They represent fractions of a whole number. For instance, in 2.84, there are two decimal places: the tenths place (8) and the hundredths place (4).
The more decimal places, the more precise the number. However, for many practical uses, you don't need extreme precision.
Let鈥檚 consider another example, 3.456. Here, 4 is the tenths place, 5 is the hundredths place, and 6 is the thousandths place.
rounding rules
Rounding numbers follows a set of rules to help you decide whether to round up or down.
  • If the digit in the next smallest decimal place (to the right) is 5 or greater, you round up.
  • If it is less than 5, you keep the digit in the target decimal place the same and drop the remaining digits.
In our exercise, the number was 2.84, and the hundredths place (4) is less than 5, so we keep the tenths place (8) the same. Thus, 2.84 rounded to the nearest tenth is 2.8.
prealgebra
Prealgebra is the foundation for most math concepts you'll encounter later on. In prealgebra, rounding numbers is a basic skill that comes in handy across different aspects of math and science.
By understanding how to round numbers effectively, you can easily simplify complex problems and arrive at approximations more quickly. This is a skill you will use frequently in everyday life as well as in more advanced mathematics.
It helps to practice different problems to get a good grip on when and how to round numbers appropriately.

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