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Chapter 5: Problem 81

In the following exercises, round each number to the nearest hundredth. $$4.098$$

Short Answer

Expert verified
4.10

Step by step solution

01

Identify the hundredth place

The given number is 4.098. Identify the digits in the hundredth place (1/100 or 0.01). In this number, the hundredth place is occupied by the digit 9.
02

Look at the thousandth place

To determine if the number in the hundredth place should be rounded up or stay the same, look at the digit in the thousandth place (1/1000 or 0.001). In this case, the digit in the thousandth place is 8.
03

Apply rounding rules

The rule for rounding is: if the digit in the place to the right (thousandth place) is 5 or greater, round up the hundredth place by 1. Since the digit is 8, which is greater than 5, round 9 up by 1.
04

Write the final rounded number

After rounding, replace all digits to the right of the hundredth place with zeros. So, 4.098 rounded to the nearest hundredth is 4.10.

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Key Concepts

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

Place Value
Understanding place value is crucial when working with decimals. Place value tells us the value of each digit in a number based on its position. For decimals:
  • The first digit to the right of the decimal point is the tenths place (0.1).
  • The second digit to the right is the hundredths place (0.01).
  • The third digit to the right is the thousandths place (0.001).
In the number 4.098, the digit 0 is in the tenths place, the digit 9 is in the hundredths place, and the digit 8 is in the thousandths place. Knowing these positions helps us apply rounding rules accurately.
Rounding Rules
Rounding makes numbers simpler while keeping them close to the original value. When rounding decimals, remember these rules:
  • If the digit to the right of your rounding place is 5 or more, round up.
  • If the digit to the right is less than 5, keep the rounding place the same.
For example, in 4.098 when rounding to the nearest hundredth, look at the thousandths place. Since 8 (the digit here) is greater than 5, we round the hundredths place (9) up by 1. Therefore, 4.098 becomes 4.10.
Decimal Places
Decimal places indicate how many digits are to the right of the decimal point. The more decimal places a number has, the more precise it is. Common decimal places include:
  • Hundredths (two digits after the decimal point)
  • Thousandths (three digits after the decimal point)
When rounding to the nearest hundredth, we focus on the first two digits after the decimal point. For example, in 4.098, rounding to the nearest hundredth gives us 4.10. This representation means we've simplified yet kept the number as accurate as possible based on the given decimal places.

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