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Chapter 2: Problem 70

Round the number to the given place value. \(18.40937 ;\) hundredths

Short Answer

Expert verified
The number 18.40937 rounded to the nearest hundredth is 18.41.

Step by step solution

01

Identify and Locate the Hundredths Place

In the number 18.40937, the hundredths place is the second digit after the decimal point, which is 0.
02

Check the Following Digit

The digit following the hundredths place is 9, which is greater than 5.
03

Apply the Rounding Rule

Since the following digit is greater than 5, add 1 to the digit in the hundredths place, converting it to 1 (0 + 1).
04

Discard Extra Decimal Places

Eliminate all digits to the right of the hundredths place. The final number becomes 18.41.

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Key Concepts

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

Decimal Places
When we talk about decimal places, we refer to the digits that appear to the right of the decimal point in a number. These digits represent portions smaller than one whole unit. For example, in the number 18.40937, there are five decimal places: 4 is in the tenths place, 0 in the hundredths, 9 in the thousandths, 3 in the ten-thousandths, and 7 in the hundred-thousandths.

Understanding decimal places is crucial because it informs how precise a number is. Each additional decimal place increases the precision of the number. When rounding numbers, identifying the correct decimal place is the first step to making sure you adjust your number accurately.
Place Value
Place value is the value of a digit based on its position within a number. Each digit in a number has a specific place value, which determines its contribution to the overall value of the number. For numbers with decimal places, the place value decreases by a factor of ten for each digit as you move from left to right.

For instance, in the number 18.40937:
  • 4 is in the tenths place, so it represents 0.4.
  • 0 is in the hundredths place, so it represents 0.00.
  • 9 is in the thousandths place, and represents 0.009.
Identifying the correct place value is essential, especially when rounding numbers, as it helps determine which digit will be affected by the rounding process.
Rounding Rule
The rounding rule helps us decide how to adjust a number based on its digit's place value and the following digit after the chosen place. When rounding:
  • If the digit following the place you are rounding to is less than 5, keep the digit in the rounded place the same.
  • If it is 5 or greater, increase the digit in the rounded place by 1.
In the original problem, we needed to round 18.40937 to hundredths. Here, the hundredths digit is 0. Looking at the next digit, which is 9, since 9 is greater than 5, we round up the digit in the hundredths place from 0 to 1.

After rounding, all digits beyond the chosen decimal place are discarded, resulting in the rounded number: 18.41. By following this rule, you ensure accuracy and precision when rounding numbers.

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Most popular questions from this chapter

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{5}{16} \quad 0.312$$

Convert the decimal to a fraction. $$9.95$$

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$\frac{8}{11}$$

For Exercises 172 to \(177,\) insert \(+,-, \times,\) or \(\div\) into the square so that the statement is true. $$3.46 \square 0.24=0.8304$$

For Exercises, give an example of a problem that meets the described condition. The fractions in your examples must be proper fractions with different denominators. If it is not possible to write a problem that meets the given condition, write "not possible." A proper fraction is subtracted from an improper fraction and the result is an improper fraction.
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