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Chapter 2: Problem 80

Round the number to the given place value. \(2.975268 ;\) hundred-thousandths

Short Answer

Expert verified
The decimal number \(2.975268\) rounded to the hundred-thousandths place value is \(2.975263\).

Step by step solution

01

Identify the hundred-thousandths place

In the decimal number 2.975268, the first place after the decimal point is tenths, the second place is hundredths, the third is thousandths, the fourth is ten thousandths, the fifth is hundred thousandths, and the sixth is millionths. Therefore, the digit 2 in the number 2.975268 is in the hundred-thousandths place.
02

Look at the following digit for rounding

The following digit after the digit in hundred-thousandths place is 8. Now, if this digit is 5 or more, round up the last digit in the hundred-thousandths place, otherwise keep it the same.
03

Perform the rounding

Since the digit following the hundred-thousandths place is 8, which is greater than 5, round up the last digit in the hundred-thousandths place, which is \(2\), to \(3\). The resulting number, rounded to the hundred-thousandth place is \(2.975263\).

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Key Concepts

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

Decimal Place Value
Understanding decimal place value is essential when working with decimals. It refers to the position of digits to the right of the decimal point and determines the digit's value. Each place has a specific value.
  • The first position right after the decimal is the tenths place.
  • The second position is the hundredths place.
  • The third is the thousandths place.
  • The fourth is the ten-thousandths place.
  • The fifth is the hundred-thousandths place.
These positions help us in identifying the value of each digit. Grasping this concept is crucial when rounding decimals, as rounding depends on the place value of the digits.
Hundred-thousandths
The hundred-thousandths place is the fifth digit to the right of the decimal point. It is crucial because it allows for very fine distinctions in value. When working with the number 2.975268, we identify the fifth digit as being in the hundred-thousandths place.
In this case, that digit is 2. Knowing the hundred-thousandths place means we understand precisely where to look when rounding to this level. It is important to spot it accurately when following rounding rules.
Rounding Rules
Rounding involves adjusting a number to make it simpler or to fit a specific required precision. The most important rule in rounding is to look at the digit directly after the place value you're rounding to.
  • If that digit is 5 or greater, increase the digit in your target place by one.
  • If there's less than 5, keep the target digit the same.
In our example, the number was 2.975268 and we needed to round to the hundred-thousandths place. We looked at the sixth digit, 8, which is greater than 5. Therefore, we increased the digit 2 in the hundred-thousandths place to 3, giving us 2.975263.
Place Value Identification
Identifying place value is the first step in any rounding exercise. Place value identification allows you to spot which digit needs attention based on the task requirements.
  • Start from the decimal point and count the places to your target value.
  • Identify the relevant digit, in this case, for the hundred-thousandths, it is the 2 in 2.975268.
Once you know which digit is in the hundred-thousandths place, you can apply the rounding rules effectively. Misidentifying the place can lead to incorrect rounding so it's essential to double-check this step.

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Most popular questions from this chapter

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{2}{3} \quad \frac{7}{10}$$

The amount of an employee's earnings that is subject to federal withholding is called federal earnings. Find the federal earnings for an employee who earns \(\$ 694.89\) and has a withholding allowance of \(\$ 132.69 .\) Use the formula \(F=E-W,\) where \(F\) is the federal earnings, \(E\) is the employee's earnings, and \(W\) is the withholding allowance.

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$\frac{7}{4}$$

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{8}{15} \quad 0.543$$

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