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Chapter 4: Problem 83

Round 34.54389 to the nearest: Ten-thousandth.

Short Answer

Expert verified
34.5439

Step by step solution

01

- Identify the Digit of Interest

Locate the ten-thousandth place in the number 34.54389. This is the fourth digit to the right of the decimal point, which is '4'.
02

- Look at the Next Digit

Look at the digit immediately to the right of the ten-thousandth place, which is the hundred-thousandth place. This digit is '3'.
03

- Apply Rounding Rules

Since the digit we observed in Step 2 ('3') is less than 5, we do not round up the ten-thousandth place digit ('4'). Instead, we leave it as it is.
04

- Construct the Rounded Number

Replace the digits to the right of the ten-thousandth place with zeros (if any), and drop the remaining decimal places. Therefore, the rounded number is 34.5439.

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Key Concepts

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

Decimal Places
Decimal places are crucial in mathematics and everyday life. They represent positions of digits to the right of the decimal point in a number. Each position has a specific place value. For instance:
  • First place after the decimal: tenths (0.1)
  • Second place: hundredths (0.01)
  • Third place: thousandths (0.001)
  • Fourth place: ten-thousandths (0.0001)
Understanding decimal places helps us grasp the concept of smaller or more precise measurements. In our example, the number 34.54389 has five decimal places. When rounding, we should know the significance of each place.
Rounding Rules
Rounding is a way to simplify numbers, making them easier to work with. To round any number, follow these basic steps:
  • Identify the digit that needs rounding based on place value.
  • Look at the digit immediately to its right.
  • If this right-side digit is 5 or higher, we round up. Otherwise, we round down or keep the digit as is.
Let鈥檚 apply these rules to round our number 34.54389 to the nearest ten-thousandth. First, identify the ten-thousandths place, which is '4'. Then, look at the next digit, '3'. Since '3' is less than 5, we leave '4' as it is. Thus, the rounded number is 34.5439.
Ten-thousandth Place
The ten-thousandth place in a decimal number is the fourth digit to the right of the decimal point. It is a very small value, specifically 0.0001. Knowing this place value helps in accurate rounding and representation of numbers. For example:
In the number 34.54389, the ten-thousandth place is occupied by '4'. By understanding and identifying this place, we can apply rounding rules correctly.

We checked the next digit, '3'. Since '3' is less than 5, we didn鈥檛 change '4'. Therefore, the number rounded to the nearest ten-thousandth is 34.5439. This method ensures precision in mathematical calculations and everyday applications.

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Most popular questions from this chapter

Subtract. $$ 6.003-2.3 $$

Find decimal notation for \(\frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7},\) and \(\frac{5}{7} .\) Observe the pattern and guess the decimal notation for \(\frac{6}{7}\).

The Colavitos own a house in Louisiana with an assessed value of \(\$ 187,300\). For every \(\$ 1000\) of assessed value, they pay \(\$ 4.90\) in property taxes each year. How much do they pay in property taxes each year?

Add. $$ \begin{array}{r} 641.803 \\ +\quad 14.935 \\ \hline \end{array} $$

The following were done on a calculator. Estimate to determine whether the decimal point was placed correctly. $$ 28.46901 \div 4.9187-2.5081=3.279813473 $$
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