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Chapter 4: Problem 84

Round 34.54389 to the nearest: Thousandth.

Short Answer

Expert verified
34.544

Step by step solution

01

Identify the thousandth place

First, locate the digit in the thousandth place of the number 34.54389. The digits after the decimal point are 5, 4, 3, 8, 9. Therefore, the digit in the thousandth place is 3.
02

Look at the next digit

Next, observe the digit immediately to the right of the thousandth place, which is the ten-thousandth place. In this case, the digit is 8.
03

Apply rounding rules

According to rounding rules, if the digit in the next place (ten-thousandth place) is 5 or higher, we round up the digit in the thousandth place by one. Since 8 is greater than 5, we round up the digit 3 to 4.
04

Rewrite the number

Replace the digits after the thousandth place with zeros, and remove any trailing zeros beyond the decimal point. Therefore, 34.54389 rounded to the nearest thousandth is 34.544.

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Key Concepts

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

Thousandth Place
One of the first steps in rounding numbers to a specific decimal place is understanding where that place is in the number. For rounding to the thousandth place, you need to count three digits to the right of the decimal point. For example, in the number 34.54389, the digits after the decimal point are 5, 4, 3, 8, and 9. The third digit (3) to the right of the decimal point is the thousandth place. Knowing this helps you identify which digit to consider for rounding.
Rounding Rules
Rounding follows specific rules that help keep numerical values accurate while simplifying them. The basic rule is to look at the digit immediately to the right of the place you are rounding to. In this example, to round 34.54389 to the nearest thousandth, you look at the digit in the ten-thousandth place, which is 8.
If this digit is 5 or higher, you round the digit in the thousandth place up by one. If it's 4 or lower, you keep the digit in the thousandth place the same. Since 8 is greater than 5, we round the digit 3 up to 4. Understanding these rules makes rounding straightforward and eliminates guesswork.
Decimal Points
Decimals are a way to represent fractions using the base ten system, and they are crucial in rounding processes. The decimal point separates the whole number part from the fractional part. Each digit after the decimal point indicates a fraction: the first digit is the tenths place, the second digit is the hundredths place, and the third digit is the thousandths place.
Properly identifying the place of each digit relative to the decimal point is essential for accurate rounding. In our example of 34.54389, the decimal point is after 34, making 5 the tenths place, 4 the hundredths place, and 3 the thousandths place. Knowing this helps you apply rounding rules correctly.

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Most popular questions from this chapter

Add. $$ \begin{array}{r} 81.008 \\ +\quad 3.409 \\ \hline \end{array} $$

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