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Chapter 1: Problem 18

Round each decimal to two decimal places. $$5.164493$$

Short Answer

Expert verified
The number 5.164493 rounded to two decimal places is 5.17.

Step by step solution

01

Identify the Number to Round Up

In the given number \(5.164493\), the number to round up is 4 because it is in the second decimal place.
02

Look at the Digit to the Right

Look at the digit after the number identified to be rounded, which in this case is 4. The digit is 6.
03

Determine if You Should Round Up or Down

Since the digit 6 is more than 5, the number is rounded up. This means we should increase the 4 in the second decimal place by 1.
04

Perform the Rounding

Rounding up 4 we get 5. Therefore, the number rounded to two decimal places becomes \(5.17\).

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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 the positions that come after the decimal point in a number. They help us understand the precision of a number. For example, in the number 5.164493, each digit after the decimal, like 1, 6, 4, 4, 9, and 3, represents a decimal place.

When rounding decimals, we often specify how many decimal places we want. This number tells us how precise we need the approximation to be. Rounding to two decimal places, for example, means our final number will have two digits after the decimal point. These digits are significant in calculations where precision is important. Thus, understanding decimal places is crucial when dealing with rounding in mathematics.
Rounding Rules
Rounding rules are essential for deciding how a number should be brought to a simpler or more convenient form, particularly when dealing with decimals. To round correctly, we need to follow specific guidelines that help maintain accuracy.

Here's a helpful overview:
  • Identify the place you are rounding to. For two decimal places, look at the second digit after the decimal point.
  • Look at the next digit to the right (third decimal place) to decide whether to increase the second digit by one.
  • If this next digit is 5 or more, round up. If it's less than 5, leave the number as it is.
In our example, we looked at 5.164493. Since the third digit is 6, which is greater than 5, we round up the second decimal place from 4 to 5. That's why the rounded number is 5.17.

Following these rules ensures consistency and accuracy when working with numbers.
Step by Step Instructions
Following a step-by-step process can simplify rounding decimals and eliminate confusion. Here's an easy guide to rounding, using our example number 5.164493.

Start by finding the number in the second decimal place, which is 4 in our example.
  • Step 1: Identify the digit to round, here it's the second decimal place.
  • Step 2: Check the next digit, or the third decimal place, which is 6.
  • Step 3: Determine whether to round up or down based on the third digit's value.
Since the third digit is 6, which is greater than 5, we go to Step 4.

Increase the second decimal place (from 4 to 5) to round up. Now, our final rounded number is 5.17.
This methodical approach ensures rounding is done accurately, even with more complicated decimal numbers.

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Most popular questions from this chapter

Which property of real numbers justifies each statement? $$x y=y x$$

Which property of real numbers justifies each statement? $$(x+y)+z=z+(x+y)$$

In electronic data processing, the process of sorting records into sequential order is a common task. One sorting technique, called a selection sort, requires \(C\) comparisons to sort \(N\) records, where \(C\) and \(N\) are related by the formula $$ C=\frac{N(N-1)}{2} $$ How many comparisons are necessary to sort 10,000 records?

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