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Chapter 1: Problem 26

Round the given value to the next greater whole number. $$71.00015$$

Short Answer

Expert verified
72

Step by step solution

01

Understand the Problem

We are given the number 71.00015 and asked to round it to the next greater whole number. To do this, we need to identify the digits involved and determine how rounding works with them.
02

Identify the Whole and Decimal Parts

The whole number part of 71.00015 is 71, and the decimal part is 0.00015. We need to determine whether to round this number up. Since we are asked to round up to the next greater whole number, we don't consider the usual rounding rules.
03

Apply the Rounding Up Rule

Since we want the next greater whole number irrespective of the decimal value, we simply add 1 to the whole number part. This means 71.00015 rounded to the next greater whole number becomes 72.

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Key Concepts

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

Whole Numbers
A whole number is basically a number without fractions or decimals; it stands on its own and isn't part of a larger figure. Consider whole numbers as the integers you're already familiar with, like 0, 1, 2, 3, and so forth. These numbers are straightforward because they do not have any digits after the decimal point. In our original exercise, the number 71.00015 contains 71 as its whole number part. Understanding the component of whole numbers allows for better grasping when switching back and forth between decimal and whole number calculations. Whole numbers are important because they simplify calculations and can make rounding easier.
Decimal Values
Decimal values are the numbers you see when a point (.) is used to indicate a fraction of a whole number. In 71.00015, 0.00015 is the decimal value. It represents a small part added onto the whole number, which in this case is 71. Decimals show the precision in numbers, often used when exact values are necessary, like in financial calculations. However, in certain situations, you might want to ignore these for simplicity, which is where rounding comes in handy. A deeper understanding of decimal values helps in recognizing what may be rounded or adjusted when focusing on whole numbers.
Rounding Rules
Rounding is a mathematical approach used to approximate numbers. The basic idea is to create a simpler, often more digestible number, either by rounding up or down.
  • **Standard Rounding:** Typically involves rounding up if the next decimal place is 5 or more, and rounding down if it's less than 5.
  • **Rounding Up:** Specifically means increasing the number to the nearest desired place. This might happen regardless of the actual digits present in the decimal, especially when you need a guaranteed higher whole number, as in the original exercise.
In our exercise, because we wanted the next greater whole number, we applied the rounding up rule regardless of the tiny decimal, increasing 71 to 72 directly. Learning these rules gives you flexibility and precision in managing numbers, precisely tailoring numbers to meet different scenarios.

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Most popular questions from this chapter

A small-appliance manufacturer finds that the profit \(P\) (in dollars) generated by producing \(x\) microwave ovens per week is given by the formula \(P=\frac{1}{10} x(300-x)\) provided that \(0 \leq x \leq 200 .\) How many ovens must be manufactured in a given week to generate a profit of 1250 dollar ?

Rewrite the group of numbers ordered from least to greatest. $$43,69,46,44,52,51$$

Rewrite the group of numbers ordered from least to greatest. $$0.6,-1.6,-1.4,1.7,1.2,-0.5$$

A farmer has a rectangular garden plot surrounded by \(200 \mathrm{ft}\) of fence. Find the length and width of the garden if its area is \(2400 \mathrm{ft}^{2}\).

Write the following decimal numbers in scientific notation and in E-notation. $$0.0000096$$
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