/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 5 a. Estimate the sum: \(171+90+22... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 5

a. Estimate the sum: \(171+90+226\) b. Determine the actual sum. c. Was your estimate higher, lower, or the same as the actual sum?

Short Answer

Expert verified
The estimated sum is 490, the actual sum is 487; the estimate is slightly higher.

Step by step solution

01

Estimating the Sum

To estimate the sum of the numbers, we round each number to the nearest ten. The number 171 rounds to 170, 90 remains 90, and 226 rounds to 230. Adding these estimates together gives us: \(170 + 90 + 230 = 490\)
02

Calculating the Actual Sum

Now calculate the actual sum of the original numbers: \(171 + 90 + 226 = 487\)
03

Comparing Estimates to Actual

Compare the estimated sum to the actual sum. Our estimate was 490 and the actual sum is 487. Hence, the estimate of 490 is slightly higher than the actual sum of 487.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Rounding Numbers
Rounding numbers helps in simplifying calculations by adjusting each number to a more manageable value. To round a number to the nearest ten, you identify which two multiples of ten it falls between. Then, decide which of these multiples it is closer to. For instance:
  • The number 171 falls between 170 and 180. Since it is closer to 170, we round down to 170.
  • The number 90 is already a multiple of ten, so it remains 90.
  • The number 226 lies between 220 and 230. Since it is closer to 230, we round up to 230.
These rounded numbers are then used in further calculations such as estimating sums, leading to easier arithmetic.
Addition
Addition is the process of finding the total when two or more numbers are combined. When we add numbers like 171, 90, and 226, we are calculating their sum. This operation can be straightforward or a bit more complex depending on the numbers involved.Adding estimated values helps us quickly determine an approximate total. For instance, using our rounded numbers from before, we estimate: \[170 + 90 + 230 = 490\].On the other hand, calculating the exact sum of the original numbers yields:\[171 + 90 + 226 = 487\].While estimates provide quick approximations, actual addition results in precise totals, which is necessary when exactness is crucial.
Comparing Estimates
Comparing estimates to actual sums involves looking at both the rounded and exact calculations to determine any discrepancies between them. This process can provide insight into the accuracy of estimations. In the example of estimating and calculating the sum of 171, 90, and 226:
  • The estimate was 490.
  • The actual sum was 487.
Here, the estimated sum was higher than the actual sum by a small margin. These comparisons help us understand how rounding and estimation can influence the accuracy, often being slightly higher or lower than precise calculations. Understanding this relationship is crucial in checking whether estimates are close enough for practical purposes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Multiply vertically. Verify your answer using a calculator. a.$$\begin{array}{r} 34 \\\ \times \quad 4 \\\ \hline \end{array}$$ $$\text { b. } \begin{array}{r} 529 \\\ \times \quad 8 \\\ \hline \end{array}$$ c.$$\begin{array}{r} 67 \\\ \times \quad 5 \\\ \hline \end{array}$$ d.$$\begin{array}{r} 807 \\\ \times \quad 9 \\\ \hline \end{array}$$ e.$$\begin{array}{r} 125 \\\ \times \quad 8 \\\ \hline \end{array}$$ f.$$\begin{array}{r} 2001 \\\ \times \quad 25 \\\ \hline \end{array}$$ g.$$\begin{array}{r} 75 \\\ \text { g. } \times 52 \\\ \hline \end{array}$$ h$$\begin{array}{r} 1967 \\\ \times \quad 105 \\\ \hline \end{array}$$
Some of the fastest-growing jobs that earn the highest income and require a bachelor鈥檚 degree are listed in the following table with their median annual salaries for 2007. $$\begin{array}{|l|l|} \hline \text { OCCUPATION } & 2007 \text { MEDIAN ANNUAL SALARY, } \$ \\\ \hline \text { Network systems and data } & 68,224 \\\ \text { communications analysts } & {} \\\ \hline \text { Computer software engineers, } & 83,138 \\\ \text { applications } & {} \\\ \hline \text { Personal financial advisors } & 67,662 \\\ \text { Financial analysts } & 70,408 \\\ \text { Computer systems analysts } & 73,091 \\\ \hline \end{array}$$ a. Round each median salary to the nearest hundred. b. Round each median salary to the nearest thousand. c. Is the median salary of personal financial advisors as much as that of network systems and data communications analysts? Justify your answer.
Evaluate each expression. Check your answers with a calculator. a. \(7(20+5)\) b. \(7 \cdot 20+5\) c. \(7 \cdot 20+7 \cdot 5\) d. \(20+7 \cdot 5\) e. Which two of the preceding arithmetic expressions have the same answer? f. State the property that produces the same answer for that pair of expressions.
Evaluate each expression. Check your answers with a calculator. a. \(20(100-2)\) b. \(20 \cdot 100-2\) c. \(20 \cdot 100-20 \cdot 2\) d. \(100-20 \cdot 2\) e. Which two of the preceding arithmetic expressions have the same answer? f. State the property that produces the same answer for that pair of expressions.
List all possible factorizations of the following numbers. a. 6 b. 15 c. 35 d. 22
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.