Problem 15 Estimate by rounding as directed... [FREE SOLUTION] (2024)

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Chapter 4: Problem 15

Estimate by rounding as directed. $$ \begin{aligned} &198.67432-24.5007\\\ &\text { nearest ten } \end{aligned} $$

Short Answer

Expert verified

The estimated result is 180.

Step by step solution

01

Understand the problem

The problem requires estimating the result of subtracting two numbers by rounding them to the nearest ten. The given numbers are 198.67432 and 24.5007.

02

Round the first number to the nearest ten

Round 198.67432 to the nearest ten. The digit in the tens place of 198.67432 is 9, and the next digit (hundreds place) is 1. Since the digit in the tens place is closer to 20, round up. So, 198.67432 rounds to 200.

03

Round the second number to the nearest ten

Round 24.5007 to the nearest ten. The digit in the tens place of 24.5007 is 4, and the next digit is 2. Since 4 is closer to 0 than to 10, round down. Hence, 24.5007 rounds to 20.

04

Subtract the rounded numbers

Subtract the rounded numbers from step 2 and 3: 200 - 20.

05

Calculate the result

Perform the subtraction: 200 - 20 = 180.

Key Concepts

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

nearest ten

When we are asked to round to the nearest ten, we look at the tens and units place of a number. For instance:
If we have 198.67432, we observe the digit in the tens place, which is '9', and the digit right before it (units place), which is '1'.
If the units digit is 5 or more, we round up. If it's less than 5, we round down.
So, for 198.67432, even though the 1 in the units place might normally cause us to round down, there's a trick here!
Ultimately, we rounded 198.67432 to 200 because the digit in the tens place is 9, which rounds to the next nearest hundred. For numbers like 24.5007, the digit in the tens place is '4', and the units digit is '2'.
Since 2 is less than 5, we round down, resulting in 20.
Applying these rules helps us to simplify numbers, making calculations easier.

estimation

Estimation is a fundamental concept in mathematics that helps in quickly finding an answer without needing an exact figure.
Here’s why it’s useful:

  • Simplifies complex calculations
  • Saves time
  • Offers a quick check on the accuracy of detailed calculations

When estimating, it’s important to round numbers to the nearest ten, hundred, or other convenient value.
This gives a general sense of the size of the numbers and the result of the operation.
For example, in our exercise, by rounding 198.67432 to 200 and 24.5007 to 20, subtraction becomes straightforward.
Learn to estimate well, and you’ll find yourself more comfortable with numbers in daily life and exams.

subtraction

Subtraction is a basic arithmetic operation that represents the operation of removing objects from a collection.
In our task, after rounding the numbers, we needed to subtract 20 from 200. Here’s how subtraction works step-by-step:
When subtracting smaller numbers from larger numbers, you essentially reduce the quantity.
For instance:

  • Start with the larger number: 200.
  • Subtract the smaller number: 200 - 20.
  • The result is 180.

Subtracting rounded numbers simplifies the process and provides an approximation close to the exact result.
It’s much easier to deal with especially when working with large or very detailed numbers.
Understanding subtraction and practicing it with rounding and estimation will improve accuracy and speed in solving mathematical problems.

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Problem 15 Estimate by rounding as directed... [FREE SOLUTION] (3)

Most popular questions from this chapter

What is the cost of 12.6 gal of gasoline at \(\$ 2.89\) per gallon? Round theanswer to the nearest cent.Add. $$ 4 \frac{1}{3}+2 \frac{1}{2} $$Simplify. $$ 200+40 \div 4 $$Add. $$ \begin{array}{r} 4203.28 \\ +\quad 3.39 \\ \hline \end{array} $$Add. $$ \begin{array}{r} 9.104 \\ +123.456 \\ \hline \end{array} $$
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Problem 15 Estimate by rounding as directed... [FREE SOLUTION] (2024)
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