Estimation - Examples, Exercises and Solutions

Understanding Estimation

Complete explanation with examples

Estimation

In fact, estimation allows us to guess (hence the redundancy) the supposed result, without performing the exact calculation.
That is, in certain cases, we don't need to know the solution precisely, a rough idea is sufficient to solve a particular mathematical problem.

Sometimes we are asked to compare mathematical expressions, draw deductions from one exercise to another, round numbers to simplify a calculation, and other similar tasks. 

For example:

It can be estimated that half of 1603 is approximately 800.

B - 50% of 1603  Estimation

Detailed explanation

Practice Estimation

Test your knowledge with 14 quizzes

Approximately what is \( \frac{190}{48} \) as a percentage?

Examples with solutions for Estimation

Step-by-step solutions included
Exercise #1

Approximately what is 625 \frac{6}{25} as a percentage?

Step-by-Step Solution

We look for the closest fraction to be able to divide the numerator by the denominator:

525 \frac{5}{25}

We break down the denominator into a multiplication exercise:

55×5 \frac{5}{5\times5}

We simplify:

15 \frac{1}{5}

We convert the fraction into a percentage

15×100=1005= \frac{1}{5}\times100=\frac{100}{5}=

20% 20\%

Answer:

20%

Video Solution
Exercise #2

Approximately what is 3470 \frac{34}{70} written as a percentage?

Step-by-Step Solution

To solve this problem, we'll convert the fraction 3470 \frac{34}{70} into a percentage by following these steps:

  • Step 1: Calculate the decimal equivalent of 3470 \frac{34}{70} .

  • Step 2: Multiply the decimal by 100 to convert it into a percentage.

Now, let's work through each step:
Step 1: Perform the division 3470 \frac{34}{70} . The result of dividing 34 by 70 is approximately 0.4857.
Step 2: Convert this decimal into a percentage by multiplying by 100:
0.4857×100%=48.57% 0.4857 \times 100\% = 48.57\% .

Since we want an approximate percentage from the given choices, we round 48.57% 48.57\% to the nearest whole number, which is 50% 50\% .

Therefore, the solution to the problem is 50% 50\% .

Answer:

50% 50\%

Video Solution
Exercise #3

Approximately what is 8011 \frac{80}{11} written as a percentage?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert the fraction 8011 \frac{80}{11} into a decimal number.
  • Step 2: Multiply the resulting decimal by 100 to find the percentage.
  • Step 3: Identify the correct choice from the provided options.

Now, let's work through each step:
Step 1: Divide 80 80 by 11 11 . The result is approximately 7.27 7.27 , as 11 11 goes into 80 80 7 times with a remainder.
Step 2: Multiply 7.27 7.27 by 100 100 to convert it to a percentage: 7.27×100=727% 7.27 \times 100 = 727\% . However, since the question asks for an approximation, use rounding to the nearest hundred percent: approximately 800% 800\%.
Step 3: Among the choices provided, the closest approximate percentage is 800%, corresponding to choice 4.

Therefore, the solution to the problem is 800%.

Answer:

800%

Video Solution
Exercise #4

Approximately what is 145 \frac{14}{5} as a percentage?

Step-by-Step Solution

We are looking for the closest fraction to be able to divide the numerator by the denominator:

155=3 \frac{15}{5}=3

Convert the fraction into percentage:

3×100=300 3\times100=300

300% 300\%

Answer:

300%

Video Solution
Exercise #5

Approximately what is 19 \frac{1}{9} as a percentage?

Step-by-Step Solution

To find the approximate percentage of 19 \frac{1}{9} , we follow these steps:

  • Step 1: Use the formula to convert the fraction to a percentage. This involves multiplying the fraction by 100:
Percentage=19×100 \text{Percentage} = \frac{1}{9} \times 100

Calculating the above expression gives us:

Percentage11.11% \text{Percentage} \approx 11.11\%

This result is approximately equal to 10% when rounding to the nearest whole number, which corresponds to choice 1 in the list of possible answers.

Therefore, the approximate percentage of 19 \frac{1}{9} is 10%.

Answer:

10%

Video Solution

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