Estimation and Approximation: Master the Art of Approximating Numbers

Question 1

Estimate the volume of a sphere with a radius of 5 cm. Use the formula V = (4/3)πr³. Which answer is closest?

Accepted Answer

524 cm³

Answer

400 cm³

Answer

600 cm³

Answer

800 cm³

Question 2

Which operation transforms 3.14159 into 3.14?

Accepted Answer

Round 3.14159 to the nearest hundredth

Answer

Truncate 3.14159 to the nearest integer

Answer

Estimate 3.14159 to the nearest tenth

Question 3

Calculate and express the result with the correct number of significant figures: 12.345 + 23.4

Accepted Answer

35.75

Answer

35.745

Answer

35.8

Answer

36

Question 4

Express 0.0000457 in scientific notation.

Accepted Answer

4.57 x 10^-5

Answer

45.7 x 10^-6

Answer

457 x 10^-7

Answer

4.57 x 10^-6

Question 5

Use the compatible numbers technique to estimate the sum of 234 and 456.

Accepted Answer

700

Answer

680

Answer

690

Answer

710

Question 6

Convert 2.3 x 10^6 to standard notation.

Accepted Answer

2,300,000

Answer

230,000

Answer

23,000

Answer

2,300

Question 7

Round 12,345 to the nearest thousand.

Accepted Answer

12,000

Answer

13,000

Answer

14,000

Answer

15,000

Question 8

Round the number 123.456 to the nearest ten.

Accepted Answer

124

Answer

120

Answer

123

Answer

130

Question 9

Express the number 0.000000123 in scientific notation.

Accepted Answer

1.23 x 10^-7

Answer

123 x 10^-6

Answer

1.23 x 10^7

Answer

123 x 10^7

Question 10

Which estimation technique involves rounding numbers to compatible values to find an approximate sum?

Accepted Answer

Compatible numbers estimation

Answer

Front-end estimation

Answer

Rounding estimation

Answer

Mental estimation

Question 11

Estimate the product of 23 and 47 using compatible numbers.

Accepted Answer

1,200

Answer

1,000

Answer

1,400

Answer

1,600

Question 12

In which scenario would estimation be most appropriate?

Accepted Answer

Estimating the number of people attending an event.

Answer

Calculating the exact area of a circle.

Answer

Solving a complex algebraic equation.

Answer

Measuring the length of a room with a ruler.

Question 13

Identify the common error when rounding numbers.

Accepted Answer

Not considering the place value of the digit being rounded.

Answer

Rounding to the nearest number.

Answer

Dropping digits that are significant.

Answer

Changing the value of the number being rounded.

Question 14

A rectangular garden has a length of 15 feet and a width of 12 feet. What is the estimated area of the garden?

Accepted Answer

180 square feet

Answer

160 square feet

Answer

200 square feet

Answer

220 square feet

Question 15

Which of the following operations will result in the greatest loss of accuracy?

Accepted Answer

Multiplying two numbers

Answer

Rounding a number to the nearest hundredth

Answer

Converting a fraction to a decimal

Answer

Adding two numbers

Question 16

Scientific notation is most commonly used in which of the following fields?

Accepted Answer

Chemistry

Answer

Biology

Answer

History

Answer

Literature

Question 17

Which of the following is NOT an advantage of using estimation techniques?

Accepted Answer

Guarantees an accurate answer

Answer

Saves time

Answer

Provides a reasonable approximation

Answer

Reduces the need for precise calculations

Question 18

When rounding a negative number, the result will always be a number that is:

Accepted Answer

Negative

Answer

Positive

Answer

Zero

Answer

Indeterminate

Question 19

Which of the following symbols is used to indicate that a number is an approximation?

Accepted Answer

≈

Answer

=

Answer

>

Answer

<

Question 20

Estimate the square root of 82 without using a calculator.

Accepted Answer

9

Answer

10

Question 21

Express 6,543,210 in scientific notation.

Accepted Answer

6.54321 x 10^6

Answer

65.4321 x 10^5

Question 22

Convert the number 0.0000000567 to scientific notation.

Accepted Answer

5.67 x 10^-8

Answer

5.67 x 10^-6

Answer

56.7 x 10^-9

Answer

567 x 10^-10

Question 23

Which of the following rules is NOT typically used when rounding numbers?

Accepted Answer

Round to the nearest even number.

Answer

Round to the nearest whole number.

Answer

Round to the nearest tenth.

Question 24

Express the number 6,543,210 in scientific notation.

Accepted Answer

6.54321 × 10^6

Answer

6.54321 × 10^-6

Answer

654,321 × 10^-3

Answer

6,543,210

Question 25

Which of the following is the correct rounding rule for the digit in the tenths place when rounding to the nearest hundredth?

Accepted Answer

Round up if the digit is 5 or greater; round down if it is less than 5.

Answer

Round up if the digit is 4 or greater; round down if it is less than 4.

Answer

Round up if the digit is 6 or greater; round down if it is less than 6.

Question 26

Express the number 0.000045 in scientific notation.

Accepted Answer

4.5 × 10^-5

Answer

0.45 × 10^-4

Answer

45 × 10^-6

Answer

450 × 10^-7

Question 27

Which of the following is an example of a significant digit?

Accepted Answer

The first non-zero digit in a number

Answer

The last digit in a number

Answer

A zero that is placed between two non-zero digits

Answer

A zero that is placed after the decimal point

Question 28

When adding a list of decimal numbers, which part should be aligned?

Accepted Answer

Decimal points

Answer

First digit

Answer

Last digit

Answer

Place value columns

Question 29

The area of a rectangle is approximately 250 square feet. If the length is 15 feet, estimate the width.

Accepted Answer

17 feet

Answer

15 feet

Answer

20 feet

Answer

25 feet

Question 30

Which of the following is not a valid reason to use estimation?

Accepted Answer

To get an exact answer

Answer

To make informed decisions

Answer

To simplify calculations

Answer

To check the reasonableness of an answer

Question 31

Which estimate is suitable for a number between 29 and 32?

Accepted Answer

30

Answer

25

Answer

40

Answer

35