Worksheet Solutions: Guesstimation | Mental Mathematics for Class 8 PDF Download

Fill in the Blanks

Q1: The guesstimation method for addition involves rounding the original numbers __________.
Ans: up or down

Q2: To estimate the total cost while shopping, you can round prices to the nearest __________.
Ans: 50 cents

Q3: When estimating the square root of a number, you aim to find a number that, when multiplied by itself, approximates the original number. This number is called the __________.
Ans: square root

Q4: The Rule of 70 is used to estimate how long it takes for money to __________.
Ans: double

Q5: When paying off a loan, the monthly interest rate is usually the annual interest rate divided by __________.
Ans: 12

Q6: The Rule of 110 helps estimate how long it takes for your money to __________.
Ans: triple

Q7: To calculate a 7.75% sales tax, you can approximate it as slightly less than __________%.
Ans: 8%

Q8: The formula to estimate the monthly payment for a loan of $P in N months with a monthly interest rate of i is M ≈ __________.
Ans: (Pi)/(1 - (1 + i)^(-N))

Q9: The square root of most numbers is not a whole number, so your estimate is likely to contain a __________ or decimal point.
Ans: fraction

Q10: The relative error in guesstimation methods should ideally be kept __________ for accurate estimates.
Ans: small

Multiple Choice Questions

Q1: What is the main advantage of using Snapchat's temporary messages?
(a) Messages are saved indefinitely
(b) Messages can be viewed by anyone
(c) Messages are easy to share with friends
(d) Messages disappear after being viewed
Ans: (d) Messages disappear after being viewed

Q2: What is the Rule of 70 used for?
(a) Estimating square roots
(b) Calculating sales tax
(c) Estimating how long it takes money to double
(d) Finding the square of a number
Ans: (c) Estimating how long it takes money to double

Q3: When rounding numbers in guesstimation, what should you aim for to improve accuracy?
(a) Round up both numbers
(b) Round down both numbers
(c) Round in opposite directions
(d) Don't round numbers
Ans: (c) Round in opposite directions

Q4: What is the approximate monthly interest rate if the annual interest rate is 6%?
(a) 0.06
(b) 0.5
(c) 0.005
(d) 0.5%
Ans: (c) 0.005

Q5: How can you estimate the square root of a number like 87?
(a) Divide by 10
(b) Divide by 9
(c) Take the average of 9 and 10
(d) Divide by 2
Ans: (c) Take the average of 9 and 10

True and False

Q1: True/False: Snapchat's messages are permanent and can be viewed multiple times.
Ans: False

Q2: True/False: The Rule of 70 helps estimate how long it takes money to quadruple.
Ans: False

Q3: True/False: To improve accuracy in guesstimation, it's better to round both numbers in the same direction.
Ans: False

Q4: True/False: The monthly interest rate is typically higher than the annual interest rate.
Ans: False

Q5: True/False: The square root of most numbers is a whole number.
Ans: False

Short Answer Questions 

Q1: Explain the main advantage of using Snapchat's temporary messages.
Ans: Snapchat's temporary messages are advantageous because they disappear after being viewed, making it easier to share personal and temporary content without the concern of it being saved or viewed again in the future.

Q2: Describe how to estimate the total cost while shopping using guesstimation.
Ans: To estimate the total cost while shopping, you can round the prices of items to the nearest 50 cents (or other convenient amounts) as the cashier adds them up. Mentally add these rounded prices to get a ballpark estimate of the total.

Q3: How can you estimate the square root of a number using guesstimation? Provide an example.
Ans: To estimate the square root of a number using guesstimation, first find a number that, when squared, comes closest to the original number. Then, divide this number by 2 to get a reasonable estimate. For example, for the square root of 19, you might start with 4 as the closest square root, then estimate it as 4/2 = 2. But you can refine this estimate further.

Q4: Explain the Rule of 70 and provide an example.
Ans: The Rule of 70 is used to estimate how long it takes for money to double when invested at a certain annual interest rate. To use it, divide 70 by the annual interest rate. For example, with a 5% interest rate, it takes approximately 70/5 = 14 years for money to double.

Q5: How can you estimate the monthly payment for a loan using a monthly interest rate of i, borrowed amount P, and a loan term of N months?
Ans: You can use the formula M ≈ (Pi) / (1 - (1 + i)^(-N)). This formula provides an estimate of the monthly payment for the loan.

Q6: Explain how to estimate sales tax for a purchase using a given percentage.
Ans: To estimate sales tax for a purchase, multiply the purchase amount by the given percentage (expressed as a decimal). This gives you the estimated tax amount. For example, if the purchase is $100 and the sales tax is 7%, estimate it as 100 x 0.07 = $7.

Q7: What is the Rule of 110, and how does it work?
Ans: The Rule of 110 is used to estimate how long it takes for an investment to triple. To apply it, divide 110 by the annual interest rate. For example, with a 5% interest rate, it takes approximately 110/5 = 22 years for an investment to triple.

Q8: Explain how to estimate a 7.75% sales tax using the Rule of 70 and a 6% annual interest rate.
Ans: The Rule of 70 is used for estimating how long it takes for money to double, not for estimating sales tax. To estimate a 7.75% sales tax on a purchase, you would multiply the purchase amount by 0.0775 (7.75% expressed as a decimal).

Q9: Why might the square root of most numbers not be a whole number?
Ans: The square root of most numbers is not a whole number because many numbers are not perfect squares (the result of multiplying a number by itself). Square roots of non-perfect squares typically result in irrational numbers or fractions, which are not whole numbers.

Q10: In guesstimation, why is it important to keep the relative error small when making estimations?
Ans: It is important to keep the relative error small in guesstimation because a small relative error indicates that your estimate is close to the actual value. A larger relative error would mean a less accurate estimate, which defeats the purpose of guesstimation – making quick and reasonably accurate approximations for practical purposes.