Estimating a Product of Whole Numbers

Introduction

The whole numbers are first rounded as specified, i.e., rounded to the nearest ten, hundred and so on. Then the product of the rounded whole numbers is found to estimate the product of whole numbers.

Problem 1

Estimate the product 573 94 by first rounding each number so that it has only one non-zero digit.

Solution

Step 1:

We round each number such that it has only one non-zero digit

573 is a three-digit number. So its first digit is going to be the only non-zero digit and the other two digits would be zeros. It means rounding to nearest hundred. Since the tens digit, 7 is greater than 5, we round up 573 to 600.

Step 2:

94 is a two-digit number. Its first digit is going to be the only non-zero digit and the other digit would be zero. It means rounding to nearest ten. Since the ones digit, 4 is less than 5, we round down 94 to 90.

Step 3:

The estimate of the product after rounding

= 600 90 = 54,000

Problem 2

Estimate the product 2092 167 by first rounding each number so that it has only one non-zero digit.

Solution

Step 1:

We round each number such that it has only one non-zero digit

2092 is a four-digit number. So its first digit is going to be the only non-zero digit and the other three digits would be zeros. It means rounding to nearest thousand. Since the hundreds digit, 0 is less than 5, we round down 2092 to 2000.

Step 2:

167 is a three-digit number. Its first digit is going to be the only non-zero digit and the other two digits would be zero. It means rounding to nearest hundred. Since the tens digit, 6 is greater than 5, we round up 167 to 200.

Step 3:

The estimate of the product after rounding

= 2000 200 = 400,000