Estimating and Rounding

Estimating is an excellent skill to have for the high school equivalency test and everyday life.  When you go shopping or out to eat, for example, you may not always have your calculator or a piece of paper with you. You can learn to do all kinds of math in your head with a few tips and techniques.  On the high school equivalency test, you can catch many of your mistakes by estimating the answer and asking yourself if the answer makes sense.

To be able to estimate, you have to know how to round off numbers, so that is where we will begin.

Rounding and Place Value
Rounding is a way of making numbers easier to read and easier to use.  If we round numbers, we can estimate more easily.  To round whole numbers you must know the place value of every digit in a whole number.  Refer to the place value chart below if you need to refresh.

In the above chart:
The 6 is in the millions place.
Its value is 6 millions or 6,000,000.

The 4 is in the hundred thousands place.
Its value is 4 hundred thousand or 400,000.

The second 2 is in the tens place.
Its value is 2 tens or 20.

We read and write this number as: 6 million, four hundred fifty-two thousand, 5 hundred twenty-one or 6,452,521.

Notice that the commas are used to separate digits into groups of three.  Starting at the right end of the number count 1,2,3 comma-1,2,3 comma.
Commas are usually used in numbers with five digits or more, such as 62,109 and 1,430,112.
Four-digit numbers can use a comma or not.  For example, both 3200 and 3,200 are correct.

 

Try a few:
What is the value of the underlined digit?

1. 18,662
2. 209,341
3. 768,019
4. 1,925,678
5. 215, 374,291
6. 47,592
7. 7,957
8. 4,297,422
9. 427, 495
10. 69,410

 

Answers:
1.  8 thousand or 8,000
2.  4 tens or 40
3.  7 hundred-thousands or 700,000
4.  5 thousands or 5,000
5.  1 one or 1
6.  9 tens or 90
7.  9 hundreds or 900
8.  9 ten-thousands or 90,000
9.  4 hundred-thousands or 400,000
10.  4 hundreds or 400 (back to top)

 

Reading and Writing Large Numbers
Writing large numbers can be cumbersome and difficult.  Here are a few rules to keep in mind:

To read a large number, read the first group of digits before the comma. The names of the commas are:
_ _ _, (trillion) _ _ _ , (billion) _ _ _ , (million) _ _ _ , (thousand) _ _ _

For example, 301, 456, 257, 912, 542 would be read as:
three hundred  one (trillion), four hundred fifty-six (billion), two hundred fifty seven (million), nine hundred twelve (thousand), five hundred forty-two
(Do not say the word “and” between the numbers.  The one exception to this will be discussed later in the decimal section.)

Hyphens are normally used in writing numbers from 21 (twenty-one) to 99 (ninety-nine) and in writing fractions when they are written in words 5/8 (five-eighths).

Zeros are sometimes used to fill up a three-place period, but they are not read.  062 is read “sixty-two” and 008 is read “eight”.

EXAMPLE 1: Write 13, 023 using words.
                        thirteen thousand twenty-three

EXAMPLE 2: Write 459, 312 using words.
                         four hundred fifty-nine thousand, three hundred twelve

EXAMPLE 3:  Write 5, 690, 185 using words.
                        five million, six hundred ninety thousand, one hundred eighty-five


Now it’s your turn:
Write each number using digits.

1. six hundred forty-five thousand, three hundred ten 
2. eighty-seven thousand, four hundred sixteen 
3. ten thousand, eighty-nine 
4. eight million, four hundred twenty thousand, one hundred six 
5. one thousand two hundred fifty-nine 
6. forty-five thousand, ninety-nine
7. eight hundred seventy-five thousand, four hundred thirty-eight 
8. seven million, six hundred fifty thousand, three hundred 
9. three hundred nineteen million, two thousand, one hundred ten 
10. seventy-eight million, nine hundred twenty-two thousand, three hundred fifty-one 

Answers
1. 645,310; 2. 87,416; 3. 10,089; 4. 8,420,106; 5. 1,259; 6. 45,099; 7. 875,438; 8. 7,650,300; 9. 319,002,110; 10. 78,922,351 (back to top)

 

 

Rounding Whole Numbers
We do not always use exact numbers. For example, a sports announcer might estimate that 30,000 people attended a football game when there were really 29,768 people there.

Often an estimate is more useful than an exact amount.  A contractor may estimate the cost of new aluminum siding for your house.  The contractor would calculate the cost of materials and labor, using rounded numbers.

Suppose that you have $49 in your pocket.  You would probably say, “I have about $50 in my pocket.” 

Or say you are eating dinner out and the bill comes to $14.72.  You might say to yourself, “That is close to $15, so that is what I’ll base my tip on.”  (If you’re cheap you might say I’ll tip on $14, but according to rounding rules, $14.72 is really closer to $15 than $14.)

When you round off a number, you are finding a whole number that is closest to that number and easy to work with.  This allows you to work problems quicker and even to do them in your head.  We will talk more about estimating in the next section.

Here are the rounding rules for whole numbers:

EXAMPLE 1Round 89 to the nearest ten.
            STEP 1:  Underline the tens digit.   89

            STEP 2:  Look at the number to the right of the underlined number.   89      
                           Is it 5 or greater?  YES, so add 1 to the underlined number.
                           ( 8 becomes 9)

            STEP 3:  Change all remaining numbers past the tens spot to zeros.
                                    90

            So 89 becomes 90 when rounded to the nearest ten.

EXAMPLE 2:  Round 257 to the nearest hundred.  Is 257 closer to 200 or 300?  Let’s see.
            STEP 1:  Underline the digit in the hundreds place.
                            257

            STEP 2:  Look at the number to the right of the underlined digit. 257  
                         Is it 5 or greater?  YES, so add 1 to the underlined digit (3).
                         257 becomes 357

            STEP 3:  Change all remaining digits to the right of the underlined number to zero.
                         357 becomes 300

            So 257 rounded to the nearest hundred is 300.

EXAMPLE 3:  Round 1475 to the nearest thousand.
            STEP 1:  Underline the thousands place.  1475

            STEP 2:  Look at the number to the right of the thousands place. 14
                          Is it 5 or greater?  NO,  so the 1 stays the same.

            STEP  3:  Every digit to the right of the thousands place becomes zero.
                         1000

So 1475 rounded to the nearest thousand becomes 1000.  Therefore, 1475 is closer to 1000 than to 2000.


You try it:
1.  Round 663 to the nearest hundred.
2.  Round 2776 to the nearest thousand.  
3.  Round 7004 to the nearest thousand.         
4.  Round 81,765 to the nearest ten.
5.  Round 482,580 to the nearest hundred-thousand.
6.  Round 654,387 to the nearest hundred.
7.  Round 789,257 to the nearest ten-thousand.
8.  Round 4, 654, 201 to the nearest million.
9.  Round 43, 457 to the nearest thousand.
10. Round  471, 523 to the nearest ten.

Answers:
1. 700  The number past the hundreds place is 5 or more, so add 1 to the hundreds place.
2. 3000  The number past the thousands place is 5 or more, so add 1 to the thousands place.
3. 7000  The number to the right of the thousands place is less than 5, so the thousands place remains the same.
4. 81,770  The number to the right of the tens place is 5 or more, so add 1 to the tens place.
5. 500,000  The number to the right of the hundred-thousands place is 5 or more, so add 1 to the hundred-thousands place.
6. 654,400  The number to the right of the hundreds place is 5 or more, so add 1 to the hundreds place.
7. 790,000  The number to the right of the ten-thousands place is 5 or greater, so add 1 to the ten-thousands place.
8. 5,000,000  The number to the right of the millions place is 5 or more, so add 1 to the millions place.
9. 43,000  The number to the right of the thousands place is less than 5, so the number in the thousands place remains the same.
10. 471,520  The number to the right of the tens place is less than 5, so the number in the tens place remains the same. (back to top)

 

To finish off this section, let’s try a few word problems:
Choose the correct answer to each problem.

1.     Sam and Sue bought a new car for $12,942. Which of the following rounds the price of the car to the nearest thousand dollars? 

2.     The Electrical Parts Factory made 875,112 connectors during the month of January.  What is the number of connectors produced rounded to the nearest ten thousand? 

3.     Of the following people, whose weight is 160 pounds when rounded to the nearest ten? 

4.     Max Gilliam won his school’s senior class election with 438 votes.  Rounded to the nearest hundred, how many votes did he receive? 

5.     A real estate appraiser told Mrs. Suzold that the value of her home was $147,500.  Which of the following expresses the value of the house to the nearest ten thousand dollars? 

Answers: 1. $13,000; 2. 880,000; 3. Juan at 156 pounds; 4. 400; 5. $150,000 (back to top)