TABE Level D Math: Estimation

When you don’t need an exact answer to a computation, you can use estimation to find an approximate answer. Estimation takes advantage of certain math shortcuts to make a calculation quicker and easier. You can also get a better number sense by estimating answers instead of picking up a calculator.

Rounding to a Place Value
The idea of rounding a number to a place value is best illustrated by examples. Take the number 4736.
- Round 4736 to the nearest thousand. You have to determine if 4736 is closest to 1000 or 2000 or 3000 or 4000, etc. You can quickly narrow the search from 4000 or 5000 because 4736 is between these two. Because it is closer to 5000, 4736 rounded to the nearest thousand is 5000.
- Round 4736 to the nearest hundred. You can quickly narrow the search from 4700 and 4800 because 4736 is between these two. Because it is closer to 4700, 4736 rounded to the nearest hundred is 4700.
- Round 4736 to the nearest ten. You can quickly narrow the search from 4730 to 4740 because 4736 is between these two. Because it is closer to 4740, 4736 rounded to the nearest ten is 4740.
The idea is similar when rounding a decimal number. Take the number .2463 for example.
- Round .2463 to the nearest thousandth. The thousandths place is the third place to the right of the decimal. In this case the digit 6 is in the thousandths place. You can quickly narrow the search from .2460 to .2470 because .2463 is between these two. Because it is closer to .2460, .2463 rounded to the nearest thousandth is .2460 (=.246).
- Round .2463 to the nearest hundredth. The hundredths place is the second place to the right of the decimal. In this case the digit 4 is in the hundredths place. You can quickly narrow the search from .2400 to .2500 because .2463 is between these two. Because it is closer to .2500, .2463 rounded to the nearest hundredth is .2500 (=.25).
- Round .2643 to the nearest tenth. The tenths place is the first place to the right of the decimal. In this case the digit 2 is in the tenths place. You can quickly narrow the search from .2000 to.3000 because .2643 is between these two. Because it is closer to .3000, .2643 rounded to the nearest tenth is .3000 (.3).
You might be asked to round a decimal number to the nearest unit. Suppose you have to round .2643 to the nearest unit. The units place is the first place to the left of the decimal. In this case the digit 0 is in the units place. Therefore .2643 rounds to either 0 or 1. Because it is closer to 0, .2643 rounded to the nearest unit is 0.
Round 38.09 to the nearest unit. The digit 8 is in the units place. You can quickly narrow the search from 38 to 39. Because it is closer to 38, 38.09 rounded to the nearest unit is 38.

Rule for Rounding to a Place Value
The rule for rounding was shown in these examples. Call the digit in the place value you are rounding to the “rounding digit.” Look at the digit just to the right of the rounding digit. If this digit is less than 5, leave the rounding digit as is and change the remaining digits to the right to 0. If this digit is 5 or more, increase the rounding digit by 1 and change the remaining digits to the right to 0.
Some of the TABE problems just ask you to round numbers. For most of the problems rounding is only part of the problem. Rounded numbers are used in shortcut calculations to answer questions.

These shortcuts are illustrated in the following examples.

Example A. Which of the following is the best estimate of 297.4 ÷ 10.2? A. 6000 B. 3000 C. 1000 D. 30
Round 297.4 to the nearest hundred—300. Round 10.2 to the nearest ten—10. Multiply 300 by 10 to get 3000 (b).

Example B. Which of these is the best estimate of 5910.8 ÷ 6? A. 10 B. 100 C. 1000 D. 10,000
Round 5910.8 to . The correct answer is c.

Example C. One month a contractor earns $563, $612, $890, and $392 on four jobs. About how much did the contractor earn on these four jobs? A. $2500 B. $2400 C. $2300 D. $2200

Round the numbers to the nearest hundred because the answers are written to that place value. The rounded earnings are $600, $600, $900, and $400.
Because all of these are hundreds, just add 6, 6, 9, and 4 mentally to get 25. The correct answer is $2500 (a).

Example D. Clair rounded the number 8835 to the nearest 100. Steve rounded this number to the nearest 1000. What was the difference between the two rounded numbers? A. 35 B. 100 C. 150 D. 200
To the nearest 100, 8835 rounds to 8800. To the nearest 1000, 8835 rounds to 9000. The difference between 9000 and 8800 is 200 (d).

Example E. A wedding ceremony cost $4985. There were 98 guests at the wedding. The cost per guest was about A. $10 B. $50 C. $100 D. $150
Round $4985 to $5000. Round 98 guests to 100 guests. Divide $5000 by 100 to get $50 per guest (b) A. shortcut was used in Example A (see above). Move the decimal point one place to the right when multiplying by 10. Because the number 300 is the same as 300.0, you get 3000 when you move the decimal point one place to the right. In general, move the decimal point as many places to the right as there are zeros when multiplying by 10, 100, 1000, etc. A. shortcut used in Example C. Add only the rounding digits. Then attach however many 0s required to get the answer in units. A. shortcut was used in Example E. Move the decimal point two places to the left when dividing by 100. If you move the decimal point two places to the left in $5000, you get $50.00, which is the same as $50. In general, move the decimal point as many places to the left as there are zeros when dividing by 10,100, 1000, etc.

Estimation Practice
The table below shows the areas of the world’s continents rounded to the nearest thousand square miles. Study the table. Then do problems 1 and 2.


1. Which of these is the best estimate of how many times larger North America is than Australia? A. 2 B. 3 C. 4 D. 5

2. Which of these is the best estimate of the total area of the world’s continents? A. between 40 and 50 thousand square miles B. between 50 and 60 thousand square miles C. between 60 and 70 thousand square miles D. between 70 and 80 thousand square miles

3. Kathy bought a desk that was on sale for 30% off. The original price was $399. Which of these is the best estimate of the amount of money she saved by buying the desk on sale? A. $12 B. $16 C. $120 D. $160
Richard owns a house-cleaning business. He charges customers $14.50 per hour. Do problems 4, 5, and 6 about Richard’s business.

4. A customer would like Richard to do a major spring cleaning. Richard estimates the job will take about 6 hours. Which of these is the most reasonable estimate for the total amount he will charge? A. $50 B. $60 C. $70 D. $80

5. One week Richard did four housecleaning jobs with earnings of $32.50, $41, $50.50, and $58. Which of these is the best estimate of Richard’s earnings for the four jobs? A. $180 B. $200 C. $220 D. $240

6. Eight friends spent $49.20 to throw a party. If they share the cost equally, about how much will each pay (to the nearest dollar)? A. $5.00 B. $6.00 C. $7.00 D. $8.00

7. The Kincaid family used 72 gallons of heating oil last December. If heating oil cost $1.99 per gallon, what was this heating cost to the nearest $10? A. $70 B. $100 C. $140 D. $150

8. The opening on a wrench is .2875 inches. What is this measurement rounded to the nearest tenth of an inch? A. .2 B. .288 C. .28 D. .3

9. A book has 300 pages. Joe counted 202 words on one page. To the nearest 10,000, how many words are in the whole book? A. 60,000 B. 30,000 C. 20,000 D. 6,000

10. Carol plans to take a car trip. She will take 3 CDs with her. The playing times for the CDs are shown as minutes:seconds in the table.

To the nearest 10 minutes, how long will these three CDs last? A. 150 B. 160 C. 170 D. 180

Answers:  Estimation Practice

1. b

2. b

3. c

4. d

5. a

6. b

7. c

8. d

9. a

10. d