Rounding, Estimation, and Decimal Equivalents for CBEST Exam Study Guide (page 4)
The questions on the CBEST will include number rounding, estimation, and decimal equivalents. Most teachers studying for the CBEST need only a very basic brush up on these topics in order to master them.
Numbers are made up of digits that each represent a different value according to their position in the number. For instance, in the number 4,312.796, the 2 is in the ones place and equals 2 units. The 1 is in the tens place and equals 1 ten (10). The 3 is in the hundreds place and equals 3 hundreds (300). The 4 in the thousands place equals 4 thousands (4,000). To the right of the decimal, the 7 is in the tenths place and equals seven tenths (0.7, or ). The 9 is in the hundredths place and equals 9 hundredths (0.09, or ). The 6 is in the thousandths place and equals 6 thousandths (0.006, or ).
In a rounding question, you will be asked to round to the nearest tenths, hundreds, or other place.
Sample Rounding Question
- Round 4,312.986 to the nearest tenth.
Four Success Steps for Estimation Problems
To do a problem like this, you might want to try some of the following strategies:
- See whether you can round one number up and the other one down. This works if by so doing you are adding nearly the same amount to one number as you are subtracting from the other. Rounding one up and one down makes the product most accurate. For example, if the numbers were 71 and 89, you take one from 71 to get 70 and add one to 89 to get 90. 70 × 90 is very close to 71 × 89.
- An estimation question may be on the test in order to test your rounding skills. Round the numbers to one significant digit, or to the number of significant digits to which the numbers in the answers have been rounded.
- Eliminate answers that are further away from those you obtained after doing steps 1 and 2. For example, for 71 and 89, if answers given were 70 × 85 and 70 × 90, you can eliminate the former choice because 85 is further from 89 than 90 is.
- After eliminating, you can always multiply (subtract, add, divide) out the remaining answers to make sure your answer is correct.
Find the answer by walking through the Success Steps.
- The digit is 9, so it will either stay 9 or go to 0.
- The digit 8 is to the right of 9.
- This step does not apply; 8 is not less than 5.
- The 9 goes up one because 8 is more than 5.
- Change 9 to 0 and change 2 to 3. The answer is d, 4,313.0.
(Steps 6 and 7 don't apply.)
Now try a few more rounding questions.
- Round 45.789 to the nearest hundredth.
- Round 296.45 to the nearest ten.
- Round 345,687 to two significant digits.
- The digit you need to look at is 8; it will either stay 8 or go up to 9. The number 9 is to the right of 8; 9 is more than 5, so you change 8 to 9. The answer is 45.79.
- The digit is 9; the 9 will either stay 9 or go to 0. The number 6 is to the right of 9; it is more than 5, so change 9 to 0 and apply step 5, raising the 2 to the left of 9 to 3. Now apply step 7, and change digits to the right of the tens place to 0. The answer is 300.
- Here you need to apply step 6. Two places from the left is the ten thousands digit, a 4. Now apply step 1 and work through the steps: The digit is 4, so it will either stay 4 or go up to 5. Since the right-hand neighbor is 5, change the 4 to 5. Now apply step 7 and change all digits to the right of your new 5 to zero. The answer is 350,000.
Estimation requires rounding numbers before adding, subtracting, multiplying, or dividing. If you are given numerical answers, you might just want to multiply the two numbers without estimation and pick the answer that is the closest. Most likely, however, the problem will be more complicated than that.
Sample Estimation Question
- 42 × 57 is closest to
- 45 × 60
- 40 × 55
- 40 × 50
- 40 × 60
- 45 × 50
Here's how you could use the Success Steps to answer the sample question:
- You can round 42 down and 57 up, resulting in choice d.
- Rounding the numbers to one significant digit yields d also.
- Eliminate choices. a. Eliminated: 45 is further from 42 than 40 is. b. Maybe. c. Eliminated: 50 is further from 57 than 60 is. e. Eliminated: 45 is further from 42 and 50 is further from 57.
- Check the remaining answers. The product of choice b is 2,200. The product of choice d is 2,400. The actual product is 2,394, which makes choice d the closest, and therefore the correct answer.
You may be asked to compare two numbers to tell which one is greater. In many cases, you will need to know some basic decimal and percentage equivalents.
See how many of these you already know. For questions 6–11, state the decimal equivalent.
For questions 12–14, determine which number is greater.
- a. To compare these numbers more easily, add zeros after the shorter number to make the numbers both the same length: 0.93 = 0.9300. Compare 0.9300 and 0.9039. Then take out the decimals. You can see that 9,300 is larger than 9,039
- Extending the number would yield . (A line over a number means the number repeats indefinitely.) The number 333 is less than 339.
- Instead of dividing the denominator (91) into the numerator (45), look to see whether the two choices are close to any common number. You might notice that both numbers almost equal . 45 is less than half of 91, so is less than half. Half in decimals is 0.5 or 0.50; 0.52 is greater than 0.50, so it is greater than half. Thus, choice b is greater.
You may already know that when you deposit money in an account that earns 5% interest, you multiply the money in the bank by 0.05 to find out your interest for the year. 5% in decimal form is 0.05.
To change a percent to a decimal, move the decimal point two places to the left. To change a decimal to a percent, move the decimal point two places to the right. If there is no decimal indicated in the number, it is assumed that the decimal is after the ones place, or to the right of the number.
The percent always looks larger than its decimal equivalent. Here are some examples:
Number Written as a Percent 0.05 5% 0.9 90% 0.002 0.2% 0.0004 0.04% 3 300%
Rewrite the following numbers as percents.
Rewrite the following percents as decimals.
Here are some common decimal, percent, and fraction equivalents you should have at your fingertips. A line over a number indicates that the number is repeated indefinitely.
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