Name____________________
Ad. Math Review
1.) What exponent problem can you simplify correctly and still get the common mistake? Explain.
22 will have the same correct answer even if you do it the wrong way because if you multiply the
base of 2 by the exponent 2 you still get 4. You should be multiplying the base by itself two
times.
2.) When using your calculator to simplify exponents, what is a common mistake that can be made?
If you do not use the exponent button, you would need to type the expanded form of the
number in the calculator. When doing this, it is easy to lose track of how many times you typed
the base in the calculator. This occurs especially when you have exponents that are large.
3.) Why is there a slight delay on our calculators when the exponent button is being used? (What is
the calculator doing?)
When using the exponent button on your calculator, the calculator has a slight delay because it
is multiplying the expanded form of the number all in one step.
4.) What is really happening when we find the square root of a number?
When working with square roots, the number under the radical symbol is actually the area of a
square and the answer is the length of the side of a square.
5.) How can you estimate which two numbers the square root of 26 is between? Explain.
First you would find the two perfect squares that the square root of 26 falls between. In this
case, the square root of 25 and the square root of 36 will be used. Since we know the square
root of 25 is 5 and the square root of 36 is 6, we know that the square root of 26 must fall
between the whole numbers of 5 and 6. We also know the correct answer will be closer to 5
than 6 because 26 is closer to 25 than 36.
6.) Explain the rules for base 10 exponents.
If the exponent is positive, the number of zeros to be added to the right is the same as the
exponent.
If the exponent is negative, we put one less zero as the exponent. (to the left)
As number 7 states, we are really just counting place values
7.) What are we really counting when looking at the exponent of a base 10 problem?
We are counting how many place values to move to put into standard form.
8.) If we have a base 10 with a negative exponent, what two numbers will the standard form be
between?
Zero and one
9.) What is the use for scientific notation? Explain.
Scientific notation is used for abbreviating extremely large or small numbers with base 10
exponents.
10.) If I am given 10-4 and asked to list equivalent numbers, how should I talk myself through this
process? First, put the number back into standard form. You do this by moving four place
values to the left. 0.0001. Next, say the decimal the way your math teachers have taught you.
One ten thousandth. This literally gives you the fraction. From here, look at the denominator of
the fraction and change it to exponential and expanded form. In this case the denominator of
10,000 can be changed to 104 and 10x10x10x10. Therefore you will have 1/10,000, 1/104,
1/10x10x10x10.
11.) What is a common mistake that is made when doing scientific notation problems? Explain.
Many times students only count zeros when trying to figure out the exponent needed in
scientific notation form. Ex.) 103,000,000 some students will say 1.03x106 instead of the correct
answer of 1.03x108. Another common mistake is made when you put numbers back into
standard form. Ex.) 2.1092x109. Students will add9 zeros when only 5 are needed.(We already
have four place values after the decimal so we only need 5 more.)
12.) What two things can I tell instantly when looking at the exponent in a scientific notation
problem? I can tell which directions to go with the decimal and how many place values to
move. Ex.) 3.6x10-7. Since the exponent is negative I know I go left. I know to go 7 place values
since the exponent is 7.0.00000036 Seven place values between the old and new
decimals.
13.) Use a pattern to show that anything to the first power is the base number and anything to the
zero power is 1.
54=625
53=125
52=25
51=5
50=1
14.) What makes a perfect square “perfect” compared to other square root problems? Explain.
A perfect square is a square where the lengths of the sides of the square are whole numbers.
15.) Draw a model of the square root of 64 equals 8.
If you were to draw this square on grid paper, you would draw a square with the area of 64 units
squared and each side would be 8 units long
16.) Fred’s answer for the square root of 16 equals 8. What common mistake did he make? What
did he do to get 8 for an answer?
Fred made a common mistake with exponents. He multiplied the base by the exponent.
Basically Fred is saying that 82 is 8x2 which is 16. In all actuality 82 is 64.
17.) Billie said an equivalent answer for the number10-6 is 0.0000001. Is he correct? If not explain
why? Billie is incorrect. He went the right direction but he counted zeros instead of place
values. The correct answer is 0.000001
18.) Sampson was asked to put 317,000,000 into scientific notation form. He wrote 3.17x10 6. What
did he do wrong and what is the correct answer? Sampson is wrong because he added 6 zeros.
He only needed to add 4 zeros.
19.) Susie was asked to put 3.14x105 back into standard form. She wrote 31,400,000. Explain her
common mistake. Susie added 5 zeros when she only needed three zeros. Susie already had 2
place values after the decimal.
20.) She was also asked to put 2.86x107 back into standard form. On this problem, she wrote
2.8,600,000. Why is this wrong? Explain. What is the correct answer? This time she added the
correct number of zeros but she left the original decimal in her answer. The correct answer
would be 28,600,000.
21.) What is a common mistake made when people are ordering numbers in scientific notation
form? When people are ordering scientific notation, they often only look at the first part
instead of the exponent. Since the exponent shows us place value