Repeating Decimals as Fractions
What are the steps to convert a repeating decimal to a fractions?
1. Assign the decimal as the variable.
2. Multiply by 10 (or 100, 1000, etc)
3. Subtract the variable from one side and the repeating decimal from the other.
4. Divide to solve for the variable.
How do we estimate square roots that ARE NOT PERFECT SQUARES?
We determine the perfect square above and below. Then, we estimate by trial and error until close enough. Our answer is an approximation.
How do we find roots of perfect squares and perfect cubes?
We look for what numbers would be squared or cubed to that perfect square or perfect cube. If it is a square root, we know the answer could be positive or negative. We know a cube root can only be positive or negative.
IE:
root2 4 = +- 2
What the inverse operation of an exponent?
Finding the root. So the inverse of squared is square root. The inverse of cubed is cube root.
How do we write a large/small number in scientific notation?
We move the decimal until there is ONE NON-ZERO digit in front of the decimal creating the Mantissa. Rewrite as an expression with the Mantissa multiplied by a power of 10 based upon the number of places we moved the decimal.
How do we add/subtract SN? How do we multiply/divide?
Add/Subtract
Change the smaller exponent if needed. Add or subtract the Mantissas. Keep the exponent. Confirm the answer is in SN.
Multiply/Divide
Multiply the Mantissas then add the exponents.
Divide the Mantissas then subtract the exponents.
Confirm the answer is in SN.
Write 0.1 (with the 1 repeating) as a decimal.
1/9
Estimate the root.
square root. 5
approx2.2
Evaluate the below.
square root 36
+- 6
Evaluate the below.
z^2 = 1
+- 1
Write in SN: 3,608,000,000
3.608 x 109
Multiply. Answer must be in SN.
(8.1 x 108) (1.2 x 10-4)
9.72 x 104
Write 0.12 (with the 12 repeating) as a decimal.
12/99 = 4/33
Estimate the root.
square root. 20
approx 4.4
Evaluate the below.
3 root 125
5
Evaluate the below.
x3 = -64
-4
A) 47.5 x 10-18
B) 0.891 x 1010
C) 1.4000 x 106
D) 5.92 x 107
A is not SN because there are TWO non-zero digits in front of the decimal
B is not SN because there is NO non-zero digit in front of the decimal
C is not SN because the zeros at the end of the decimal should be removed
D is in SN
Subtract. Answer must be in SN.
2.77 x 106 - 7.2 x 105
2.05 x 106
Write 0.2 (with the 2 repeating) as a fraction.
2/9
Estimate the root.
3root 51
approx 3.7
Evaluate the below.
square root 121
+- 11
Evaluate the below.
g2 = 36
+- 6
Compare with <, >, or =
1.47 x 10-5 0.00000147
**Be sure to convert to SN in your answer**
1.47 x 10-5 > 1.47 x 10-6
(5.98 x 10^7) / (2.6x10^4)
2.3 x 103
Write 0.45 (with the 45 repeating) as a fraction.
45/99 = 5/11
Estimate the root.
3root. 25
approx 2.3
Evaluate the below.
3 root -64
-4
Evaluate the below.
m3 = 125
5 (Why is it not
+-??)
Compare with <, >, or =
5.891 x 108 589,100,000
**Be sure to convert to SN in your answer**
5.891 x 108 = 5.891 x 108
8.4 x 108 + 8.5 x 106
8.485 x 108