UNIT I
Part 1
Maggie, Brian, and Joe are solving a division problem with scientific notation.
Step by step process
1. Maggie divided the numbers, then she separated the coefficients and the exponents.
6.89 x 10⁻⁴
—————
7.5 x 10⁻⁶
Then,
6.89 x 10⁻⁴
——
——
7.5
10⁻⁶
2. Next, she calculated the coefficient:
6.89
—— = 0.9187
7.5
= 0.92
3. Then,she simplified the exponents:
10⁻⁴
—— = 10 ⁻⁴- (⁻⁶)
10⁻⁶
= 10 ⁻⁴⁻⁶
= 10⁻¹⁰
4. Finally, she combined the results. Simplify further and move the decimal
0.92 x 10⁻¹⁰
= 9.2 x 10⁻¹¹
Maggie made a mistake in the 3rd and 4th step of simplify the
exponents and combining the result.
Simplified the exponents:
10 ⁻⁴
—— = 10 ⁻⁴- (⁻⁶)
10⁻⁶
= 10 ⁻⁴ (⁶)
= 10²
Combined the results. Simplify further and move the decimal.
0.92 x 10²
= 9.2 x 10³
Step by step process
1. Brian divided the numbers, then he separated the coefficients and the exponents.
6.89 x 10⁻⁴
—————
7.5 x 10⁻⁶
Then,
6.89 x 10⁻⁴
——
——
7.5
10⁻⁶
2. Next, he calculated the coefficient:
6.89
—— = 0.9187
7.5
= 0.92
3. Then,he simplified the exponents:
10⁻⁴
—— = 10 ⁻⁴–(⁻⁶)
10⁻⁶
= 10 ⁻⁴⁻⁶
= 10⁻¹⁰
4. Finally, he combined the results. Simplify further and move the decimal
0.92 x 10⁻¹⁰
= 9.2 x 10⁻⁻⁹
Brian made a mistake in the 3rd and 4th step of simplify the
exponents and combining the result.
Simplified the exponents:
10⁻⁴
—— = 10 ⁻⁴- (⁻⁶)
10⁻⁶
= 10 ⁻⁴ (⁶)
= 10²
Combined the results. Simplify further and move the decimal.
0.92 x 10²
= 9.2 x 10³
Step by step process
1. Joe divided the numbers, then he separated the coefficients and the exponents.
6.89 x 10⁻⁴
—————
7.5 x 10⁻⁶
Then,
6.89 x 10⁻⁴
——
——
7.5
10⁻⁶
2. Next, he calculated the coefficient:
6.89
—— = 0.9187
7.5
= 0.92
3. Then,he simplified the exponents:
10⁻⁴
—— = 10 ⁻⁴–(⁻⁶)
10⁻⁶
= 10 ⁻⁴(⁶)
= 10²
4. Finally, he combined the results. Simplify further and move the decimal
0.92 x 10²
= 9.2 x 10³
Joe is correct, He got the right answer.
Part 2:
Jerry, Beth, and Adam are all solving the same exponential problem, but have different
approaches.
Step by step process
1. First, He write the equation.
25²ˣ = 125¹⸍³
2. Then he rewrite the bases as powers of 5 in step two.
25 and 125 can be written as power of 5: 25 = 5² and 125 = 5³
Then he used the representations: (5²)²ˣ = (5³)¹⸍³
3. Next, he make the exponent simpler.
5²(²ˣ) = 5².²ˣ = 5⁴ˣ
5³(¹⸍³)= 5³.¹⸍³= 5¹
(5²(²ˣ) = 5¹ )
4. Then, he equate the exponents in step 4.
5⁴ˣ = 5¹ (cancel both number 5)
4x = 1
5. Last , he find a solution for x:
4x = 1
— —
(Cancel both number 4 in 4x )
4
4
—
4
x= 1/4
Jerry’s solution is correct. He correctly transformed the bases,
simplified the exponents and solved the result correctly.
Step by step process
1. First, She write the equation.
25²ˣ = 125¹⸍³
2. Then, she multiply 25²ˣ to itself .
25²ˣ (25²ˣ ) = 125 ⁶ˣ
Then she copied 125¹⸍³
125 ⁶ˣ = 125¹⸍³
3. Next, she equate the exponents in step 3.
125 ⁶ˣ = 125¹⸍³(cancel both number 125)
6x = 1/3
4. Last , she find a solution for x:
6x = 1
—
3
X = 6/1 (1/3) Cross multiplication (1x1=1) (6x3=18)
x= 1/18
Beth’s solution is incorrect.She didn’t rewrite the bases as powers of
5 in step 2.
2. Beth should rewrite the bases as powers of 5 in step two.
25 and 125 can be written as power of 5: 25 = 5² and 125 = 5³
Then used the representations: (5²)²ˣ = (5³)¹⸍³
Step by step process
1. First, He write the equation.
25²ˣ = 125¹⸍³
2. Then he multiply both exponents to number 3.
He used the representations:
25²ˣ(³) = 125¹⸍³(³)
3. Next, he make the exponent simpler. Multiply 2x to 3= 6x, then ⅓ x 3=1
25⁶ˣ = 125
4. He rewrite the bases as powers of 5.
5². ⁶ˣ = 5³
Then, he multiply the exponent
5¹²ˣ = 5³
5.Last , he find a solution for x:
5¹²ˣ = 5³ (Cancel number 5 on both side)
12 x = 3
x = 3/12
x= 3/12
Adam’s solution is incorrect. He didn’t rewrite the bases as powers
of 5 in step 2.
2. Adam should rewrite the bases as powers of 5 in step two.
25 and 125 can be written as power of 5: 25 = 5² and 125 = 5³
Then used the representations: (5²)²ˣ = (5³)¹⸍³
Part 3
Did Jerry multiply correctly? If so, explain his process. If not, then explain the error(s).
(4x³+2x²)(3x²+ 5x – 6)
=12x⁶+26x⁴+17x³-12x²
Step by step process
1. Multiply 4x³ by each term in the second polynomial:.
4x³ .3x² = 12x⁵
4x³ . 5x = 20x⁴
4x³ . – 6 = –24x³
2. Multiply 2x² by each term in the second polynomial:
2x² . 3x² = 6x⁴
2x² . 5x = 10x³
2x² . – 6 = –12x²
3. Then, he add all the terms together and combine like terms:
12x⁵ + 20x⁴ –24x³ 6x⁴ + 10x³ –12x²
4. He combined all like terms:
12x⁵ only one term with x⁵
20x⁴ + 6x⁴
= 26x⁴
–24x³ + 10x³ = –14x³
–12x² only one term with x²
Next, copy the result:
12x⁵ + 20x⁴ –14x³ –12x²
Jerry's final result are incorrect, he made an error in the multiplication
or combining like terms.
Jerry should multiply like this:
4x³ . – 6 = –24x³
2x² . 5x = 10x³
Then, he should combine the terms: