liz - 8^2 x 8^6 = 8^18
chris - 8^3 x 8^6 =8^9
jen - 8^3 x 8^6 = 64^9
a) who completed it correctly
b) what did the other 2 do wrong
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Miriam and Priya are dividing numbers written in scientific notation. (3 points)
Miriam’s expression: Priya’s expression:
2.8x109 2.8x102
1.4x104 1.4x10-3
Without completing the division, explain how can you determine that their answers will have the same value.
What is the value of their expressions written in scientific notation?
What is the value of their expressions written in standard form?
chris is correct
the base does not change, and you add exponents
2.8/1.4 = 2 regardless of the power of 10
when dividing, subtract exponents
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@oobleck , can you please elaborate on the second question ?
a) Liz completed it correctly.
b) Chris and Jen both made a mistake. They multiplied the exponents instead of adding them. In exponential notation, when you multiply two numbers with the same base, you add the exponents. So, the correct calculations for Chris and Jen should be:
Chris: 8^3 x 8^6 = 8^(3+6) = 8^9
Jen: 8^3 x 8^6 = (2^6)^3 x (2^6)^6 = 64^3 x 64^6 = 64^(3+6) = 64^9
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To determine that Miriam and Priya's answers will have the same value without completing the division, you can look at the bases (2.8 and 1.4) and the exponents (9 and -3). Since the base is the same (2.8), and the exponents have opposite signs (9 and -3), you can conclude that their answers will have the same value.
The value of their expressions written in scientific notation would be:
Miriam: 2.8 x 10^9
Priya: 2.8 x 10^-3
The value of their expressions written in standard form would be:
Miriam: 2,800,000,000
Priya: 0.0028