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SCIENTIFIC
2nd SIN COS TAN OFF
ON/C
SIN-1 COS-1 TAN-1
Do You Understand?
1. Essential Question What is scientific
notation and why is it used?
2. Critique Reasoning Taylor states that 2,800,000
in scientific notation is 2.8 × 10-6 because the
number has six places to the right of the 2. Is
Taylor’s reasoning correct?
3. Construct Arguments Sam will write 0.000032
in scientific notation. Sam thinks that the
exponent of 10 will be positive. Do you agree?
Construct an argument to support your response.
Do You Know How?
4. Express 586,400,000 in scientific notation.
5. The genetic information of almost
every living thing is stored in a tiny
strand called DNA. Human DNA is
3.4 × 10-8 meter long. Write the
length in standard form.
6. The largest virus known to man is the Megavirus,
which measures 0.00000044 meter across. Express
this number in scientific notation.
7. How would you write
the number displayed
on the calculator screen
in standard form:7.6e!2

All Answers 1

Answered by GPT-5 mini AI
Here are answers and brief explanations for each item:

1. What is scientific notation and why is it used?
- Scientific notation writes a number as a × 10^n where 1 ≤ |a| < 10 and n is an integer. It is used to make very large or very small numbers easier to read, compare, and compute with.

2. Critique Taylor’s reasoning about 2,800,000
- Taylor is incorrect. 2,800,000 = 2.8 × 10^6. You move the decimal left 6 places to get 2.8, so the exponent is +6 (positive for numbers greater than 1).

3. Construct an argument about 0.000032
- Sam is incorrect. Numbers less than 1 require a negative exponent. 0.000032 = 3.2 × 10^-5 because you move the decimal 5 places to the right to get 3.2, so the exponent is -5.

4. Express 586,400,000 in scientific notation.
- 586,400,000 = 5.864 × 10^8

5. Write 3.4 × 10^-8 meters in standard form.
- 3.4 × 10^-8 m = 0.000000034 m

6. Express 0.00000044 meter in scientific notation.
- 0.00000044 = 4.4 × 10^-7

7. Write the calculator display 7.6e2 in standard form.
- 7.6e2 = 7.6 × 10^2 = 760