Standard Form / Scientific Notation

Understanding Standard Form

By Tiberchous Eristhee

​Scientific Notation

Watch the video, taking notes on the main steps shown by Mr. J. Then, answer the following multiple-choice questions based on the video's content.

Multiple Choice

What are the two essential parts of any number written in scientific notation?

• A fraction and an integer

• A coefficient and a negative exponent

• A coefficient and a power of 10

• A standard number and a decimal

Multiple Choice

What is the correct range for the coefficient (the first number) in scientific notation, as described in the video?

• Any number greater than 1

• It must be greater than or equal to 1, and less than 10

• It must be less than 1

• It must be an integer (a whole number)

Multiple Choice

When converting a large number to scientific notation, what does the exponent on the power of 10 tell you?

• The number of zeros in the original number.

• The number of non-zero digits in the coefficient.

• The number of places the decimal point was moved.

• Whether the original number was a decimal or an integer.

Multiple Choice

Distance from Earth to the Sun: 149,600,000,000 meters. What is this number in scientific notation?

• $$14.96\times10^{10}\ meters$$

• 1 $$1.496\times10^{10}\ meters$$

• $$149.6\times10^9\ meters$$

• $$1.496\times10^{11}\ meters$$

Multiple Choice

Estimated number of stars in the Milky Way Galaxy: 200,000,000,000 stars. What is this number in scientific notation?

• $$20\times10^{10}stars$$

• $$2.0\times10^{10}stars$$

• $$2.0\times10^{11}\ stars$$

• $$0.2\times10^{12}\ stars$$

Multiple Choice

The speed of light is approximately 299,792,458 meters per second. Which option is the correct scientific notation for this value, rounded to three significant figures?

• $$2.99\times10^8m/s$$

• $$3.00\times10^8\ m/s$$

• $$29.9\times10^7\ m/s$$

• $$3.0\times10^9m/s$$

Multiple Choice

The height of Mount Everest: Approximately

$$8.84886\ \times10^3\ metres.\ Which\ of\ the\ following\ values\ is\ that\ equal\ to?$$

• 8,848.86 metres

• 8,000 metres

• 884 metres

• 0.884 metres

Open Ended

A scientist is comparing the size of a galaxy $$9\times10^{20}\ km\$$ to the distance a light-year covers $$9.46\times10^{12}\ km$$ . Why is scientific notation the preferred way to write and compare these measurements instead of standard form? (Hint: Think about efficiency and clarity).

Open Ended

602,000,000,000,000,000,000,000 (Avogadro's number) as $$6.02\times10^{23}$$ . Another student writes it as $$60.2\times10^{22}$$ . Explain which student is correct based on the definition shown in the video, and describe the error made by the incorrect student.

Open Ended

The coefficient in scientific notation must be between 1 and 10 (e.g., 1.2, not 12 or 0.12). Explain why this rule is essential for the notation to be standardized and effective for communication among scientists and mathematicians.

Math Response

Bonus:

$$0.5234\ x\ 10^{20}$$

Type answer here

Correct Answer: 0.5234\times10^{20}=52340000000000000000

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