Compare the following by writing them In Scientific Notation

To compare the values of 46310^-7 and 14.6310^-7, we can write them both in scientific notation:

463*10^-7 = 4.63 x 10^-5

14.63*10^-7 = 1.463 x 10^-5

Now we can see that 4.63 x 10^-5 is a larger number than 1.463 x 10^-5. Therefore, 46310^-7 is larger than 14.6310^-7.

What is scientific notation?

Scientific notation is a method of writing very large or very small numbers in a more concise and standardized format. It expresses a number as the product of a coefficient and a power of 10.

How to write a number in scientific notation?

To write a number in scientific notation, we first move the decimal point so that only one non-zero digit remains to the left of it. Then we multiply the result by a power of 10 which represents the number of places we moved the decimal point. The exponent is positive for very large numbers and negative for very small numbers.

Examples:

500,000 = 5 x 10^5 (move the decimal point 5 places to the left)

0.005 = 5 x 10^-3 (move the decimal point 3 places to the right)

5.6 x 10^4 (already in scientific notation)

0.00007 = 7 x 10^-5 (move the decimal point 5 places to the right)

Comparing the given numbers:

500,000 = 5 x 10^5

0.005 = 5 x 10^-3

5.6 x 10^4

0.00007 = 7 x 10^-5

Among the given options, the number written in scientific notation is option c) 5.6 x 10^4.

Why use scientific notation?

Scientific notation is useful because it allows us to express very large or very small numbers in a more manageable and standardized format. It is commonly used in scientific and mathematical contexts, as well as in engineering, finance, and other fields where large or small numbers are encountered.

Advantages of scientific notation:

It is concise and standardized, making it easier to compare and perform calculations with large or small numbers.

It eliminates the need for writing many zeros, which can be time-consuming and error-prone.

It makes it easier to express very small or very large numbers in a way that is more easily understood.

Examples of numbers in scientific notation:

The speed of light is approximately 3 x 10^8 meters per second.

The mass of the Earth is approximately 5.97 x 10^24 kilograms.

The diameter of a hydrogen atom is approximately 1 x 10^-10 meters.

Rules for writing numbers in scientific notation: 

The coefficient must be a number between 1 and 10 (inclusive).

The exponent must be an integer, and represents the number of places the decimal point was moved.

The exponent is positive for very large numbers, and negative for very small numbers.

In summary, scientific notation is a useful tool for expressing very large or very small numbers in a more concise and standardized format. It is commonly used in scientific and mathematical contexts, and has several advantages over other ways of expressing large or small numbers. 

What is 463*10^-7 in scientific notation?

a) 4.63 x 10^-4

b) 4.63 x 10^-5

c) 4.63 x 10^-6

d) 4.63 x 10^-7

Answer: d) 4.63 x 10^-7 

Explanation: To write a number in scientific notation, we express it as a product of a coefficient and a power of 10. In this case, the coefficient is 4.63 and the power of 10 is -7, giving us 4.63 x 10^-7. 

What is 14.63*10^-7 in scientific notation?

a) 1.463 x 10^-6

b) 1.463 x 10^-5

c) 1.463 x 10^-4

d) 1.463 x 10^-7

Answer: b) 1.463 x 10^-5 

Explanation: Again, we express the number as a product of a coefficient and a power of 10. The coefficient is 1.463 and the power of 10 is -7, giving us 1.463 x 10^-5. 

Which number is larger, 46310^-7 or 14.6310^-7?

a) 46310^-7

b) 14.6310^-7

c) They are equal

d) Cannot be determined

Answer: a) 463*10^-7

Explanation: We can compare the two numbers by writing them both in scientific notation, as shown above. We can see that 4.63 x 10^-5 is larger than 1.463 x 10^-5, so 46310^-7 is larger than 14.6310^-7.