Comparing Numbers in Scientific Notation

The video tutorial explains how to compare numbers written in scientific notation. It covers two main situations: when exponents are different and when they are the same. For different exponents, the number with the larger exponent is greater. For the same exponents, the number with the larger factor is greater. Examples are provided for each case to illustrate the concepts. The video concludes with a summary of the methods discussed.

What is the first step in comparing numbers written in scientific notation?

• Convert them to standard form.

• Check if the exponents are the same or different.

• Compare the factors directly.

• Add the exponents together.

If two numbers in scientific notation have different exponents, how do you determine which is larger?

• Convert both to standard form and compare.

• The number with the smaller exponent is larger.

• Compare the factors.

• The number with the larger exponent is larger.

In the example of 3.4 x 10^7 and 1.61 x 10^8, which number is larger?

• Cannot be determined.

• They are equal.

• 1.61 x 10^8

• 3.4 x 10^7

What is the result of comparing 3.4 x 10^-5 and 1.61 x 10^-9?

• 3.4 x 10^-5 is larger.

• 1.61 x 10^-9 is larger.

• They are equal.

• Cannot be determined.

Why is 3.4 x 10^-5 greater than 1.61 x 10^-9?

• Because 3.4 is greater than 1.61.

• Because -5 is closer to zero than -9.

• Because -9 is closer to zero than -5.

• Because the factors are equal.

When comparing numbers with the same exponents, what should you compare?

• The exponents.

• The factors.

• The sum of the exponents and factors.

• The difference between the exponents.

In the example of 3.4 x 10^7 and 1.61 x 10^7, which number is larger?

• Cannot be determined.

• 3.4 x 10^7

• They are equal.

• 1.61 x 10^7

What should you do if the exponents are the same when comparing numbers in scientific notation?

• Compare the exponents again.

• Compare the factors.

• Convert to standard form.

• Add the exponents.

In the final example, what is the result of comparing 3.4 x 10^-5 and 1.61 x 10^-5?

• 1.61 x 10^-5 is larger.

• They are equal.

• 3.4 x 10^-5 is larger.

• Cannot be determined.

What is the key takeaway from the video on comparing numbers in scientific notation?

• Always convert to standard form first.

• Ignore the exponents and compare factors directly.

• Focus on comparing exponents first, then factors if needed.

• Scientific notation is not useful for comparison.