Question

ActivityAccording to a survey conducted in 2007, there were an estimated 6.99 × 107 dogs, 3.61 × 107 cats, and 8.3 × 106 birds kept as pets in the United States. In this activity, you’ll add these three numbers in both standard form and in scientific notation and check whether you get the same sum.Question 1First, add the numbers using standard form.Part AConvert each of the three pet populations to standard form.Part BFind the total population of pet dogs, cats, and birds in standard form.Question 2Now add the populations in scientific notation.Part ARewrite each estimate so they all have the same power of 10.Part BNow that the three numbers have the same power of 10, find the sum using the Distributive Property.Part CIs the sum from part B in scientific notation? If not, write the sum in the scientific notation.Part DNow that you’ve added the populations in two different ways, compare your results. Are the answers you found in questions 1 and 2 the same? How can you tell?

Answer 1

To add the pet populations in standard form, convert each number to standard form and then add them together. To add the populations in scientific notation, rewrite the numbers with the same power of 10, then find the sum using the Distributive Property. The answers in questions 1 and 2 are the same, showing that the two methods yield the same result.

Step-by-step explanation:

Question 1

Part A: To convert each of the pet populations to standard form, we need to express them in the form a × 10^b, where a is a number between 1 and 10 and b is an integer. For example, 6.99 × 10^7 would be in standard form, but 6.99 × 10^7 would not. So, the conversions will be:

• Dogs: 6.99 × 10^7
• Cats: 3.61 × 10^7
• Birds: 8.3 × 10^6

Part B: To find the total population of pet dogs, cats, and birds in standard form, we simply add the converted numbers together. So, the sum is 6.99 × 10^7 + 3.61 × 10^7 + 8.3 × 10^6.

Question 2

Part A: To rewrite each estimate with the same power of 10, we need to adjust the exponents by moving the decimal point. Let's rewrite the numbers with an exponent of 7:

• Dogs: 6.99 × 10^7
• Cats: 3.61 × 10^7
• Birds: 8.3 × 10^7

Part B: Now that the three numbers have the same power of 10, we can find the sum using the Distributive Property. So, the sum is (6.99 + 3.61 + 8.3) × 10^7.

Part C: The sum from part B is already in scientific notation.

Comparison

The answers found in questions 1 and 2 are the same. This means that the standard form and the scientific notation methods yield the same result when adding the pet populations.