The population of a city is given as 3.45×10⁶. A nearby city has a population of 1.3×10⁵. What is the sum of the populations of the two cities in scientific notation?

Question

A. 3.58×10⁶
B. 4.75×10¹¹
C. 35.8+10⁵
D. 4.75×10⁵

Answer 1

To find the sum of the populations of the two cities, we can simply add the two numbers together.

3.45×10⁶ + 1.3×10⁵

To add these numbers in scientific notation, we need to line up the decimal places by moving the smaller number until it lines up with the larger number. In this case, we need to move the 1.3×10⁵ six places to the left to line up with the 3.45×10⁶.

1.3×10⁵ = 0.00013 × 10⁶ = 0.13×10⁶

Now we can add the two numbers:

3.45×10⁶ + 0.13×10⁶ = 3.58×10⁶

So, the sum of the populations of the two cities is 3.58×10⁶.

The correct answer is A. 3.58×10⁶.

Answer 2

An empty dump truck weighs about 2.8×10⁵ pounds. How many does it weigh if 15,300 pounds of trash is added? The answer should be in scientific notation.
A. 4.33×10⁵ pounds
B. 15,302.8 pounds
C. 2.953×10⁵ pounds
D. 29,530 pounds

Answer 3

To find the weight of the dump truck with the added trash, we need to add the weight of the truck to the weight of the trash.

2.8×10⁵ pounds + 15,300 pounds

Since the added weight of the trash is not in scientific notation, we can rewrite it as:

15,300 = 1.53×10⁴

Now we can add the two numbers:

2.8×10⁵ pounds + 1.53×10⁴ pounds = 2.8×10⁵ pounds + 1.53×10⁴ pounds = 2.953×10⁵ pounds

So, the weight of the dump truck with the added trash is 2.953×10⁵ pounds.

The correct answer is C. 2.953×10⁵ pounds.

Answer 4

The half-life of uranium-235 is 700,000,000 years. The half-life of uranium-238 is 4.463×10¹¹ years longer. What is the half-life of uranium-238? The answer should be in decimal form.
A. 516,300,000,000
B. 11,463,000,000
C. 4.4637 × 10¹¹
D. 447,000,000,000

Answer 5

To find the half-life of uranium-238, we need to find the difference between the half-life of uranium-238 and uranium-235.

The half-life of uranium-238 is the half-life of uranium-235 plus the additional time of 4.463×10¹¹ years.

Half-life of uranium-238 = Half-life of uranium-235 + 4.463×10¹¹ years

The half-life of uranium-235 is given as 700,000,000 years.

Half-life of uranium-238 = 700,000,000 years + 4.463×10¹¹ years

To simplify this, we need to express 700,000,000 years in scientific notation:

700,000,000 = 7×10⁸ years

Now we can add the two numbers:

Half-life of uranium-238 = 7×10⁸ years + 4.463×10¹¹ years

To add the numbers in scientific notation, we need to align the decimals:

7×10⁸ years = 0.7×10¹⁰ years

Half-life of uranium-238 = 0.7×10¹⁰ years + 4.463×10¹¹ years = 5.163×10¹¹ years

So, the half-life of uranium-238 is 5.163×10¹¹ years.

The correct answer is A. 516,300,000,000.

Answer 6

A mobile phone holds 1.28 × 10¹¹ bytes of storage. You can also pay more money to get an additional 384,000,000,000 bytes. How much storage would your phone have if you buy the additional bytes? The answer should be in scientific notation.
A. 385.28 × 10¹¹
B. 385,280,000,000
C. 5.12 × 10¹¹
D. 512 × 10⁹

Answer 7

To find the total storage of the mobile phone after buying the additional bytes, we need to add the original storage to the additional storage.

1.28 × 10¹¹ bytes + 384,000,000,000 bytes

Since the additional storage is not in scientific notation, we can rewrite it as:

384,000,000,000 = 3.84 × 10¹¹

Now we can add the two numbers:

1.28 × 10¹¹ bytes + 3.84 × 10¹¹ bytes = 1.28 × 10¹¹ bytes + 3.84 × 10¹¹ bytes = 5.12 × 10¹¹ bytes

So, the mobile phone would have a total storage of 5.12 × 10¹¹ bytes.

The correct answer is C. 5.12 × 10¹¹.