Question

I need help, I don't quite get this. This assignment is worth a lot so please help! Thanks, just look at the image and please tell me how you did it.

Answer 1

Answer:

  1.98•10¹⁰

Step-by-step explanation:

To find the total number of messages sent in a month, multiply the number of teenagers by the number of messages each sent. That product is ...

  22,000,000 × 900 = 19,800,000,000

To provide the answer in the requested form, you must convert this number to scientific notation. That means you express the number as a product of a mantissa and a power of 10.

The mantissa is the leading significant digits, with the first one written to the left of the decimal point. In this number, the mantissa is 1.98.

The power of 10 used is the number that must multiply the mantissa so that the result is 19,800,000,000. In other words, you want to express the number 10 billion as a power of 10:

  19,800,000,000 = 1.98×10,000,000,000

Since you're familiar with powers of 10, you know the exponent of 10 is the number of zeros the number has: 10. So, this number is ...

  1.98•10¹⁰

In plain text, we use a caret (^) to signify an exponent (and an asterisk for multiplication), so we would write the number as

  1.98*10^10.

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Comment on the attachment

Your scientific or graphing calculator has a mode for displaying numbers in scientific notation. You can use that to find or check your answer.

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Comment on scientific notation

Scientific notation is closely related to place value. Since you understand our place value number system, you know that the value of each place in a decimal number is 10 times that of the place to its right and 1/10 that of the place to its left. In "expanded form", the number 1234.56 can be written as ...

  1234.56 = 1000 +200 +30 +4 +0.5 +0.06

or as ...

  1234.56 = 1·1000 +2·100 +3·10 +4·1 +5·0.1 +6·0.01

and using powers of 10 as ...

  1234.56 = 1·10³ +2·10² +3·10¹ +4·10⁰ +5·10⁻¹ +6·10⁻²

As you might guess, the corresponding powers of 10 continue to increase for digits to the left of those in this number, and they continue to decrease for decimal fraction digits to the right of those in this number. The power of 10 in this expanded form is exactly the same power of 10 that is used in scientific notation when the leading digit of the number is in the corresponding decimal place. That is, this number would be written in scientific notation as 1.23456·10³.