In this problem, you will practice added, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.

Question

In this problem, you will practice added, subtracting, multiplying, and dividing numbers written in scientific notation. For each part, use the following numbers.

3.2 x 10^4, 1.95 x 10^6, 8.03 x 10^-8, 2.56 x 10^-2, 4.82 x 10^12
Choose one of the scientific numbers from the list and subtract it from
1,845.19 (or subtract 1,845.19 from the number you choose). Show your
work.

Answer 1

Let's choose the number 3.2 x 10^4.

To subtract it from 1,845.19, we need to convert 1,845.19 to scientific notation.
1,845.19 = 1.84519 x 10^3

Now, we can subtract 3.2 x 10^4 - 1.84519 x 10^3:

(3.2 x 10^4) - (1.84519 x 10^3)
= 3.2 x 10^4 - 1.84519 x 10^3

Since both numbers have the same power of 10 (10^4), we can subtract their coefficients:
(3.2 - 1.84519) x 10^4
= 1.35481 x 10^4

Answer 2

To subtract a number written in scientific notation from 1,845.19, we need to convert 1,845.19 into scientific notation.

Since 1,845.19 does not contain any zeros after the decimal point, we can write it as 1.84519 x 10^3.

Let's choose the number 3.2 x 10^4 from the list and subtract it from 1,845.19:

1,845.19 - (3.2 x 10^4)

Subtracting the two numbers, we have:

1.84519 x 10^3 - 3.2 x 10^4

To subtract numbers in scientific notation, the exponents must be the same. We can rewrite 1.84519 x 10^3 as 0.184519 x 10^4 to match the exponent of 10^4 in 3.2 x 10^4.

Now we have:

0.184519 x 10^4 - 3.2 x 10^4

We can subtract the coefficients:

0.184519 - 3.2 = -3.015481

Since the coefficient is negative, we can rewrite it as:

-3.015481

So, subtracting 3.2 x 10^4 from 1,845.19 gives us approximately -3.015481.

Answer 3

To subtract a number written in scientific notation from 1,845.19, you need to convert 1,845.19 into scientific notation.

1,845.19 can be written as 1.84519 x 10^3 in scientific notation.

Next, you can subtract the scientific number of your choice from 1.84519 x 10^3. Let's say we choose 3.2 x 10^4.

1.84519 x 10^3 - 3.2 x 10^4

To perform this subtraction, you need to make sure both numbers have the same exponent. In this case, you can rewrite 1.84519 x 10^3 as 1.84519 x 10^4, so the exponents match.

1.84519 x 10^4 - 3.2 x 10^4

Now, you can subtract the decimal parts:

1.84519 - 3.2 = -1.35481

Finally, you keep the exponent of 10^4, since both numbers have the same exponent:

-1.35481 x 10^4

Therefore, when subtracting 3.2 x 10^4 from 1,845.19, the result is approximately -1.35481 x 10^4.