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
Let's choose 1.95 x 10^6 and subtract it from 1,845.19:
1,845.19 - 1.95 x 10^6
To subtract two numbers written in scientific notation, we need to make sure their exponents are the same. So, let's convert 1,845.19 to scientific notation:
1,845.19 = 1.84519 x 10^3
Now we can subtract:
1.84519 x 10^3 - 1.95 x 10^6
Since the exponents are the same, we can directly subtract the coefficients:
1.84519 - 1.95 = -0.10481
Therefore,
1,845.19 - 1.95 x 10^6 = -0.10481 x 10^3
We can also write this in standard form:
-0.10481 x 10^3 = -104.81
So, 1,845.19 - 1.95 x 10^6 = -104.81.
To subtract a number written in scientific notation from 1,845.19, we need to convert 1,845.19 to scientific notation.
1,845.19 = 1.84519 x 10^3
Let's subtract 1,845.19 from 3.2 x 10^4:
3.2 x 10^4 - 1.84519 x 10^3
To subtract these numbers, we need to make sure they have the same exponent. We can do this by rearranging the numbers to align the exponents:
3.2 x 10^4 = 32 x 10^3
1.84519 x 10^3 = 0.184519 x 10^4
Now we can subtract:
32 x 10^3 - 0.184519 x 10^4
= (32 - 0.184519) x 10^3
Simplifying the subtraction:
= 31.815481 x 10^3
= 3.1815481 x 10^4
Therefore, subtracting 1,845.19 from 3.2 x 10^4 results in 3.1815481 x 10^4.
To subtract a number written in scientific notation from a standard number, we need to convert the number in scientific notation to standard form.
Let's choose the number 3.2 x 10^4 from the list and subtract it from 1,845.19.
Step 1: Convert 3.2 x 10^4 to standard form
To convert a number from scientific notation to standard form, we need to multiply the coefficient (in this case, 3.2) by 10 raised to the power of the exponent (in this case, 4).
3.2 x 10^4 = 3.2 * 10 * 10 * 10 * 10 = 32,000.
Step 2: Subtract the converted number from 1,845.19
1,845.19 - 32,000 = -30,154.81.
So, subtracting 3.2 x 10^4 from 1,845.19 gives us -30,154.81.