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 two of the scientific numbers from the list and subtract them. Show
your work.
Let's choose the numbers 3.2 x 10^4 and 2.56 x 10^-2 to subtract:
3.2 x 10^4 - 2.56 x 10^-2
First, we need to make sure both numbers have the same exponent. To do this, we can convert 2.56 x 10^-2 to scientific notation with the same exponent as 3.2 x 10^4. The exponent of 3.2 x 10^4 is 4, so we can rewrite 2.56 x 10^-2 as:
0.0256 x 10^4
Now we can subtract the two numbers:
3.2 x 10^4 - 0.0256 x 10^4
Since both numbers have the same exponent, we can simply subtract the coefficients:
(3.2 - 0.0256) x 10^4
Simplifying the subtraction:
3.1744 x 10^4
So the result of subtracting 3.2 x 10^4 and 2.56 x 10^-2 is 3.1744 x 10^4.
To subtract two numbers written in scientific notation, we need to make sure that the exponents are the same.
Let's say we choose 3.2 x 10^4 and 1.95 x 10^6.
Step 1: Make sure the exponents are the same by adjusting the decimal point and exponent.
We can adjust the first number to have an exponent of 10^6 by moving the decimal point two places to the right:
3.2 x 10^4 = 0.032 x 10^6
Step 2: Perform the subtraction of the adjusted numbers.
(0.032 x 10^6) - (1.95 x 10^6) = -1.918 x 10^6
Step 3: Simplify the result, if necessary.
The result of subtracting 3.2 x 10^4 from 1.95 x 10^6 is -1.918 x 10^6.
To subtract two numbers written in scientific notation, you need to make sure that the exponents are the same. If they are not the same, you'll need to adjust them before performing the subtraction.
Let's choose two numbers from the list: 3.2 x 10^4 and 4.82 x 10^12.
First, we need to adjust the exponents of these two numbers to make them the same. In this case, we can convert 3.2 x 10^4 to scientific notation with a higher exponent.
To do that, we need to move the decimal point 8 places to the right (10^8) because we want the exponent to match the larger number (10^12). So, 3.2 x 10^4 becomes 3.2 x 10^12 x 10^-8.
Now that the exponents are the same, we can directly subtract the numbers:
(3.2 x 10^12) - (4.82 x 10^12)
Performing the subtraction gives us:
= 3.2 - 4.82 (the exponents remain the same)
= -1.62
So, the result of subtracting 3.2 x 10^4 from 4.82 x 10^12 is -1.62.
Always remember to adjust the exponents first when performing operations with numbers written in scientific notation.