9. Calculate 5.3 * 10 ^ - 3 - 6.7 * 10^-6. Express the answer in scientific notation rounding to 2 decimal places.
To subtract two numbers written in scientific notation, the exponents of the powers of ten must be the same.
Given:
5.3 * 10^-3 - 6.7 * 10^-6
Let's change the first number so that the exponent becomes -6 instead of -3. This can be done by multiplying it by 10^(-3 + 6) = 10^3:
5.3 * 10^-3 - 6.7 * 10^-6 = 5.3 * (10^-3 * 10^3) - 6.7 * 10^-6
= 5.3 * 10^(3-3) - 6.7 * 10^-6
= 5.3 * 10^0 - 6.7 * 10^-6
Since 10^0 = 1, we can simplify to:
5.3 * 10^0 - 6.7 * 10^-6 = 5.3 - 6.7 * 10^-6
To express the answer in scientific notation rounded to 2 decimal places, we can convert it back into scientific notation:
5.3 - 6.7 * 10^-6 = 5.3 - 0.0000067
= 5.2999933
Rounded to 2 decimal places, the answer is approximately 5.30.
Therefore, 5.3 * 10^ - 3 - 6.7 * 10^-6 = 5.30 * 10^0 in scientific notation.
To calculate 5.3 * 10^-3 - 6.7 * 10^-6, follow these steps:
Step 1: Convert the numbers to the same exponential form.
5.3 * 10^-3 - 6.7 * 10^-6
= (5.3 * 10^-3) - (0.0000067)
Step 2: Perform the subtraction of the decimal numbers.
(5.3 * 10^-3) - (0.0000067)
= 0.0053 - 0.0000067
= 0.0052933
Step 3: Express the answer in scientific notation.
0.0052933 can be written as 5.2933 * 10^-3.
Therefore, the answer is 5.2933 * 10^-3, rounded to 2 decimal places in scientific notation.
To calculate (5.3 * 10^-3) - (6.7 * 10^-6), we need to first convert the numbers to their decimal form:
5.3 * 10^-3 = 0.0053
6.7 * 10^-6 = 0.0000067
Then subtract the two decimal numbers:
0.0053 - 0.0000067 = 0.0052933
To express the answer in scientific notation and round it to 2 decimal places, we need to move the decimal point 3 places to the left until the first non-zero digit is to the left of the decimal point, resulting in 5.2933.
To represent this number in scientific notation, we need to determine the exponent by counting the number of places the decimal point was moved:
0.0052933 -> 5.2933 (moved the decimal point 3 places to the left)
The exponent is -3 since the decimal point was moved 3 places to the left.
Now we can express the answer as 5.29 x 10^-3, rounded to 2 decimal places in scientific notation.