(3.0 x 10^4 ) ÷ (6.2 x 10^1) =
18.6x10^3
(4.7 x 10^-3 ) ÷ (9 x 10^-4) =
42.3x10^-7
(3.0 x 10^4 ) x (6.2 x 10^1) =
18.6x10^3
(5.1 x 10^2 ) x (3 x 10^4) =
15.3x10^-2
3rd is 1.86 * 10^6
4th is 1.53 * 10^7
I don't see a question.
a and b you multiplied instead of dividing.
c and d the digits are right, the exponents are wrong and number of significant figures is wrong.
oh the question is to multiply and divide the significant figures
ohh my mistake i thought i divided
so is this correct?
3rd is 1.86 * 10^6
4th is 1.53 * 10^7
idk how you divide it
I posted after your correction.
For c, 1.86E6 is right but you're allowed only two significant figures. You should round the 1.86E6 to 1.9E6
For d, the digits are right but s.f. not. You're allowed 1 so the answer is 1.53E7 which to 1 s.f. I would round to 2E7.
so the first one is it 5x10^2?
(4.7 x 10^-3 ) divided by (9 x 10^-4) =
5x10^-6
No. My calculator gives 5.22 which would round to 1 s.f. to 5.
In order to perform these calculations, we need to understand the rules of scientific notation and how to multiply and divide numbers expressed in scientific notation.
Let's start with scientific notation. Scientific notation is a way of expressing numbers that are very large or very small. It consists of two parts: a coefficient and a power of 10. The coefficient is a number between 1 and 10 (inclusive), and the power of 10 indicates how many places the decimal point needs to be moved. In scientific notation, the coefficient is always multiplied by 10 raised to the power.
Now, let's look at multiplication and division in scientific notation:
1. Multiplication:
To multiply numbers in scientific notation, you simply multiply the coefficients and add the powers of 10. For example, (3.0 x 10^4) multiplied by (6.2 x 10^1) is calculated as follows:
(3.0 x 6.2) x (10^4 x 10^1) = 18.6 x 10^5 = 1.86 x 10^6.
2. Division:
To divide numbers in scientific notation, you divide the coefficients and subtract the powers of 10. For example, (4.7 x 10^-3) divided by (9 x 10^-4) is calculated as follows:
(4.7 ÷ 9) x (10^-3 ÷ 10^-4) = 0.522222 x 10^-3-(-4) = 0.522222 x 10^-3+4 = 0.522222 x 10^1 = 5.22222.
Now, let's solve the given calculations:
1. (3.0 x 10^4) ÷ (6.2 x 10^1) = 18.6 x 10^3.
- We divide the coefficients: 3.0 ÷ 6.2 = 0.483871.
- We subtract the powers of 10: 10^4 - 10^1 = 10^3.
- The result is 0.483871 x 10^3, which can be simplified to 18.6 x 10^3.
2. (4.7 x 10^-3) ÷ (9 x 10^-4) = 42.3 x 10^-7.
- We divide the coefficients: 4.7 ÷ 9 = 0.522222.
- We subtract the powers of 10: 10^-3 - 10^-4 = 10^-7.
- The result is 0.522222 x 10^-7, which can be simplified to 42.3 x 10^-7.
3. (3.0 x 10^4) x (6.2 x 10^1) = 18.6 x 10^5.
- We multiply the coefficients: 3.0 x 6.2 = 18.6.
- We add the powers of 10: 10^4 + 10^1 = 10^5.
- The result is 18.6 x 10^5.
4. (5.1 x 10^2) x (3 x 10^4) = 15.3 x 10^6.
- We multiply the coefficients: 5.1 x 3 = 15.3.
- We add the powers of 10: 10^2 + 10^4 = 10^6.
- The result is 15.3 x 10^6.
Please note that the final answers have been simplified where possible.