Answer:
a) 1.6×10⁻⁶
b) 2×10⁷
Explanation:
You want the product or quotient in standard form of ...
- (8×10⁻³)×(2×10⁻⁴)
- (6×10²)÷(3×10⁻⁵)
Exponents
The rules of exponents apply:
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
Scientific notation
A number is said to be in scientific notation if there is one digit to the left of the decimal point, and the multiplier is expressed to an appropriate power of 10. The power of 10 may need to be adjusted so the decimal point is in the correct place. In general, the power of 10 represents the place value of that most-significant digit.
Standard form
In the US, a number is written in standard form as a sequence of digits with an optional decimal point. Integers are written so the least-significant digit has a place-value of 1.
Elsewhere, a number is written in standard form when it is written in scientific notation.
We have given both forms a number here, so you will need to choose the one that is standard form where you are.
a) (8×10⁻³)×(2×10⁻⁴)
The product is (8×2)×10^(-3-4) = 16×10^-7 = 1.6×10^-6
= 0.0000016
b) (6×10²)÷(3×10⁻⁵)
The quotient is (6/3)×10^(2-(-5)) = 2×10^7
= 20,000,000
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