Operations with Scientific Notation Worksheet
Scientific notation is a key concept in the field of mathematics, particularly in science and engineering. It provides a way to express very large or very small numbers in a concise and convenient format. If you are a student or educator in need of practice, a scientific notation worksheet can be an invaluable tool for mastering operations with scientific notation.
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Convert 3.5 × 10^4 into standard form.
3.5 × 10^4 in standard form is 35,000.
Multiply (2.3 × 10^5) × (4 × 10^2).
To multiply (2.3 × 10^5) × (4 × 10^2), first multiply 2.3 by 4 to get 9.2, then add the exponents of the numbers being multiplied to get 10^7. So, the result is 9.2 × 10^7.
Divide (1.8 × 10^4) ÷ (3 × 10^2).
To divide (1.8 × 10^4) by (3 × 10^2), we need to simplify the expression. This equals (1.8 ÷ 3) × 10^(4-2), which simplifies to 0.6 × 10^2. Therefore, the answer is 0.6 × 10^2 or 60.
Add 7.1 × 10^3 and 9.6 × 10^2.
To add 7.1 × 10^3 and 9.6 × 10^2, you first need to make sure the exponents are the same by converting 9.6 × 10^2 to scientific notation as 0.96 × 10^3. Then, you can add the two numbers: 7.1 × 10^3 + 0.96 × 10^3 = 8.06 × 10^3.
Subtract 2.5 × 10^4 from 3.7 × 10^4.
To subtract 2.5 × 10^4 from 3.7 × 10^4, you need to subtract the coefficients while keeping the same exponent. Thus, the result would be 1.2 × 10^4.
Raise 5.4 × 10^2 to the power of 3.
To raise 5.4 × 10^2 to the power of 3, you multiply the exponents, which gives 5.4 × 10^6 (since 2 x 3 = 6).
Simplify (9 × 10^3) × (5 × 10^(-2)).
The given expression (9 × 10^3) × (5 × 10^(-2)) simplifies to 45 × 10^(3-2), which further simplifies to 45 × 10^(1) or simply 450.
Evaluate the expression (6.2 × 10^(-2)) × (8.9 × 10^(-3)).
To evaluate the expression (6.2 × 10^(-2)) × (8.9 × 10^(-3)), you multiply the numerical coefficients 6.2 and 8.9 to get 55.18, and then add the exponents of the 10 terms, which gives you 10^(-2 +(-3)) = 10^(-5). So, the final answer is 55.18 × 10^(-5).
Convert 0.00256 into scientific notation.
0.00256 in scientific notation is 2.56 x 10^-3.
Divide (2.5 × 10^4) ÷ (1.2 × 10^(-3)).
To divide (2.5 × 10^4) by (1.2 × 10^(-3)), when dividing numbers in scientific notation, divide the coefficients (2.5 ÷ 1.2) and subtract the exponents (4 - (-3)). This gives us an answer of 2.0833333 × 10^(7).
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