Scientific notation is a mathematical expression used to represent very large or very small numbers in a compact and manageable form, facilitating easier calculations and comparisons. It is expressed as the product of a number (the coefficient) between 1 and 10, and a power of ten, which indicates the scale of the number. For example, the number 6,500 can be written in scientific notation as 6.5 × 10², while 0.00045 can be represented as 4.5 × 10⁻⁴. This notation is particularly useful in scientific and engineering contexts, where it simplifies the handling of extreme values and enhances clarity in communication of measurements and calculations
What is scientific notation?
Scientific notation is a way of expressing very large or very small numbers as a product of a number between 1 and 10 and a power of ten, making it easier to read and work with.
How is the number 0.00056 expressed in scientific notation?
The number 0.00056 can be expressed in scientific notation as 5.6 × 10⁻⁴.
Why is scientific notation useful in scientific calculations?
Scientific notation is useful because it simplifies the representation of extremely large or small numbers, making calculations easier and reducing the risk of errors in handling many zeros.
Can scientific notation be used for both large and small numbers?
Yes, scientific notation can be used for both large numbers (e.g., 1,000,000 as 1.0 × 10⁶) and small numbers (e.g., 0.0001 as 1.0 × 10⁻⁴).
How do you multiply two numbers in scientific notation, such as (2 × 10²) and (3 × 10³)?
To multiply two numbers in scientific notation, you multiply the coefficients (2 × 3 = 6) and add the exponents (2 + 3 = 5), resulting in 6 × 10⁵.
How is the number 0.00067 expressed in scientific notation?
a) 6.7 × 10⁻³
b) 67 × 10⁻⁵
c) 6.7 × 10⁻⁴
d) 0.67 × 10⁻²
Answer: c) 6.7 × 10⁻⁴
What is the result of multiplying (3 × 10²) and (4 × 10³) in scientific notation?
a) 12 × 10⁵
b) 12 × 10⁶
c) 7 × 10⁵
d) 1.2 × 10⁶
Answer: a) 12 × 10⁵
Which of the following is NOT a valid scientific notation?
a) 1.0 × 10²
b) 0.5 × 10⁴
c) 10.0 × 10⁻¹
d) 3.2 × 10⁵
Answer: c) 10.0 × 10⁻¹
What is the scientific notation for the number 0.00012?
a) 1.2 × 10⁻²
b) 1.2 × 10⁻³
c) 12 × 10⁻⁴
d) 0.12 × 10⁻¹
Answer: b) 1.2 × 10⁻³
What is the scientific notation for the number 0.00000089?
a) 8.9 × 10⁻⁷
b) 89 × 10⁻⁸
c) 8.9 × 10⁻⁸
d) 0.89 × 10⁻⁶
Answer: c) 8.9 × 10⁻⁸