Convert 0.046 to standard form.
The correct Answer and Explanation is:
To convert 0.046 to standard form, you express the number as a product of a number between 1 and 10 and a power of 10. Here’s how to do it:
Step-by-Step Conversion:
- Move the decimal point: In 0.046, the decimal point must be moved two places to the right to get the number 4.6.
- Count the places moved: Since we moved the decimal point two places to the right, we will multiply by (10^{-2}).
- Write the number in standard form: So, 0.046 becomes (4.6 \times 10^{-2}).
Final Answer:
The standard form of 0.046 is (4.6 \times 10^{-2}).
Explanation:
Standard form (also called scientific notation) is useful for expressing very large or very small numbers in a more manageable way. It is written as (A \times 10^n), where (A) is a number between 1 and 10, and (n) is an integer that indicates how many places the decimal point was moved. If (n) is negative, the original number is less than 1, and if (n) is positive, the number is greater than 1.
In this case, 0.046 is a small number, so the exponent of 10 will be negative. We move the decimal two places to the right to turn 0.046 into 4.6. This shift to the right corresponds to multiplying by (10^{-2}), because every shift to the right decreases the exponent of 10 by 1.
Standard form is commonly used in scientific and engineering fields because it simplifies calculations with very large or very small numbers. For example, instead of writing many zeros in calculations involving tiny measurements like wavelengths or huge numbers like distances in space, you can work with powers of 10, which are easier to manage.
By using scientific notation, numbers like 0.046 can be written more compactly and still convey precise value.