Problem 30 - Elementary Algebra

Question

For the following problems, convert each percent to a decimal. $$ 0.00034 \% $$

Step-by-Step Solution

Answer

Question: Convert the given percentage to a decimal value: $$0.00034 \%$$ Answer: $$0.0000034$$

Step 1: Understand the conversion from percentage to decimal

To convert a percent to a decimal, we can simply divide the percentage value by 100. This is because "percent" means "per 100" or "out of 100". So, if you have a percentage, you are essentially dividing that number by 100 to get its decimal equivalent.

Step 2: Divide the percentage by 100

Now, to convert the given percentage $$0.00034 \%$$ to a decimal, we need to divide it by 100: $$ \frac{0.00034}{100} $$

Step 3: Perform the division

When we divide $$0.00034$$ by $$100$$, we get the decimal value: $$ 0.00034 \div 100 \ =\ 0.0000034 $$

Step 4: Write the final answer

The decimal equivalent of $$0.00034 \%$$ is $$0.0000034$$.

Key Concepts

Division

In mathematics, division is one of the four basic operations. It is essentially splitting a number into equal parts. It helps us understand how many times a number can fit into another. For the concept of dividing by 100, which is crucial in converting percentages, think of it as dividing a number into 100 smaller pieces. Every percentage calculation boils down to this concept of division.

For example, when converting percentage values to decimals, we divide by 100 to adjust the scale for comparison to the whole. This is because percentages are parts of 100, and dividing by 100 transforms them into part of a whole, expressed as a decimal.

To perform the division, you need to align the decimal point correctly. Moving it two places to the left effectively does the trick.

Decimal Equivalent

The decimal equivalent refers to the expression of a number in the base-10 numbering system. Decimals are part of the real numbers and help us in precise calculations, representing fractions in a convenient way.

When you convert a percentage to its decimal equivalent, like we did with 0.00034%, you simplify the percentage to a form that is easier to use in many mathematical operations.

In our example, \[ 0.00034 ext{%} ightarrow 0.0000034 \] shows the decimal equivalent, which can be used in further calculations without any need for percentage signs.

Percentage Value

Percentage values give us an idea of how a number relates to 100. This "per cent" notation is an incredibly useful way to express proportions and comparisons.

A percentage tells you how much one number represents in relation to 100 parts of another. It's commonly used in financial calculations, such as interest rates or discounts, and even in academic grading.

For instance, if you see 0.00034%, this small number shows how tiny a part of something it represents, just 0.00034 parts of 100.

Mathematics

Mathematics is an expansive field, central to science and everyday life. It's a language that forms the basis for countless operations and calculations. Concepts like percentages, decimal conversions, and division are foundational in mathematics.

These concepts help us solve problems in real life, from calculating tips to analyzing data. Mathematics allows us to interpret the world in a structured and logical way. When you work with numbers, be it percentages or decimals, you're not just performing calculations; you're applying mathematical principles that have wide-ranging applications beyond the classroom.