Problem 34 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$\frac{15}{2500}$$

Step-by-Step Solution

Answer

The fraction \(\frac{15}{2500}\) is equivalent to \(0.6\%\).

Step 1: Convert Fraction to Decimal

To convert the fraction \(\frac{15}{2500}\) to a decimal, perform the division: \(15 \div 2500 = 0.006\).

Step 2: Convert Decimal to Percent

To express a decimal as a percent, multiply the decimal by 100. Hence, \(0.006 \times 100 = 0.6\).

Step 3: Finalize the Percent Value

The final percent value is \(0.6\%\). This is already to the nearest tenth.

Key Concepts

Understanding Fractions

Fractions represent a part of a whole. You can think of them as slices of a pizza; every fraction tells you how many parts you have and the total number in a whole. The fraction \( \frac{15}{2500} \) means 15 out of 2500.
Different ways you may encounter fractions include proper, improper, and mixed numbers.

• Numerator: The top number showing how many parts you have.
• Denominator: The bottom number indicating the total parts of the whole.

To use fractions in calculations like changing them to decimals or percentages, we often perform division. For example, dividing 15 by 2500 gives us the decimal form, which is the starting point of many calculations.

Converting Decimals

Decimals are simply another way to show fractions, especially when fractions have a large denominator. They make calculations easier and are widely used in daily life, such as in money and measurements. For instance, converting \( \frac{15}{2500} \) to a decimal, we get \(0.006\). Decimals place numbers according to their position relative to the decimal point, such as tenths, hundredths, or thousandths.

• Whole number part: On the left of the decimal point.
• Fractional part: On the right side, decreasing in size from tenths onwards.

Decimals make it simple to perform arithmetic operations and conversions into percentages, which is done by moving the decimal point two places to the right.

Mastering Mathematical Conversions

Mathematical conversions involve changing numbers from one format to another, often to make calculations easier or more meaningful. Converting fractions to decimals and then to percentages involves familiar and systematic steps.
For example, to convert a fraction like \( \frac{15}{2500} \) into a decimal, division is key, giving \(0.006\), and then turning that into a percentage by multiplying by 100 gives \(0.6\%\). Conversions are basic mathematical skills used in daily problem solving.

• Fractions to decimals: A simple division.
• Decimals to percentage: Multiply by 100, motivating an understanding of how many parts out of 100 the value represents.

This logical progression helps in understanding the relationships between different numerical expressions.

Rounding Numbers Simplified

Rounding is a technique to simplify numbers while preserving their value to where it is most needed. It is particularly useful in presenting cleaner results without clutter from many decimal places. In our context, rounding \(0.6\%\) to the nearest tenth keeps it the same because it's already at that nearest precision.
Rounding involves:

• Identifying: The place value you wish to simplify.
• Four or Below: Leave the number as is.
• Five or Above: Increase the previous digit by one.

This technique is widely applied in making financial figures, measurements, and estimates easier to understand and communicate. Understanding rounding helps present efforts in measurements, reporting, and predictions clearly, keeping their context intact.