Problem 36 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$0.51$$

Step-by-Step Solution

Answer

0.51 as a percent is 51%.

Step 1: Understand the Problem

We need to express the decimal, \(0.51\), as a percent. Percentages are another way of expressing fractions out of 100.

Step 2: Convert the Decimal to a Fraction

To convert the decimal \(0.51\) to a percentage, we first understand that it is equivalent to \(51/100\). This is because moving the decimal two places to the right converts \(0.51\) to the fraction \(51\) over \(100\).

Step 3: Convert the Fraction to a Percent

To convert a fraction to a percent, we multiply by 100. Therefore, \( \frac{51}{100} \times 100 = 51\% \).

Step 4: Check for Rounding

Since we have a whole number, \(51\), as our percentage, there is no need to round to the nearest tenth.

Key Concepts

Percentages

Percentages are a way to express numbers as parts of 100. When you see a percentage, imagine it as a fraction with a denominator of 100. For instance, 25% means 25 out of 100 or simply 25/100. Understanding percentages helps make comparisons easy. You can quickly see how one quantity relates to another in terms of the full amount.

To convert a decimal to a percentage, you simply multiply it by 100. This moves the decimal point two places to the right. For example, converting the decimal 0.51 to a percentage involves performing the calculation: 0.51 × 100, which yields 51%. This shows that the decimal 0.51 represents 51% of a whole.

Decimal to Fraction Conversion

Decimals can be effortlessly converted into fractions by understanding their place values. When you have a decimal, like 0.51, think about its position relative to the decimal point. Each place has a fractional counterpart.

For example, in the number 0.51, the '5' is in the tenths place, and the '1' is in the hundredths place. To convert this into a fraction, recognize that the decimal 0.51 is equal to 51/100. This is because moving the decimal two spaces to the right gives us 51, and the denominator 100 reflects the two decimal places the number extends in a fraction form.

• Convert 0.1 to a fraction: 1/10
• Convert 0.75 to a fraction: 75/100, which simplifies to 3/4
• Convert 0.3 to a fraction: 3/10

Always remember that the key to this conversion is identifying the right denominator, based on how far the decimal extends.

Mathematical Rounding

Rounding is a mathematical method used to reduce the number of digits without restricting the precision we need for calculations. It makes complex numbers simpler and more understandable, by focusing on the most significant figures.

When rounding, we look at the digit immediately after the position you want to round to. If this digit is 5 or higher, you round up. If it's less than 5, you round down. For instance, to round the number 51.27 to the nearest tenth:

• The digit in the tenths place is 2, and the digit after it is 7.
• Since 7 is greater than 5, you round the 2 up to 3.
• 51.27 rounded to the nearest tenth becomes 51.3.

This technique is useful especially when converting decimals to percentages and the result isn't a whole number, ensuring your final answer is neat and presentable.