Problem 14 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth, if necessary. $$1.3$$

Step-by-Step Solution

Answer

1.3 as a percent is 130%.

Step 1: Understand the Problem

The task is to convert the decimal number 1.3 into a percentage. A percentage is a fraction out of 100, so we will transform 1.3 into a form where its hundredths place can be expressed.

Step 2: Convert Decimal into Percent

To convert a decimal to a percent, multiply the decimal number by 100. This moves the decimal point two places to the right.

Step 3: Perform the Multiplication

Calculate 1.3 multiplied by 100:\[1.3 \times 100 = 130\]This shows that 1.3 as a percentage is 130%.

Step 4: Round if Necessary

Since there are no additional decimal places after moving the decimal point, rounding is not required. The result stays as 130%.

Key Concepts

Decimal to Fraction Conversion

Converting decimals to fractions is a fundamental math skill that helps us better understand numbers. To convert a decimal to a fraction, identify the decimal's place value. For a decimal such as 1.3, the digit 3 is in the tenths place. This means 1.3 can be expressed as the fraction \(\frac{13}{10}\). Here’s how you can do it step-by-step:

• Write down the number as the numerator (top number of the fraction). For 1.3, it becomes 13.
• The denominator (bottom number of the fraction) is determined by the decimal place. Since 3 is in the tenths place, use 10 as the denominator.

So, the decimal 1.3 becomes the fraction \(\frac{13}{10}\). Fractions like \(\frac{13}{10}\) are often called improper fractions because the numerator is greater than the denominator.

Rounding Decimals

Rounding decimals is a useful skill that makes numbers easier to handle. It involves adjusting a decimal to a specific place value. When you round 1.3, it is already a clean number with just one decimal place, so it is often considered to already be rounded to the nearest tenth. But what if you had 1.36?

• Identify the place value you need to round to. For rounding to the nearest tenth, look at the hundredths place.
• If the digit in the hundredths place is 5 or greater, round up. With 1.36, the 6 tells us to round up, resulting in 1.4.
• If it is less than 5, do not round up, like in 1.34, resulting in a rounded figure of 1.3.

Rounding allows for simplicity and ease in calculations and estimations.

Percentages in Mathematics

Percentages are a way of expressing ratios as fractions of 100. They are essential in various real-world applications like statistics, finance, and everyday life. To convert a decimal to a percentage, simply multiply it by 100. Let's explore how this works:

• Take the decimal number, for example, 1.3.
• Multiply it by 100 to shift the decimal two places to the right, which gives you 130.

After the calculation, you obtain a percentage. Therefore, 1.3 expressed as a percentage is 130%. Using percentages helps to compare and understand proportions more easily. This is why they are so prevalent in mathematical expressions and everyday use.