Problem 35 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$\frac{20}{1200}$$

Step-by-Step Solution

Answer

\(\frac{20}{1200} = 1.7\%\)

Step 1: Convert Fraction to Decimal

The first step in converting the fraction \( \frac{20}{1200} \) into a percent is to convert it into a decimal. Divide the numerator (20) by the denominator (1200) to get the decimal form. So, \( 20 \div 1200 = 0.0166666\ldots \).

Step 2: Multiply by 100 to Get Percentage

Next, to convert the decimal to a percentage, multiply by 100. So, \( 0.0166666\ldots \times 100 = 1.66666\ldots \).

Step 3: Round to the Nearest Tenth

Finally, round the result from the previous step to the nearest tenth to get the final percentage. Since 1.66666... rounds to 1.7, the fraction expressed as a percentage is 1.7%.

Key Concepts

Fraction to Decimal

Converting a fraction to a decimal is a simple process that involves basic division. You take the top number of the fraction, called the numerator, and divide it by the bottom number, known as the denominator.
For example, in the fraction \( \frac{20}{1200} \):

• The numerator is 20.
• The denominator is 1200.

Perform the division: \( 20 \div 1200 = 0.0166666\ldots \). This gives you the decimal equivalent.
Fraction to decimal conversion is useful when you need to perform additional operations or comparisons between numbers. Decimals can be easier to work with than fractions in many situations, especially when it comes to calculations.

Decimal to Percent

Once you have a decimal number, converting it to a percent is straightforward. The key is to multiply the decimal by 100 to shift the decimal point two places to the right.
This transforms the decimal into its percentage equivalent.

• For example, with the decimal \( 0.0166666\ldots \), multiplying by 100 gives \( 1.66666\ldots \).

Think of this as moving the decimal point two places to the right. Percentages are often more intuitive to understand as they describe a portion of a whole, in this case, 1.66666% is a small part of 100.
It's also important to note that converting decimals to percentages is a good way to quantify things like scores, ratios, and probabilities in a way that is easy to interpret.

Rounding Decimals

Rounding decimals is essential to simplify numbers, making them easier to understand and use in practical applications. The goal is to limit the number of decimal places, which helps in making quick and clear decisions.
In rounding, you observe the number at the desired decimal place (the tenths place, for example) and the digit right next to it (the hundredths place).

• If that next digit is 5 or more, you increase the tentative rounding digit by 1.
• If it's less than 5, you leave the digit as it is.

Let's take the decimal \( 1.66666\ldots \):

• Look at the first digit after the decimal, 6 (hundredths), which is greater than 5.
• So, you round 1.66666 up to 1.7.

Rounding is particularly helpful when you need to make estimations or simplify results from calculations, such as converting a decimal to a neatly rounded percentage.