Question

Write each decimal number as a percent. $$0.42$$

Short answer

Question: Convert the decimal number 0.42 to a percentage. Answer: 42%

Step-by-step solution

Multiply the decimal number by 100

To convert the decimal number \(0.42\) into a percentage, we need to multiply the decimal number by \(100\). $$0.42 \times 100$$

Calculate the result

Multiplying the decimal number \(0.42\) by \(100\) gives us: $$0.42 \times 100 = 42$$

Add the percent symbol

Finally, add the percent symbol "%" to the result: $$42 \%$$ So, the decimal number \(0.42\) can be written as \(42\%\).

Key concepts

Decimal to Percent Conversion

Understanding how to convert a decimal to a percent is a fundamental skill in math, as it allows you to express numbers in different ways for comparison and calculation purposes. The key is knowing that 'percent' means 'per hundred.' Hence, when you want to change a decimal into a percent, you are essentially finding how many parts out of a hundred the decimal represents.

To accomplish this, multiply the decimal by 100. This process shifts the decimal point two places to the right, transforming the decimal value into a whole number that represents the percentage. For instance, converting the decimal 0.42 to a percent involves multiplying it by 100, which shifts the decimal two places to the right, yielding 42— our percentage. It's crucial to remember to add the percent sign (%) at the end to indicate that the number is now a percentage.

Multiplying Decimals

When multiplying decimals, the process is similar to multiplying whole numbers, but you have to keep track of the position of the decimal point. To multiply a decimal by 100, like in the step-by-step solution we have for the exercise, you can simply move the decimal point two places to the right without having to perform long multiplication. However, when multiplying by other numbers, here's a helpful tip: first, ignore the decimals and multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in both numbers you multiplied, and add that many decimal places back in, from right to left, in the product.

For example, if you multiplied 0.42 by another decimal like 3.5, first multiply 42 by 35 to get 1470. Since the original numbers had a combined total of three decimal places (two from 0.42 and one from 3.5), you would then place a decimal in the product to have three places after the decimal, giving you 1.470 or simply 1.47 when you get rid of the trailing zero.

Percentages in Math

Percentages are used widely in everyday life and are crucial in various fields such as statistics, finance, and education. A percentage represents a fraction of 100 and is used to specify how large or small one quantity is relative to another quantity. The symbol for percentage is the '%', and essentially, a percentage tells us how many parts out of 100 there are of something.

Working with percentages, you're often either finding a part based on the whole (what percent one number is of another) or finding the whole based on a part (what number a certain percent represents). Understanding percentages involves converting them to and from decimals and fractions, calculating percentage increases or decreases, and solving for the whole or part in a given problem. Enhancing your proficiency with percentages can ultimately boost your quantitative reasoning and make you adept at interpreting data in a range of real-world contexts.