Problem 30 - Algebra 1

Question

Write as a decimal rounded to the nearest hundredth. Then write as a percent. $$ \frac{100}{201} $$

Step-by-Step Solution

Answer

The fraction \( \frac{100}{201} \) as a decimal rounded to the nearest hundredth is 0.50 and as a percentage it is 50%.

Step 1: Convert To Decimal

To convert a fraction to a decimal, the numerator should be divided by the denominator. So, perform the division \( \frac{100}{201} \) which equals 0.4975124378109453.

Step 2: Round To The Nearest Hundredth

The obtained decimal after division is quite lengthy and needs to be rounded to the nearest hundredths place. The hundredths place is two digits after the decimal point. So, round 0.4975124378109453 to 0.50 as per the instruction.

Step 3: Convert To Percent

To convert a decimal to a percentage, multiply the decimal by 100 and add the percent sign. So, multiply 0.50 by 100 to get 50%. Add the '%' sign after the result for the appropriate representation.

Key Concepts

Decimal Conversion

Decimal conversion is the process of changing a fraction into a decimal.In mathematics, fractions consist of a numerator (top part) and a denominator (bottom part).To convert a fraction to a decimal, you divide the numerator by the denominator.

For example, in the exercise \( \frac{100}{201} \), to find its decimal form, divide 100 by 201.
This process involves performing the division: 100 ÷ 201 = 0.4975124378109453.This decimal can often have many digits, but that's okay! It represents our original fraction but in decimal form.

Remember: no matter how lengthy a decimal is, every position after the decimal point still holds value towards the number's accuracy.This practice of converting allows one to visualize and utilize numbers in different formats across various calculations and contexts.

Rounding Numbers

Rounding is essential to make decimal numbers easier to work with. It simplifies recognizing and using approximate values in everyday situations. Rounding to the nearest hundredth means you'll look at the third digit to the right of the decimal point.

For the decimal 0.4975124378109453, focus on the first three digits: 497. Anything 5 or greater encourages rounding up.
Therefore, the digit '7' in the third place makes '49' increase to '50'. Thus, 0.4975124378109453 rounds to 0.50. This gives a cleaner number for simple mathematical operations or comparisons.

• Always identify which place value you're rounding to.
• Check the digit right after the rounded place: 5 or more rounds up, less than 5 stays the same.
• This helps in quickly estimating and simplifying numbers that might otherwise be challenging to work with directly.

Fractions

Fractions are a fundamental way to represent numbers that are not whole.They indicate a part of a whole and help in understanding divisions and distributions.

Every fraction includes a numerator and a denominator, such as \( \frac{100}{201} \). The numerator '100' signifies how many parts we have, while the denominator '201' specifies the total number of equal parts the whole is divided into.
Understanding fractions as parts of a whole gives a clear visualization of divided quantities.

• Fractions can be converted into decimals or percentages for a different representation but display the same value.
• This conversion process aids in comparing, summing, and integrating fragmented and varied numerical information.
• Stay comfortable switching between formats as each provides unique advantages depending on the context.

Mastering these conversions makes it easier to interpret and communicate mathematical concepts in diverse and practical scenarios.