Problem 34 - Algebra 1: Concepts and Skills

Question

In Exercises \(32-37\), convert the units. Round the result to the nearest tenth. 168 days to weeks

Step-by-Step Solution

Answer

168 days is equivalent to approximately 24 weeks.

Step 1: Understand the conversion rate

There are 7 days in a week. This means that we must divide the number of days by 7 to convert them into weeks.

Step 2: Apply the conversion rate to given days

Take the given number of days (168) and divide it by 7 to obtain the equivalent number in weeks.

Step 3: Round the result to the nearest tenth

Take the result from step 2 and round it to the nearest tenth. This is the final answer.

Key Concepts

Days to Weeks Conversion

Converting days into weeks is a simple yet fundamental unit conversion that you might encounter in homework or real-life situations. This conversion helps to better understand time periods by using the larger unit of weeks for longer durations. The primary step of this conversion is knowing the basic fact: there are 7 days in a week.

• To convert days to weeks, simply divide the number of days by 7.
• For example, when converting 168 days to weeks, you calculate: \( 168 \div 7 = 24 \) weeks.

This process allows you to express time spans in terms more intuitive for weekly schedules.
By breaking down the number of days, the conversion makes it easier to plan and manage larger timeframes.

Rounding to the Nearest Tenth

After converting days to weeks, sometimes you will need to present the answer as a decimal rounded to the nearest tenth. This ensures uniformity and precision, especially useful in mathematical contexts.

• Identify the tenths place in your decimal number.
• Check the digit immediately to the right (the hundredths place).
• If that digit is 5 or greater, round up your tenths place by one. Otherwise, leave it as is.

By applying this method, you can provide accurate readings in situations that require a more precise figure.

Conversion Rate Understanding

Understanding the concept of conversion rates is crucial in mathematics and sciences as it forms the basis for translating one unit of measure into another. A conversion rate is simply the factor you multiply or divide by to make the change from one unit to another.

• In our example, the conversion rate from days to weeks is \( \frac{1}{7} \) because there are 7 days in a week.
• This means when you have any number of days, you divide by 7 to get the number of weeks.

This concept extends beyond time conversions, being useful in many areas like currency, length, and volume. Understanding conversion rates will simplify your ability to switch between different units confidently. It empowers you with a toolkit for handling diverse mathematical problems.