Problem 73 - Prealgebra

Question

If you have a penny dated anytime from 1959 through \(1982,\) its original weight was 3.11 grams. If the penny has a date of 1983 or later, the original weight was 2.5 grams. Write the two weights in words.

Step-by-Step Solution

Answer

3.11 grams is three point one one grams, and 2.5 grams is two point five grams.

Step 1: Identify Penny Date Categories

There are two categories for penny dates: those dated from 1959 through 1982, and those dated 1983 or later. Each category has a different original weight.

Step 2: Assign Weight to First Category

For pennies dated from 1959 through 1982, the original weight is 3.11 grams.

Step 3: Assign Weight to Second Category

For pennies dated 1983 or later, the original weight is 2.5 grams.

Step 4: Convert Numerical Weight to Words for First Category

The numerical weight 3.11 grams is translated into words as 'three point one one grams.'

Step 5: Convert Numerical Weight to Words for Second Category

The numerical weight 2.5 grams is translated into words as 'two point five grams.'

Key Concepts

Unit Conversion

Unit conversion is really common in math and science. It helps us change a measurement from one unit to another. Here, we're working with grams, the unit for weight. Knowing how to switch between units can make problem-solving much easier. For these old pennies, we're not changing units, but it's critical to understand what a gram represents. A gram is a metric system unit that's surprisingly lightweight.

• 1 gram is roughly the weight of a paperclip.
• It’s part of the metric system, which is very user-friendly because it’s based on powers of ten.
• This makes conversions, like from grams to kilograms, simple and straightforward.

Understanding units gives context and makes the numbers meaningful. It’s especially helpful in calculations or when comparing different measurements.

Weights in Words

Translating numerical weights into words is a nice skill for clarity in communication. When you state numbers verbally, it ensures everyone is on the same page. In our penny exercise, we converted 3.11 and 2.5 grams into words. This is important when you need to write a check, fill out a form, or even in legal documents. You can avoid misunderstandings.

Converting numbers to words goes like this:

• For the weight 3.11, you say, 'three point one one grams.' Each digit after the decimal point is stated separately.
• For the weight 2.5, you say, 'two point five grams.' It’s straightforward and eliminates confusion.

When you rely on words, you make the information clear to all audiences, regardless of their familiarity with numbers.

Numerical Translation

Numerical translation might sound complex, but it involves turning numbers into different forms, such as words or mathematical expressions. Understanding how to translate numbers helps in evaluating data and communicating effectively. In this exercise, you transformed the numeric weights of pennies into words. Doing this speaks volumes in real-life scenarios where numbers need to be exact in spoken or written form.

When doing numerical translations:

• Express numbers clearly, especially decimal numbers.
• Ensure many digits are understood by stating them individually, like 'point one one.'
• This impacts communication in sectors like banking, law, and education, where accuracy is key.

This concept is useful beyond pennies, making numerical data precise and comprehensible.