Can you think of situations in which it might be preferable to compute with decimals rather than fractions or to compute with fractions rather than decimals, give examples of each situation and tell why you think that number form is preferable
A water tank will be drained at a constant rate of 42.4 liters per hour starting at 9:00 A.M. After one hour, the change in the amount of water in the tank can be represented as –42.4. Which of the following represents the total change in the amount of water in the tank by 9:00 A.M. the next day?
Certainly! There are situations in which it may be preferable to compute with decimals rather than fractions, and vice versa. Let's explore examples for both cases:
1. Computing with Decimals:
- Financial calculations: When working with money, decimals are often more practical. For instance, calculating interest on a loan or computing profits and losses in business transactions can be better represented using decimals.
- Scientific measurements: Decimal notations are commonly used in scientific calculations, such as calculating distances, volumes, or weights. Decimals provide greater precision and are more compatible with measuring tools that provide readings with decimal places.
Why decimals are preferable:
Decimals often offer greater simplicity and ease of use in both calculation and representation. They are the standard format used in many real-world applications, making them more familiar and convenient in everyday life.
2. Computing with Fractions:
- Cooking and baking: Fractions are frequently used in recipes and cooking measurements. For example, when halving or doubling a recipe, working with fractions allows for straightforward adjustments.
- Construction and engineering: Fractions enable precise measurements in construction and engineering, especially with materials like lumber, where specific lengths need to be cut or installed.
Why fractions are preferable:
Fractions can be more precise and accurate for certain calculations, especially when dealing with exact or non-recurring values. Fractions also retain their fractional form, providing valuable context or meaning in certain fields, such as cooking or measurements.
It's important to note that the preference for decimals or fractions depends on the specific context and the nature of the values being computed. Decimal or fraction form can be chosen based on practicality, convenience, precision, or conventions within a particular field.
It is better to use fractions when it is on top of other fractions, for example 2/3+2/4
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2/5-2/6
Because then you can get a common demoninator and cancel
For decimals I don't know pretty much everything else