an approximation has been

USAGE SUMMARY

The phrase "an approximation has been" is correct and usable in written English.
It can be used when discussing a value or estimate that is not exact but is close enough for a particular purpose. Example: "In our calculations, an approximation has been made to simplify the complex data."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

4 human-written examples

Although the behavior of the bond coat is highly nonlinear, an approximation has been developed which permits accurate description of undulation development under quite general conditions.

Acta Materialia

Such an approximation has been done in several ways.

Mathematical Sciences

Such an approximation has been studied in the context of long block codes [13,14] as well as [15].

EURASIP Journal on Wireless Communications and Networking

Despite this, such an approximation has been shown to be very tight in the entire SNR region [9, 13, 24].

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

55 human-written examples

Recently, another method called A-harmonic approximation has been widely applied to prove the optimal partial regularity for nonlinear elliptic systems or subelliptic systems in the Heisenberg group and Carnot groups; see [23 29].

Journal of Inequalities and Applications

Obtaining the outage probability in this simple form allows us to easily study and know the effect of each system parameter on the system performance instead of dealing with the long/complex expressions derived in Section 3. Notice that such an accurate approximation has been widely used in the conventional cooperative diversity systems.

EURASIP Journal on Wireless Communications and Networking

A phenomenological model based on a Bragg Williams approximation has been proposed to describe the observed behaviour in terms of the evolution of the magnetic contribution to the total entropy change.

Acta Materialia

An improved algorithm with a 3 k-3) approximation has been proposed [ 139] with polynomial running time.

BMC Medical Informatics and Decision Making

We notice that the series solutions converge rapidly; the absolute error was obtained with only a few perturbative terms, so we say that a good approximation has been achieved, the validity range applies to the entire domain of equation (49) and there is no restriction to a smaller domain.

Advances in Difference Equations

In order to simplify the calculation a Pade approximation has been employed [Cohen A. Rheol. Acta.

Polymer

The tested specimens have been numerically modeled to calibrate the analytical tools, and a satisfactory approximation has been obtained between experimental and numerical results.

Engineering Structures

Expert writing Tips

Best practice

When using "an approximation has been", ensure the context clearly explains why an approximation was necessary and any potential limitations it introduces.

Common error

Avoid presenting an approximation as a precise value. Always acknowledge that it's an estimation with inherent uncertainties.

Linguistic Context

The phrase "an approximation has been" functions as a passive construction indicating that the act of approximating has occurred. Ludwig confirms its grammatical correctness. It typically introduces a statement where a precise calculation or measurement wasn't possible or practical.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, the phrase "an approximation has been" is grammatically correct, according to Ludwig, and serves to indicate that an estimate or simplified method has been used in place of a precise calculation. Its usage is most common in scientific contexts where acknowledging the potential limitations of the method is important. While the phrase is relatively rare, understanding its implications is crucial for clear and accurate communication, particularly in technical fields. It's important to clarify why an approximation was necessary and acknowledge its inherent uncertainties. The provided alternatives and writing guidance can help refine your expression for better clarity and precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

an estimation was made

Replaces "approximation" with "estimation", focusing on the act of estimating.

a rough estimate was used

Emphasizes the lack of precision in the estimate.

an estimate has been determined

Highlights the conclusion of the estimation process.

an approximate value was used

Focuses on the value obtained through approximation.

a simplified calculation was performed

Highlights the simplification aspect of the approximation.

a working assumption was applied

Suggests the approximation is a basis for further work.

a heuristic approach was taken

Implies the use of a practical, though not necessarily optimal, method.

a model has been simplified

Focuses on the model being made more understandable.

an educated guess was utilized

Highlights the intuitive, informed nature of the estimate.

a back-of-the-envelope calculation occurred

Emphasizes the quick and informal nature of the approximation.

FAQs

How can I use "an approximation has been" in a sentence?

You can use "an approximation has been" to indicate that a value or result isn't exact but is sufficiently close for the purpose at hand. For example, "In the absence of complete data, "an approximation has been" used to estimate project costs."

What are some alternatives to saying "an approximation has been"?

Depending on the context, you can use phrases like "an estimation was made", "a rough estimate was used", or "an approximate value was used".

Is it always acceptable to use approximations in calculations?

While approximations can simplify complex problems, it's important to acknowledge their limitations and potential impact on the accuracy of the results. The appropriateness of using "an approximation has been" depends on the specific context and acceptable error margin.

What's the difference between "an approximation has been" and "an exact calculation has been"?

"An approximation has been" indicates that a simplified method was used to estimate a value, whereas "an exact calculation has been" means a precise method was used to determine an accurate value.