Question

\(\quad\) Write \(9.0046\) to (a) 3 s.f., (b) 2 s.f., (c) 1 s.f.

Short answer

Question: Round the number 9.0046 to the specified significant figures: a) 3 s.f., b) 2 s.f., and c) 1 s.f. Answer: a) 9.00, b) 9.0, and c) 9.

Step-by-step solution

Identify the significant figures and round to 3 s.f.

In this part, we will round 9.0046 to 3 significant figures (s.f.). The first three significant figures are 9, 0, and 0. Since the next digit (4) is less than 5, the third digit (0) remains the same. Therefore, we have: 9.0046 rounded to 3 s.f. is 9.00.

Identify the significant figures and round to 2 s.f.

In this part, we will round 9.0046 to 2 significant figures (s.f.). The first two significant figures are 9 and 0. Since the next digit (0) is less than 5, the second digit (0) remains the same. Therefore, we have: 9.0046 rounded to 2 s.f. is 9.0.

Identify the significant figures and round to 1 s.f.

In this part, we will round 9.0046 to 1 significant figure (s.f.). The first significant figure is 9. Since the next digit (0) is less than 5, the first digit (9) remains the same. Therefore, we have: 9.0046 rounded to 1 s.f. is 9.

Key concepts

Rounding Numbers

Rounding numbers is an essential skill in arithmetic and daily life. It simplifies numbers, making them easier to work with. When rounding, you focus on the digit you want to round to, considering the number immediately after it.

Here's a simple way to round numbers:

• Identify the digit at the place you want to round to.
• Look at the digit right after it.
• If the following digit is 5 or greater, increase the rounding digit by one.
• If the following digit is less than 5, keep the rounding digit the same.

This method helps in reducing complexity without losing too much accuracy. For example, if rounding 9.0046 to 3 significant figures, check the fourth digit, which is 4. Since it's less than 5, 9.0046 becomes 9.00.
By understanding rounding, you can manage numbers more effectively in both academic and real-world situations.

Precision in Mathematics

Precision in mathematics refers to how detailed a numerical representation is. The more significant figures a number has, the more precise it is. But why does precision matter? It helps in maintaining accuracy, especially in scientific calculations.

In mathematics, using too many digits can make things unnecessarily complicated. This is why understanding significant figures helps. By using appropriate precision, you balance simplicity and accuracy without making your calculations either too complex or losing critical details.

For example, when calculating the distance covered in a journey involving real-time scenarios, having too much precision might not be practical. Rounding to suitable significant figures ensures that calculations are both manageable and meaningful.

Number Representation

Number representation varies based on context and purpose. It's crucial in conveying accurate information in mathematics. Numbers can have integer parts, decimal parts, and can be represented with varying levels of detail.

Using significant figures is a way to denote numbers with an appropriate level of precision. For example, representing 9.0046 with different significant figures can change how precise this number is:

• 3 significant figures: 9.00
• 2 significant figures: 9.0
• 1 significant figure: 9

Each variation has its own context of use. Fewer significant figures simplify the number, while more figures add detail and accuracy.

Understanding these concepts helps you present numbers effectively, knowing when to be detailed and when simplification is enough. This knowledge is particularly important in fields like engineering, science, and finance where both precision and simplicity are necessary.