Question

Write \(0.550\) to (a) 2 s.f., (b) 1 s.f.

Short answer

Question: Round the number 0.550 to (a) 2 significant figures and (b) 1 significant figure. Answer: (a) 0.550 rounded to 2 significant figures is 0.55. (b) 0.550 rounded to 1 significant figure is 0.6.

Step-by-step solution

Identify the significant figures

The number we are given is 0.550. Significant figures are all the digits from the first non-zero digit to the last non-zero digit. In this case, the significant figures are 5 and 5.

Round the number to 2 significant figures (a)

To round the number 0.550 to 2 significant figures, we have to find the second significant digit, which is the second 5. Since the digit to the right of the second 5 is 0, the second 5 doesn't change, and we get 0.55 as the rounded number. (a) 0.550 rounded to 2 significant figures is 0.55.

Round the number to 1 significant figure (b)

To round the number 0.550 to 1 significant figure, we have to find the first significant digit, which is the first 5. Since the digit to the right of the first 5 is 5 (greater than or equal to 5), the first 5 gets rounded up by 1, resulting in 6. (b) 0.550 rounded to 1 significant figure is 0.6.

Key concepts

Understanding Significant Figures

Significant figures play a crucial role in the precision of numbers. They help us understand how accurately a number is measured or presented. The rule of thumb is to start counting significant figures from the first non-zero digit. For example, in the number 0.550, the significant figures are 5 and 5. Zeros preceding these digits are not counted as significant.
It's important to recognize significant figures because they tell us which digits in a number are reliable and meaningful. Thus, in scientific and mathematical contexts where precision is crucial, counting significant figures correctly ensures accurate data representation.
Always remember that when you perform operations like addition or multiplication, it's the number of significant figures that determines the accuracy level required for the answer.

Mastering Decimal Rounding

Decimal rounding involves adjusting the digits of a number to fit the required number of significant figures. This is often needed in scientific calculation to limit the number of significant figures and ensure consistency in reporting results. For example, if you have the number 0.550 and you need to round it to 2 significant figures, you look at the third digit after the decimal point to decide whether the second figure should change.
When the digit immediately following your chosen significant figure is 5 or more, you round up. If it's less than 5, you round down. For 0.550, the digit after the second significant figure is 0 (less than 5), so rounding to 2 significant figures gives you 0.55.
Practicing decimal rounding helps you keep data clear and prevents complications that can arise from overly precise or inaccurately reported numbers.

Exploring Numerical Approximation

Numerical approximation is the practice of finding a simple numerical value that is close to the exact value. It is especially useful when dealing with complex calculations in which a rounded result suffices instead of an exact one. Approximations often use rounded numbers for ease of computation and clarity of analysis.
In the example of 0.550, we approximate it to 2 and 1 significant figures. Rounded to 1 significant figure gives us 0.6, which is easy to work with in simple calculations. This approximation is helpful when you need to provide a quick answer or when high precision isn't necessary.
Remember, a good approximation maintains a balance between simplicity and precision. It allows for efficient computation while still keeping the results meaningful and accurate enough for the task at hand.