Question

Write \(0.0982\) to (a) 3 d.p., (b) 2 d.p., (c) I d.p., (d) 2 s.f., (e) 1 s.f.

Short answer

Question: Convert the decimal number 0.0982 into the following formats: 3 decimal places, 2 decimal places, 1 decimal place, 2 significant figures, and 1 significant figure. Answer: 0.0982 can be converted as follows: - 3 decimal places: 0.098 - 2 decimal places: 0.10 - 1 decimal place: 0.1 - 2 significant figures: 0.099 - 1 significant figure: 0.1

Step-by-step solution

Convert 0.0982 to 3 d.p.

To convert the number to 3 decimal places (d.p.), we need to look at the fourth decimal place. If it's 5 or greater, we round up; otherwise, we round down. In this case, the fourth decimal place is 2, which is less than 5, so we round down. The result is 0.098.

Convert 0.0982 to 2 d.p.

To convert the number to 2 decimal places (d.p.), we need to look at the third decimal place. If it's 5 or greater, we round up; otherwise, we round down. In this case, the third decimal place is 8, which is greater than 5, so we round up. The result is 0.10.

Convert 0.0982 to 1 d.p.

To convert the number to 1 decimal place (d.p.), we need to look at the second decimal place. If it's 5 or greater, we round up; otherwise, we round down. In this case, the second decimal place is 9, which is greater than 5, so we round up. The result is 0.1.

Convert 0.0982 to 2 s.f.

To convert the number to 2 significant figures (s.f.), we need to look at the second significant digit. If the following digit is 5 or greater, we round up; otherwise, we round down. In this case, the second significant digit is 9 and the following digit is 8, which is greater than 5, so we round up. The result is 0.099.

Convert 0.0982 to 1 s.f.

To convert the number to 1 significant figure (s.f.), we need to look at the first significant digit. If the following digit is 5 or greater, we round up; otherwise, we round down. In this case, the first significant digit is 0 and the following digit is 9, which is greater than 5, so we round up. The result is 0.1.

Key concepts

Rounding Numbers

Rounding numbers is a fundamental part of mathematics that helps in simplifying complex calculations by keeping numbers concise without significantly altering their value. When rounding a number, you need to determine which part of the number you want to round. For instance, when you round to 3 decimal places (3 d.p.), you look at the fourth decimal place to decide whether to round up or down.

The general rule for rounding is simple:

• If the digit to the right of the place you are rounding to is 5 or more, you increase the rounding digit by 1.
• If it is less than 5, you keep the rounding digit the same.

For example, rounding 0.0982 to 2 decimal places, the third decimal (8) is greater than 5, so we round up, turning it into 0.10. The concept of rounding brings clarity and makes numbers easier to comprehend,
especially when dealing with long decimal expansions.

Significant Figures

Significant figures are used to express a number to reflect its precision. Unlike decimal places, which focus on the position after the decimal, significant figures consider all digits that contribute to the number's precision.
This includes how a number is expressed rather than a specific decimal place.

Counting significant figures starts from the first non-zero digit. For example, in the number 0.0982:

• The first significant figure is the digit '9'.
• The second significant figure is '8'.

If you needed to express 0.0982 to 1 significant figure, you would only consider '9' and check the next digit ('8') to determine rounding—resulting in 0.1.
Remember, significant figures give a better understanding of the number's accuracy and help in maintaining precision during calculations.

Mathematical Precision

Mathematical precision is crucial for accurate calculations, especially in scientific contexts where exact numbers play significant roles.
Mathematical precision involves not only the physical properties of numbers but how detail and certainty are communicated through numbers and rounding methods.

The lens of mathematical precision helps in determining how much detail to include in computations.

• In a setting where precise measurements are needed, more significant figures or decimal places may be required.
• However, in simpler cases or estimations, fewer figures could suffice.

When you simplify numbers by rounding, be it through decimal places or significant figures, you need to understand and decide the level of certainty required in your result.
Use mathematical precision to maintain balance between simplicity and exactness, especially when computations involve multiple steps.