Question

Perform the indicated operations. Give exact answers. \(5.886-3.143=\) ______

Short answer

2.743

Step-by-step solution

Understand the Problem

We are tasked with subtracting the number 3.143 from 5.886. This is a straightforward arithmetic subtraction problem.

Align the Decimal Points

Before performing the subtraction, ensure that the decimal points of the two numbers are aligned properly to ensure accurate subtraction.

Perform the Subtraction

Begin subtracting from the rightmost digit to the leftmost digit: 1. Subtract the thousandths place: 6 - 3 = 3 2. Subtract the hundredths place: 8 - 4 = 4 3. Subtract the tenths place: 8 - 1 = 7 4. Subtract the units place: 5 - 3 = 2 Combine these results to get 2.743.

Key concepts

Subtraction

Subtraction is one of the basic operations in arithmetic. It involves finding the difference between two quantities. In simpler terms, it helps us figure out what remains when one number is taken away from another. For example, when we subtract 3.143 from 5.886, we determine how much more 5.886 is than 3.143. Subtraction is used in various daily tasks, like calculating change, balancing budgets, or even measuring distances. It is important to keep in mind that subtraction is not commutative, which means changing the order of the numbers will give different results. Always subtract the smaller number from the larger to get a positive result.

Decimal Alignment

Decimal alignment is very crucial when performing subtraction with decimal numbers. If decimals are not aligned correctly, the result of the subtraction can be incorrect. To ensure accuracy:

• Line up the numbers vertically so that the decimal points are directly above one another.
• This alignment ensures that each digit is in the correct place value – thousandths with thousandths, hundredths with hundredths, and so on.
• Carefully line up the numbers from right to left, filling in any missing places with zeroes, if needed, to avoid mistakes.

Once the decimal points are aligned, you can proceed with the subtraction knowing that each digit represents the correct place value.

Step-by-Step Problem Solving

Solving a problem step-by-step is an effective method to ensure that you do not miss any part of a complex arithmetic procedure. This approach breaks down the problem into manageable steps:

• First, understand what the problem asks. In this case, subtract 3.143 from 5.886.
• Second, prepare the numbers by aligning the decimals to set up for subtraction.
• Then, perform the subtraction, starting from the rightmost digit, which is the thousandths place, and move leftwards.

This organized method allows you to handle each part of the problem systematically, reducing the chance for errors, and making complex calculations seem simpler. It is also helpful for maintaining accuracy throughout the process.

Exact Answers

An exact answer is key when we talk about precision, especially in mathematics and scientific calculations. Exact answers reflect the precise result of a calculation without rounding or approximating. For example, when subtracting 3.143 from 5.886, it is essential to get the exact result, which is 2.743, without rounding off the decimals. Exact answers are vital in fields such as engineering, physics, and accounting because they ensure accuracy and reliability in computations. Ensure you perform each step carefully to maintain this precision and double-check your results to confirm they are exact.