Final answer:
Place value is important in mathematics because it helps us understand the value of each digit in a number and how it contributes to the overall value of the number. It allows us to perform operations accurately and efficiently, helps with estimation and approximation, and is crucial in working with significant figures.
Step-by-step explanation:
Place value is important in mathematics because it helps us understand the value of each digit in a number and how it contributes to the overall value of the number. The place values are determined by the position of the digits relative to the decimal point. For example, in the number 231.45, the digit 2 represents 200, the digit 3 represents 30, and the digit 1 represents 1. Understanding place value allows us to perform operations, such as addition, subtraction, multiplication, and division, accurately and efficiently.
Place value also helps us with estimation and approximation. Instead of working with numbers to a high precision with many decimal places, we can round the numbers to a certain number of decimal places, which makes calculations easier and more practical in real-world situations.
Additionally, place value is important in working with significant figures. The number of digits to the right of the decimal point in the result of addition or subtraction should be the same as the number of digits to the right of the decimal point in the least precise number used in the calculation. Having a good understanding of place value helps us determine the appropriate number of significant figures to use in various mathematical operations.