Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (d) 2,300,000.1 (7)

검증된 단계별 안내

Identify the number of significant figures required: 7.

Examine the given number: 2,300,000.1.

Count the significant figures in the given number: 2,300,000.1 has 8 significant figures.

Round the number to 7 significant figures. Since the 8th digit is 1, which is less than 5, the 7th digit remains unchanged.

The rounded number with 7 significant figures is 2,300,000.

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주요 개념

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Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for accurately reporting measurements and calculations in scientific contexts.

Rounding Rules

Rounding rules dictate how to adjust numbers to the desired level of precision. When rounding, if the digit to the right of the last significant figure is 5 or greater, the last significant figure is increased by one. If it is less than 5, the last significant figure remains unchanged. These rules ensure that the rounded number reflects the appropriate level of accuracy.

Scientific Notation

Scientific notation is a method of expressing numbers as a product of a coefficient and a power of ten, which simplifies the representation of very large or very small numbers. It is particularly useful in chemistry for maintaining significant figures, as it clearly indicates the precision of the measurement. For example, 2.3 x 10^6 retains three significant figures while being easily readable.