Final answer:
To count significant digits in a number without a decimal point, start from the first nonzero digit on the left, disregarding leading zeros and trailing zeros unless they are significant by being between non-zeros or denoted by a decimal.
Step-by-step explanation:
When gauging the significance of digits in a number, especially in the context of significant figures, the positioning of the decimal point plays a pivotal role. If the decimal is absent, the default assumption is that the decimal point is to the right of the last digit. Hence, when encountering a number without a marked decimal, you start counting significant digits from the right side only if there are trailing zeros which usually aren't significant unless specified by a decimal point. On the other hand, counting significant digits from the first nonzero digit from the left through all subsequent digits to the right establishes the number of significant figures in the measurement, unless it concludes with a zero lying to the left of an absent decimal point – which may or may not be significant depending upon the accuracy of the measuring device or stated mathematically.
As a rule, zeros that appear at the beginning of a decimal number (‘leading zeros’) are not counted as significant; they simply place the significant digits in their proper positional columns. For instance, 4200+540 equals 4740; if we did not have any specified precision beyond whole numbers, we'd consider only the significant figures and round accordingly. The same goes for trailing or right-end zeros in a measurement like 150 mm; without additional context, it can be difficult to determine if the zero is significant.
Therefore, while counting digits to determine the number of significant figures in a number without a decimal point, we typically disregard leading and trailing zeros unless they are sandwiched between significant figures or indicated as significant by a decimal point.