Show how converting numbers to scientific notation can help you decide which digits are significant.
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Scientific measurements are recorded in a way such that every digit is certain plus one uncertain digit. These digits are termed significant figures and they indicate the reliability of a measuring device. Significant figures refer to the entire number of digits that are recorded in any measurement. Non-zero digits are always significant. The zeros that are present between two non-zero digits are called captive zeros. Captive zeros are always significant. The zeros that are present at the end of a number are called trailing zero. Trailing zeros are significant only if there is a decimal point in the number. Zeros that are present at the start of a number are called leading zeros. Leading zeros are never significant.
The simple and convenient way of presenting large and small numbers in decimal form is called scientific notation. It is written in the form of a number between 1 to 10 multiplied with a suitable power of 10 which can be positive or negative. The power of 10 is not considered while counting the significant digits. The conversion of a number to scientific notation is helpful in determining the correct number of significant figures in any value or measurement as it eliminates all leading zeros and reduces the number of the trailing zeros.
For instance, the scientific notation of the value 0.0000007352 is represented as, 7.352×10-7. This conversion eliminates all the leading zeros which are not significant, making it easier to identify that there are four significant figures in the number.
The conversion of any value to the scientific notation eliminates all the leading zeros and reduces the number of trailing zeros of any value. As a result, it helps to determine the exact number of significant figures.