How many significant figures are in each of the following? a. 100 e. 0.0048 b. 1.0 ×10^2 f. 0.00

How many significant figures are in each of the following?...

Key Concepts

Scientific Notation

Scientific notation expresses numbers in the form of a coefficient multiplied by a power of ten. In this notation, all digits in the coefficient are inherently significant, making it a useful method to clearly represent the number of significant figures.

Significant Figures

Significant figures indicate the digits in a number that carry meaningful information about its precision. This concept is crucial for conveying the exactness of measurements and calculations, effectively distinguishing between certain and uncertain digits.

Leading Zeros

Leading zeros are zeros that appear before the first nonzero digit in a number. They serve only as placeholders for the decimal point's position and are not considered significant, as they do not reflect any measured precision.

Captive Zeros

Captive zeros are zeros located between nonzero digits. Because they are sandwiched between significant values, they are always considered significant and contribute to the overall precision of the number.

Trailing Zeros

Trailing zeros are zeros at the end of a number. Their status as significant or not depends on the context, such as the presence of a decimal point. When a number includes a decimal point, trailing zeros are significant and indicate measured precision.

Transcript

00:01 We have to find out the number of significant figures in each case and for that we have to consider the rules.

00:07 So they are that all non -zero resets are significant.

00:13 The zeros present between two non -zero digits are also significant.

00:18 The zeros present on the right side of non -zero digit that are also significant and the zeros present left side of the non -zero digit that is non -zero digit that is non -zero.

00:30 Non -significant.

00:31 Okay.

00:32 So first of all we have given 100.

00:37 So here we have one as non -zero digits and two zeros are present on the right side.

00:43 So there are three significant figures.

00:57 Then in next part we have given 1 .0 multiplying 10 raise to power 2.

01:09 So so that is we have the power 10 rest of power 2.

01:16 This is not to be considered.

01:19 When we are finding out the number of significant figures, don't consider this 10 rest to power 2 or any base value and the exponent value.

01:33 We will only consider this value here.

01:36 So we have 1 .0.

01:38 So 0 is present on the right side.