ERROR SIGNIFICANT FIGURE AND ROUNDING OFF:

INTRODUCTION:

Estimation is a sort of rounding off. Estimation is employed in daily life as well as in areas such as mathematics and physics. Many physical numbers are estimated by rounding off the actual value to the next whole number, such as the amount of money, the distance travelled, the length measured, and so on.

Significant numbers or figures can be described as a specific number or set of digits that can accurately communicate the significance of a number. For example, the number 5.548 has four significant digits. These crucial figures help to clarify the numbers. They’re also known as significant digits.

ROUNDING OFF:

It’s easier to round off a number by preserving its value but moving it closer to the next number. This is used for whole numbers and decimals in hundreds, tens, tenths, and other places. The number of crucial figures that result is just the number of reliable known figures. There are three major figures in the number 25.6. The presence of non-zero digits is always meaningful. There are six major digits in 7.24364.  As a result, 98 has two significant numbers, while 98.7 has three.

RULES FOR ROUNDING DECIMAL NUMBER:

The following are the decimal number rounding rules:

1. Look to the right of the rounding digit to determine it.
2. Consider the digits on the right hand side to be equivalent to zero if they are less than 5.
3. If the digits on the right hand side are larger than or equal to 5, add +1 to that digit and treat the rest of the numbers as zero.

RULES FOR ROUNDING WHOLE NUMBER:

The following are the whole number rounding rules:

1. Always use the smaller place value for a more accurate final result.
2. Look for the next smaller location, which is to the right of the rounded-off number. If you’re rounding off a numeral from the tens place, for example, seek for a digit in the ones place.
3. The digit in the smallest location is left unaltered if it is less than 5. Rounding down is when a number becomes 0 after a certain number of digits.
4. If the smallest digit is more than or equal to 5, the digit is multiplied by one. Any numerals following that become zero. 

EXAMPLE:

Rounding to the nearest tenth of a percent: Assume the value is 0.23.

To complete the process, follow the steps below:

The digit at the tenth position has been identified as 2.

The smallest spot is then assigned the number 3.

The place digit with the least value is less than 5. As a result, the digit is rounded down.

After rounding off, we get 0.2 as the final value.

SIGNIFICANT FIGURE:

Significant figures are used to establish the number that is presented in the form of digits. In a meaningful way, these digits represent numbers. Significant digits is a word that is frequently used instead of figures. All values beginning with the first non-zero digit on the left are considered significant numbers, and the number of significant digits can be calculated from this.

Significant Figures Rules:

732756. The non-zero digits are all important. There are six significant digits in the number 732756.
732757. Between any two non-zero digits, all zeros are significant. 228 .0036, for example, has seven significant digits.
732758. All zeros to the right of a decimal point, as well as to the left of a non-zero digit, have no meaning. 0.00235, for example, has three significant digits.
732759. All zeros to the right of a decimal point are relevant only if they are followed by a non-zero digit. For example, the number 50.85 has four significant digits.

Rounding of significant figure:

To round off important numbers, there are two rules:

1. To begin, we must determine to which digit the rounding off should be applied. If the number after the rounding off digit is less than 5, all the numbers on the right side must be eliminated.

B.However, if the digit next to the rounding off digit is more than 5, we must add 1 to the rounding off digit and ignore the remaining numbers on the right side.

EXAMPLE:

CONCLUSION:

Estimation is a sort of rounding off. Estimation is employed in daily life as well as in areas such as mathematics and physics. Many physical numbers are estimated by rounding off the actual value to the next whole number, such as the amount of money. The number that is provided in the form of digits is established using significant figures. These digits represent numbers in a meaningful way. Instead of figures, the term significant digits is frequently used. In this chapter we have discussed error significant figures rounding off, rounding off of whole numbers, decimal numbers.