Significant Figures: rounding off numbers
This article would cover the rules of rounding off a given number which is simply estimation based on certain rules. Before we move on to the rules of rounding off let’s take a look at significant figures. The number of significant figures in a result is simply the number of figures that are known with some degree of reliability. The number 13.2 is said to have 3 significant figures. Non-zero digits are always significant. 3.14159 has six significant digits (all the numbers give you useful information). Thus, 67 has two significant digits, and 67.3 has three significant digits.
Most of the times though in real life, we do not use numbers just as they are, we very often use the skill of rounding off numbers to make handling the numbers easier. When you eat out with your friend, you don’t split the bill to the exact dollar amount, you split it to the nearest tens to make the division easier. A bill of 1593 for four friends can be rounded off to 1600 which significantly aids arithmetic operations of the number. A rounded number has about the same value as the number you start with, but it is less exact.For example, 576 rounded to the nearest hundred is 600. That is because 576 is closer in value to 600 than to 500. When rounding off to the nearest dollar, $3.69 becomes $4.00, because $3.69 is closer to $4.00 than to $3.00.
Like arithmetic operations of significant figures, rounding off numbers also follows certain rules;
- If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Basically the digit to be dropped is greater than 5, the last retained digit is increased by one.
- (a) Example: 38 rounded to the nearest ten is 40, 349 is rounded to 350, 17.6 is rounded off to 18.
- If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.With decimals, thus effectively this means that if the digit to be dropped is less than 5, the last remaining digit is left as it is.
- (a) Example: 33 rounded to the nearest ten is 30, 15.4 is rounded to 15.
Depending on the requirement, numbers can be rounded off to various standards. Consider an example, take the number 5678.
- 5678 rounded to the nearest ten is 5680
- 5678 rounded to the nearest hundred is 5700
- 5678 rounded to the nearest thousand is 6000
As a rule, this can be written as all the numbers to the right of the place you are rounding to become zero’s.
- If the number lies on the boundary, like in 375 or 2.745 where the last digits to be rounded off are exactly in between the two extremes. The convention here states that if the preceding digit is even, the last digit is dropped and if it is odd, the receding digit is increased by 1.
- 375 is rounded off to 380; 365 is rounded off to 360
- 745 is rounded off to 2.74; 2.755 is rounded off to 2.76
The rules to use rounding off on significant figures are discussed in this article. To learn more about science download Byju’s The Learning App to fall in love with learning.
Also, learn Errors in measurements.
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