Following this rule, 2.315 and 2.325 both round to 2.32—instead of 2.325 rounding up to 2.33—when rounded off to the nearest 100th. Again, the same rules apply. An approximate value may be sufficient for some purposes, but scientific work requires a much higher level of detail. The exercises here include skills like rounding the amount to the nearest dollar, ten dollars, hundred dollars and ten cents. The result is less accurate, but easier to use. Rounding Rules for Decimal Numbers Determine what your rounding digit is and look to the right side of it. The answer is rounded off to the same number of SF as possessed by the least precise term in the calculation. This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality: CK-12 Foundation by Sharon Bewick, Richard Parsons, Therese Forsythe, Shonna Robinson, and Jean Dupon. You would add (or subtract) the numbers as usual, but then you would round the answer to the same decimal place as the least -accurate number. 18.01 g (rounding … For example, dividing 125 by 307 on a calculator gives 0.4071661238… to an infinite number of digits. When you use your calculator to do a calculation such as 37.4 + 5.763 1 = 43.163 1, it is tempting to keep all of the decimal places given by the calculator. For example, if you were to add 1.2 and 4.71, we note that the first number stops its significant figures in the tenths column, while the second number stops its significant figures in the hundredths column. When we round 0.5 down we get this: 7.6 rounds up to 8; 7.5 rounds down to 7; 7.4 rounds down to 7-7.4 rounds up to -7-7.5 rounds down to -8-7.6 rounds down to -8 "Symmetric" Rounding. How to round off a floatig point value to two places. On this page you find our Rounding Off worksheets suited for grade levels 4 and 5 based on the Singapore math Curriculum.Grade 6 students can, of course, also use these worksheets. Example: x = 7.82 is rounded off to 7.8, again x = 3.94 is rounded off to 3.9. Plunge into practice with this set of printable rounding money worksheets, designed for students of grade 3, grade 4, grade 5, and grade 6, and gain a thorough knowledge of rounding monetary values in dollars and cents. Scientific notation provides a way of communicating significant figures without ambiguity. 4 could have been as large as 37. Any digits after that number become zero and this is known as rounding up. figs. The answer should be rounded off to  27.7 since 22.3 contains only one decimal place. 32 ----> round down to 30 Rounding to a Place Value When we round a number, we round it to the nearest place value. Click here to let us know! 3. CASE B: In rounding off numbers, the last figure kept should be increased by 1 if the first figure dropped is greater than 5.: For example, if only two decimals are to be kept, then 6.4872 becomes 6.49. A set of addition and subtraction questions, where children can use their rounding skills to help find the answer. The final example we want to show you when we are talking about rounding off whole numbers is when you need to round off a number to the nearest thousands digit. SplashLearn is an award winning math learning program used by more than 40 Million kids for fun math practice. In the worked examples in this text, we will often show the results of intermediate steps in a calculation. Join our email newsletter to receive free updates! The calculator answer is 2,085.5688, but we need to round it to five significant figures. e.g. Round off the answer to the calculation 245.233 4 - 38.715 =  206.518 4. Notice that this answer agrees with the original answer only as far as the first decimal place, 17.363  and 17.3125. What would this be equal to? MORE ELEMENTARY ADDITION Mental calculation by Rounding off or Regrouping. For multiplication or division, the rule is to count the number of significant figures in each number being multiplied or divided and then limit the significant figures in the answer to the lowest count. The final answer is then rounded to the correct number of significant figures at the very end. CASE B: In rounding off numbers, the last figure kept should be increased by 1 if the first figure dropped is greater than 5.: For example, if only two decimals are to be kept, then 6.4872 … To round a number, first decide how many significant figures the number should have. For example, the number 450 has two significant figures and would be written in scientific notation as 4.5 × 102, whereas 450.0 has four significant figures and would be written as 4.500 × 102. Rule 1. But maybe you think "7.5 rounds up to 8, so -7.5 should go to -8", which is nice and symmetrical. 7631). When performing mathematical operations, there are two rules for limiting the number of significant figures in an answer—one rule is for addition and subtraction, and one rule is for multiplication and division. So when you round 251 to the nearest 10, you're going to get 250. [ "article:topic", "rounding", "showtoc:no", "license:ccbyncsa" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FBookshelves%2FIntroductory_Chemistry%2FMap%253A_Fundamentals_of_General_Organic_and_Biological_Chemistry_(McMurry_et_al. The answer should be rounded off  to 299.14 since the least precise number used in calculating the answer contained only two decimal places. The first digit dropped is 1, so we do not round up. 3.33333. 1.12: Problem Solving - Unit Conversions and Estimating Answers, Calculations Involving Multiplication/Division and Addition/Subtraction, information contact us at info@libretexts.org, status page at https://status.libretexts.org, 8 is replaced by a 0 and rounds the 0 up to 1. The calculator gives 2,001.06 as the answer, but because 611 and 1027 has its farthest-right significant figure in the ones place, the final answer must be limited to the ones position. If the number to be dropped is less than 5, there is no change (e.g. If the calculation is an addition or a subtraction, the rule is as follows: limit the reported answer to the rightmost column that all numbers have significant figures in common. This could be the tens, hundreds, thousands, etc. For addition/subtraction: The digits reported are determined by the uncertainty in the least precise measurement (not by the number of significant figures). Any number of digits after that number becomes zero and this is known as rounding down. Back to Section 1. All numbers from a measurement are significant. Right now, the measurement contains six significant figures. Rounding off to Nearest Tens. Then, perform the addition. Although there are several conventions, in this text we will adopt the following rule: the final answer should be rounded up if the first dropped digit is 5 or greater and rounded down if the first dropped digit is less than 5. If the digit to be dropped is less than 5, then the preceding digit is left unchanged. Example 15. 137.3 s tenths place (least precise) + 70.90 s hundredths place = 208.20 s. Round the final answer to the tenths place based on 137.3 s. \( {118.7g \over 2} \) 4 sig figs = 59.35 g 4 sig figs. While rounding off measurements, we use the following rules by convention Rule 1. The number with the least number of significant figures is 1.008g; the number 2 is an exact number and therefore has infinite number of significant figures. Adding  37.449 +  5.763149  yields 43.212149, a number which agrees with the previous answer (43.1631) only in the first two digits. See screenshot: Note: In the above formula, B2: B5 is the data range you want to round … Have questions or comments? This depends on when and in what grade level students learn about rounding off. For more information contact us at info@libretexts.org or check out our status page at https://status.libretexts.org. The final example we want to show you when we are talking about rounding off whole numbers is when you need to round off a number to the nearest thousands digit. PHP_ROUND_HALF_UP - Default. In fact, estimation and rounding-off in maths go hand in hand.