So the required answer is 510 km/h.īe careful, though, since sometimes the result may look a bit Now 512 correct to the nearest 10 is 510. When adding or subtracting approximate numbers, the result should have the precision of the least precise number. The nearest 10) so we need to write the answer correct to the nearest 10. When comparing 1450 and 938, the least precise of the 2 numbers is 1450 (it is correct to Two jets flew at `938` km/h and `1450` km/h respectively. `sqrt(22.97)` should be written correct to 4 significant digits:īoth numbers have the same accuracy. When finding the square root of a number, the result has the same accuracy as the number. When multiplying `3.564` and `2.37`, our final answer should have three significant digits. When multiplying or dividing approximate numbers, the result should have the accuracy of the least accurate number.
When adding `2.3`, `5.704` and `12.67`, our final answer should be correct to one decimal place. Precision of the answer: When adding or subtracting approximate numbers, the result should have the precision of the least precise number. Is 80.53 closer to 80.5 or 80.6? When we round some more (to whole numbers), we ask is 80.53 closer to 80 or 81? Operations with Approximate Numbers Notation: We use the symbol ≈ for "is approximately equal to". Rounded to two significant digits, we have 81. The number 80.53 rounded to three significant digits is 80.5. Rounding Off Decimals Example 3 - Rounding The numbers have the same precision, as the last significant digit is in the thousandths position for both. Example 2 - Accuracy and precisionĬomparing the two numbers 0.041 and 7.673, we see that 7.673 is more accurate because it has four significant digits, where 0.041 only The precision of a number refers to the decimal position of the last significant digit. Significant digits can also give us an indication of the precision of a number. This means 26.832 cm is closer to the actual diameter of the pipe than 26.83 cm is (assuming the person measuring is doing a good job).
The measurement 26.832 cm from above is more accurate than the rounded figure 26.83 cm. The first answer is not very close to the true weight (it only has one significant digit), whereas the second one is much closer (it has 4 significant digits). The other students get an answer of 6,748 grams (that is, 6.748 kg). The students who use the first set of scales can only give whole-number answers like 7 kg. One set of scales indicates whole-numbered kilograms only, whereas the second one is in grams. The more significant digits in the number, the more accurate it indicates the measurement to be.įor example, we conduct our weight measurement activity again, but this time with 2 different scales. Significant digits give us an indication of the accuracy of a number arising from a measurement. Let's now talk about accuracy and precision of numbers. If the scales were zeroed properly, and the students were good at measuring, it is possible for the measurements to be accurate (close to the true measure) and precise (close to each other).
If this is not done, it is quite possible for the measurements to be precise (all close together) but quite inaccurate (a long way from the true measurement). We need to "zero" the scales when no object is on them. On most scales there is a "zero" adjustment. On the other hand, the p recision of measurements refers to how close the measurements are to each other. You are accurate if your measurement is very close to the true weight. The accuracy of a measurement refers to how close it is to the actual true weight of our object. Say we get several students to measure the weight of an object. So in example d) above, 3600, we assume it is a number correct to the nearest 100, since the 6 is the last non-zero integer. NOTE: We are assuming that for numbers greater than 1, the last non-zero number is significant. The measurement is between 12.295 and 12.305 The zero in this number serves as a place holder - it is not a significant digit. Let's now round our earlier measurement 26.832 cm to the nearest 10. [Another way of thinking about this is that the number of significant digits is the number of digits we write when we write the number The zero in 26.830 is significant.Ī zero digit is significant if it is not a place This suggests greater accuracy than our rounded number 26.83. Another way of thinking about this is that 26.83 is between 26.825 and 26.835.) Our rounded number 26.83 has only 4 significant digits. (This means our measurement is closer to 26.83 cm than it is to 26.84 cm.
Rounding: We can round off 26.832 to 2 decimal places and get 26.83. For example, say we measure a pipe diameter and get 26.832 cm. All digits greater than 0 in a number are significant.