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The significant figure rounder rounds numbers to the required quantity of significant figures. It works with a standard number format, e-notation, and scientific notation.
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This calculator rounds the given number to the necessary quantity of significant figures, replacing the “leftover numbers” with zeros. For example, rounding 11 to one significant figure will give 10 as an answer.
To use this significant figures rounder, enter the given number and the necessary number of significant figures, then press “Calculate.” The given number can consist of up to 30 symbols. You can use number notation, scientific notation, or e-notation as input. You can also use commas to separate thousands, but it’s unnecessary. Some examples of accepted inputs:
The number of significant figures should be less than 16, i.e., 15 is the largest number of significant figures this calculator can round to.
Let’s first define “rounding”. Rounding is the process of rewriting the number in a simpler form, while keeping its value close to the original value. For example, 1001 can be rounded to 1000. And 6.999999 can be rounded to 7. The resulting number is (slightly) less accurate than the original, but it’s much easier to pronounce and write it down.
Now, to significant figures. The number of significant figures is basically the number of figures you keep in a number. All other figures are turned into zeros.
The process of rounding a number basically means finding a number with fewer digits whose value is close to the value of the original number. For example, it is intuitively clear that 6.1 will round down to 6, since it’s “closer” to 6 than to 7. Similarly, 6.2, 6.3, and 6.4 will all round down to 6. While 6.9 will round up to 7, since it’s closer to 7 than to 6. Same with 6.8, 6.7, and 6.6. But what do we do with 6.5? It’s exactly in the middle between 6 and 7. Several different rounding rules exist. Here we will discuss the most common method. In the most common rounding method, 5 is rounded “up,” so 6.5 is rounded up to 7. The algorithm for rounding numbers, in that case, consists of the following steps:
For example, round each number to two significant figures: 1015 and 876. Let’s start with 1015:
Now let’s look at 876:
The algorithm for rounding decimals is the same as for rounding whole numbers. It is important to note that leading zeros are not significant numbers. Therefore, they are disregarded when choosing the last preserved digit. For example, round each number to three significant figures: 9.05675, 0.01234.
Starting with 9.05675, we get:
Now let’s look at 0.01234:
Imagine buying a dress in a store, which costs $15 + income tax. The income tax is 6.25%. Now you, of course, want to calculate the final price of the dress. To do that, you will first calculate the value of 6.25% as follows:
6.25% of 15 = (15/100) × 6.25 = 0.15 × 6.25 = 0.9375
Then you will calculate the final price of the dress:
Final price = 15 + 0.9375 = 15.9375
Since a hundredth of a dollar is the smallest unit we can use, we round up the resulting number to two digits after the decimal point.
In this case, rounding to hundredths is the same as rounding to 4 significant figures. (Note that you might need a different number of significant figures to round a different number to hundredths. For example, to round 5.6325 to hundredths, you would use 3 significant figures, while to round 132.125 to hundredths, you would use 5 significant figures).
Rounding 15.9375 to 4 significant figures, we get:
This means that if you pay for the dress with 20 dollars, you will get $(20 - 15.94) = $4.06 as change.