When you are learning how to round numbers, you will need to understand significant digits as well. After all, as you probably already heard, when you need to round a number, you are required to round it to an appropriate number of significant digits.
So, it is important that you have a good grasp of rounding and significant digits.
What Are Significant Digits?
Simply put, significant digits are digits that are important or interesting. Notice that they are sometimes called significant figures.
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Ultimately, significant digits are the digits that give you useful information about the accuracy of a measurement. Here’s an example. Take a look at the number 3.14159, You can say that this number has 6 significant digits. This means that each one of its digits or numerals gives you useful information.
But what about 1000? 1000 only has one significant digit. There is only one number that is interesting: the 1. You don’t know anything for sure about the hundreds, tens, or units places; the zeroes may just be placeholders; they may have rounded something off to get this value.
However, if you had the number 1000.0, this number already has5 significant digits. The reality is that the “.0″ tells you something interesting about the presumed accuracy of the measurement being made.
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In the case of the number 0.00035, this has 2 significant digits: only the 3 and 5 tell you something; the other zeroes are placeholders, only providing information about relative size. But if you add a zero to the end of the previous number, 0.000350, you now have 3 significant digits. Simply put, the last zero tells you that the measurement was made accurate to that last digit, which just happened to have a value of zero.
1006, for example, has four significant digits: the 1 and 6. These are interesting and you have to count the zeroes, because they’re between the two interesting numbers.
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In the case of the number 560, this one has two significant digits. Notice that the last zero is just a placeholder. However, if you needed to add a decimal point after the 560 (560.), you would then have 3 significant digits because the decimal point tells you that the measurement was made to the nearest unit, so the zero is not just a placeholder.
As you can see, rounding and significant digits are two very close concepts and they are usually used together.
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Expressing Numbers As Being “Accurate To” A Certain Place
As you probably already know, there are many different places and in what concerns to math, you need to be sure about what each one refers to. So, here are some examples so you can easily understand how you can use math language the right way:
- 1000.0 is accurate to the tenths place
- 1000 is accurate to the thousands place
- 560 is accurate to the tens place
- 560.0 is accurate to the tenths place
- 560. is accurate to the units place (note the decimal point)
- 1006 is accurate to the units place
- 0.00035 is accurate to the hundred-thousandths place
- 0.000350 is accurate to the millionths place (note the extra zero)