Last Updated on September 10, 2026 by Maged kamel
Round numbers to Decimal points, Significant Digits.
What is the place value for a number?
Place value, in mathematics, describes the value of every digit in a number depending on its position. These positions start from the units place (one place). The order of place value of digits in a number, from right to left, is enes/units, tens, hundreds, thousands, and ten thousands.
How do we round numbers?
This is the fourth lecture about sets. This is a revision on rounding numbers. It is a part of discrete math. To round the number of 28617 persons in a stadium, round to the nearest 1000. The place value is 8, and the digit to the right is 6, which is bigger than 5, so 28617 rounds to 29000 to the nearest thousand.
To round the number of 28617 persons in a stadium to the nearest ten thousand, the place value will be 2. The correct digit is 8, which is bigger than 5. Thus, 28617 rounds to 30000 to the nearest ten thousand.
We can use the number line to verify our solution; please refer to the next slide Image..
Rounding numbers to decimal points.
Let’s examine a new subject: rounding decimals. What is the decimal point? This point distinguishes the whole number on the left from the decimals on the right.
You can approximate a number to the nearest decimal place. The number at the left of a decimal point is a whole number. The first number to the left of the decimal point is the ones place, followed by the tens and thousands places. The number to the right of the decimal point is the tenths place, followed by the hundredths place, followed by the thousandths place, etc. Please refer to the next slide image.
To round 7.8764 to one DP, the place value is on the Number 8. To the right of the number 8 is the number 6, which is greater than 5, and the rounded number is 7.9 to the nearest 1 DP.
The following slide image shows a chart for rounding to the required decimal places and the corresponding values.
Solved examples for rounding numbers to decimal places.
Another example is rounding 5.574 to the nearest two decimal places. Since 4 is less than 5, the rounded value is 5.57.
Another example: round 3.146. Round it to the nearest hundredth: 3.14, since it requires two decimal places. Why? because 1 is 1/10, while 4 is 4/100
1 is < 5, so 4 does not change.
3.1416 is rounded to the thousandths place (3 d.p.); since it is >5, it rounds up to 3.142.
Rounding numbers to significant figures.
The next item is Significant figures, which are helpful in experiments for people who need accurate measurements. That is why they are called significant figures. You can count them from left to right. Four rules cover rounding to the nearest significant figure. Please refer to the next slide image.
For example, 1.239. Round to three significant digits. To count the three digits, start from the left and consider 1 as the first significant figure, based on rule number 1.
Look at the right of the third digit and check whether the number is < 5; if so, it remains unchanged. In our case, 1.239 will be rounded to 1.24 since 9 is <5, which is three Significant digits.
The number 1.239 will be rounded to one significant figure; the first significant figure is 1, and the rightmost digit is 2, so the final rounded number is 1.
Round 134.9 to one significant digit. The place value is 1, and the rightmost digit is 3, so the rounded number is 100 (1 SF).
Solved examples for rounding significant figures.
For example, round 0.0043 to one significant figure. To solve, ignore leading zeros (rule 3) and start with the first figure, which is 4; check the next digit; if it is less than 5, keep 4 without an upgrade; the final result is 0.004. To round 0.0165 to 2Sf, the rounded value is 0.017.
To round 1.0055 to a different SF, we first round to 1 SF. The rounded value will be 1, and the place value is 1. To round the same number to 2SF, the rounded value is 1.0 since zero is less than 5. Again, round 1.0055 to 3SF; the rounded value is 1.01. Please refer to the iimageon tthe image on the image slide for an example.
Rounding Numbers to the nearest whole number.
As we agreed before, round to the nearest whole number. The decimal point separates the whole number on the left from the fractional or decimal part on the right.
To round to the nearest whole number, check the number to the right of the decimal point. If <5, then disregard; if >5, then round up. In our case, 6 becomes 7. The nearest whole number will be 107. No fractions or decimals are to be included.
There is a good SF calculator, and I use the table to show the difference between rounding 305.459 and different Df and AnAn.
An example of SF is rounding 239.456 to the nearest hundred; this is a mixed number. For the nearest 100, the answer is to neglect the fraction.
For the Nearest hundredth, make a line between 2 and 3, check that 3 is<5, 2 will be left, and place 0 and 0 to the right; the round will be 200. There will be no fractions. The idea is to consider the whole number to the left of the decimal. Another example is rounding 78.546 to two decimal places; the result is shown in the slide image.
You can view or download the PDF for this post using the following document.
For more details on the subject, Math Is Fun provides an external resource; the following post is No. 5: Solved quizzes.
You can use a calculator from Calculator Soup to find the corresponding rounding for any number you wish.