Place Values
Saying numbers like “10”, “5” and even “1,837” can be remotely quick and straightforward, but can you pronounce the number “174,365,024,814.28” as quick and confident? Maybe you can, so good for you! But if you are someone who has trouble remembering the right way to say large numbers, you are not alone.
To build confidence in saying large or small numbers, having a strong sense of place values is extremely important.
Here’s how we name the places to the left of the decimal point:
Rounding
So, how can knowing place values help in rounding? Well, whenever you round a number, you are asked to round it to certain place values. To quickly solve these kinds of problems, knowing the foundations of place values and using your rounding rules are very crucial.
The diagram below shows the method of the “Rounding Hill” which guides you in rounding. It shows that if the number is equal to 4 or below it, the place value stays the same. If the number is equal to 5 or higher, then it moves up one place.
Some of the basic rules of rounding are:
Pay attention to what the problem is asking. For example, if the problem asks “round to the nearest tenth,” it is asking you to look at the hundredths place of the number after the decimal. Always look at the next number on the right to round to whatever place value the problem is asking.
Ex: Round 267.9483 to the nearest tenth. What number is in the tenths place? 9. What number is right of that? 4. Looking at the table below, we know that 4 is near the “0” side, which indicates that the “9” stays the same. So the answer is 267.9. Remember, when asked to round to the nearest place value, you do not need to include the numbers right of that place value.
Suppose the number was 267.9883. Now the number 8 needs to be judged. It is clearly near the “10” side in this table, so, the place value moves up. But what do we do now? Nine is the largest number right? Wrong. If 9 is rounded up, you must increase the digit left of it. For example, 267.9883 rounded to the nearest tenth is going to be 268.0. Although there is no value in the tenths place, that is still the correct answer.
Place Values and Rounding PRACTICE
What number is in the hundredths place in the number “2745.9619”
Refer back to the place value guide if needed.
Answer: 6
2. Round “7,450,925” to the nearest thousands.
a. Refer back to the rounding guide if needed.
b. Answer: 7,451,000
3. What number is in the ten-thousandths place in the number “2745.9619”
a. Refer back to the place value guide if needed.
b. Answer: 9
4. Round “7,450,925” to the nearest tens.
a. Refer back to the rounding guide if needed.
b. Answer: 7,450,930
Written by Lakshmi Potturu