GED Mathematical Reasoning: Comparing and Rounding Numbers

Example 1:

What digit is in the thousands place:  591,045 ?

 

In this first example, we are being asked to identify the digit in the thousands place given the whole number 591,045 [read: five hundred ninety one thousand, forty-five].

Before we do so, let’s spend some time reviewing whole numbers and place value.

The set of whole numbers begins with 0 and continues with 1, 2, 3, 4, and so on.

A whole number may contain one digit or many digits. For example, the number 591,045 [read: five hundred ninety one thousand, forty-five] is a whole number with 6 digits.

Each digit has value based on its placement in the number.

I’ll show the place value chart on the slide for your reference.

Reading from right to left, the ones place comes first and is followed by the tens place, hundreds place, thousands place, and so on. So as you progress from right to left, the value of a digit increases.

And there are a couple other things you should know about whole numbers and place value.

First, a comma is sometimes used to separate the thousands place from the hundreds place and to separate the millions place from the hundred thousands place, like in our first example with 591,045 [read: five hundred ninety one thousand, forty-five].

Second, zero is used as a placeholder to denote that a place has no value. For example, if you have $304 you might think of it in terms of place value as having 3 one-hundred dollar bills, no ten dollar bills, and 4 one-dollar bills.

Going back to our example, let’s compare our number 591,045 [read: five hundred ninety one thousand, forty-five] to the place value chart and determine which digit falls in the thousands spot.

So we see that the digit in the thousands place is a one.

Now let’s talk about how the place value chart helps us to compare and order numbers.

 

Example 2:

Put the following numbers in order from least to greatest:

910            1302            1349          891

 

To compare numbers, start with the largest place value and compare the digits – the greater the digit the greater the number. Also note that numbers containing fewer digits are smaller.

This means, for example two, that 910 and 891 are smaller than 1302 and 1349 since they have fewer digits.

So let’s begin by comparing 910 and 891 to determine which number is the smallest of the four.

When we compare the largest place value, the hundreds place, we see that 891 is smaller than 910, since 8 is less than 9.

Therefore 891 is the smallest of the four numbers.

And the next largest number is 910.

Now let’s compare 1302 and 1349 to determine which is third in line.

When we compare the largest place value, the thousands place, we see that both numbers contain a one. Since the digits in the thousands place are the same, we are not able to determine which number is larger so we move to the hundreds place. The digits in the hundreds place are also the same – they are three’s – so we move to the tens place. Comparing the digits in the tens place, 1302 contains a zero and 1349 contains a 4. Since zero is smaller than 4, 1302 is less than 1349, making 1302 the third number in our ordering and 1349 the largest number.

So the ordering of these four numbers from least to greatest is: first 891, then 910, then 1302, and finally 1349

Before we move on to our third example, let’s review the inequality symbols that allow us to concisely write the relationship between numbers.

So instead of writing “891 is less than 910” we can write it using inequality symbols like this:

Or instead of writing “1349 is greater than 1302” we can write it using inequality symbols like this:

Before we conclude this lesson, let’s talk about rounding with a third example.

 

Example 3:

Round to the nearest hundred: 1492

 

Rounding is an important skill to have when an exact answer is not necessary.

To round a number to a given place value, first identify the digit in the place value given and underline it.

Next, locate the digit directly to the right of that place value.

Finally, if the digit in step two is 0, 1, 2, 3, or 4 (in other words, less than 5) we “round DOWN” by keeping the underlined digit the SAME and changing all digits to the right to zero. If the digit in step two is 5 or greater (in other words 5, 6, 7, 8 or 9), we “round UP” by increasing the underlined digit by 1 and changing all digits to the right to zero.

Now let’s see these steps in action with Example 3.

The number is 1492 and we’re being asked to round to the nearest hundred.

For step one, we’ll underline the digit in the hundreds place – it is a 4

For step 2, the digit to the right is a 9

Following step 3, since the value to the right is 5 or greater, we’ll round UP by adding one to the 4 and changing all digits to the right to zero.

So the 4 becomes a 5 and the 9 and 2 become zeros.

The final, rounded, result is: 1500

 

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