How to Read Which Decimal Is Largest

Decimals

thirteen Compare and Round Decimals

Compare Decimals

Republic of chad wants to brand sure that all his students empathize the value of coin, and an important aspect of that is knowing how to accurately determine the sizes of decimals. Accept a look at the following 4 decimals.

1. 8.16
2. 8.151
3. 8.1513
4. viii.15138

Which of these is the largest? To answer the question, yous would have to compare decimals.

At first glance, you lot might say the largest number is viii.15138, as it has the most digits and may look similar the largest. But if we referred back to the affiliate on Understanding Decimal Note, we would call up that, as you go further to the right from the decimal point (.), the numbers become smaller. So in the instance 8.15138, the 3 near the stop is worth far less than the 5 2 spots to the left of the decimal indicate.

If nosotros followed this logic, then the largest number of the 4 would be 8.16, fifty-fifty though information technology has the fewest digits. When comparison decimals, we really have to start with the whole number. In this situation, it'due south eight in all four answers, so information technology doesn't come into play.

One time nosotros accept decided that the whole number is equal in all four cases, the next thing nosotros have to look at is the number direct to the right of the decimal. This is the tenths place and is worth the most in decimals. One time once more, all four answers give us a value of 1 in the tenths column, and so this will non be the determining factor. Movement i infinite to the right again and you go the hundredths place. All the numbers contain a 5, except the showtime number, where we have a 6. Therefore, this is the defining place value.

I'll become through another example, and and then you can endeavour a couple on your ain.

Which of the post-obit is the largest number?

1. 7.34
2. seven.332
3. 7.323
4. vii.3234

Following the same pattern as before, nosotros would go through the following steps.

Stride 1: First with the whole number. Which number has the largest whole number? Every bit they are all equal, this will not be the determining factor.

The whole number in all iv cases is a 7. This is non the deciding gene.

Step 2: Go to the first digit to the correct of the decimal. It works out that the digit is a 3 in all cases. Therefore, this is not the deciding factor, either.

The number in the tenths cavalcade in all iv cases is a 3. This is not the deciding cistron.

Footstep 3: Go one place to the right again. This would be the hundredths place. Hither, we find the outset difference. Answer a gives united states of america the largest number in this cavalcade. Therefore, respond a is the largest number.

The digit in the hundredths cavalcade is dissimilar for each number. In this instance, the number with the highest value in the hundredths column is the largest number.

Therefore, the largest number of the 4 is:

[latex]\LARGE7.34[/latex]

Exercise Questions

At present attempt a couple for yourself and check out the video answers.

Find the largest number.

1. 27.5
2. 27.54
3. 27.539
4. 27.5392

1. 14.001
2. thirteen.099
3. 13.999
4. xiii.001

Rounding Decimals

During the course, Republic of chad talks about the importance of money and how to work finer with it, particularly when it comes to bookkeeping. Making sure that you lot track business transactions down to the cent (or decimal). As we have 100 cents in a dollar, if we were to circular accounting totals, nosotros would be rounding to the nearest 10 cents (tenths) or even to the nearest dollar (ones).

Before we get to rounding decimals, we should commencement off with rounding in full general. The students are asked to count fittings on a table.

How many did yous count?

There are a total of 22 fittings on the table, and the students are now asked to round the number of fittings to the nearest 10. This would mean rounding up or down to 10, xx, 30, 40, and so on. This instance may seem straightforward, equally we are much closer to 20 than to 30, and if you lot answered 20, then you would exist correct. But what is the rule that we follow?

RULE: Observe the identify value we are rounding (in this example, the tens position). Look at the digit to the right of that number (in this case, the ones place). If that number is 4 or less, we round downward. If that number is v or greater, we round upward.

In our instance with the 22 fittings, we have a 2 in the ones cavalcade, so nosotros terminate up rounding down to 20. If the number in the ones column were 5 or greater, we would round up to thirty.

Allow'southward go through a couple of quick example questions earlier we move on.

Round the following numbers to the nearest ten. Recollect your place value organisation hither.

Questions

1. 12
2. 27
3. 45
4. 98

Answers

1. 12 rounds downwards to 10
2. 27 rounds up to thirty
3. 45 rounds up to 50
4. 98 rounds up to 100

Check out the reply for d. When rounding the tens cavalcade, nosotros end upwardly rounding up. We run out of room in the tens cavalcade, as the highest round number nosotros can make with information technology is 90. This forces usa to movement into the hundreds column and start with one, making the reply 100.

Now that we have rounding whole numbers solved, let's motility onto rounding decimals. Rounding decimals follows the same principles. Information technology'south of import hither to remember the place value organization, not only for whole numbers, but also for decimals. Note the following rule when dealing with numbers:

Equally you become from right to left in a number, including the decimals, the value of the digits becomes greater. When dealing with decimals, this principle ways that, equally you lot go further to the correct from the decimal, you are dealing with smaller and smaller portions of a whole number.

Start with an case.

Circular the following number to the nearest hundredth.

[latex]\LARGE123.45678[/latex]

Step 1: Identify which number is in the hundredths cavalcade.

Step 2: Look at the number directly to the right of the hundredths column. In this instance, information technology would exist the digit in the thousandths column, which is half-dozen.

Step 3: Follow the rules of rounding.

RULE: If the number is 4 or less, round down. If the number is v or greater, round up.

As nosotros have 6 in the thousandths column, we round up.

Therefore, 123.4567 rounded to the nearest hundredth is:

[latex]\LARGE123.46[/latex]

Do Questions

Round the following decimals. Brand sure to heed the identify value arrangement when answering the questions. Check the video answers to see if you are correct.

Round to the nearest tenth.

[latex]\LARGE27.71536[/latex]

Round to the nearest thousandth.

[latex]\LARGE14.75638[/latex]

Round to the nearest hundredth. This is a new concept. Earlier checking the video respond, give this one a attempt and come across how yous do.

[latex]\LARGE75.9999[/latex]

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Source: https://opentextbc.ca/mathfortrades1/chapter/compare-and-round-decimals/

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