Rounding Decimals

Objective

To know how to round any decimal number

Example

Round 49.682 to the nearest hundredth

Answer: 49.68

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Explanation

Rounding means to turn an exact answer into an approximate answer. Words that come up in rounding are "about", "estimate", "approximately", "close to", or "around".

Why would we take an exact answer and make it not exact? Often just to make the number look nice. People also round to make a number easier to do math with. Scientists round to show how accurate their measurements are.

When you round, you pick the place value that you care about. For example, when we say "round to the nearest hundredth", we're saying that we don't care about anything smaller than hundredths. That means that thousandths and every place after will be taken out (made zero). Lets look at the example above

Example

Round 49.682 to the nearest hundredth

1.) First, find the hundredths

49.682

Now let's leave off everything bigger than the hundredths

0.082

2.) Now we need to decide which is the nearest hundredth. Since 0.082 is between 0.070 and 0.080, our choices are to:

• round down to 0.070

  • Round down means we don't change the digit we're rounding to.

  • Every place smaller than that digit becomes 0.

• round up to 0.080

  • Round up means we add 1 to the digit we're rounding to.

  • Every place smaller than that digit becomes 0.

How do we know whether to round up or round down? You need to figure out which hundredth our number is closest to. Look at the place value just smaller than the one we're rounding to. In this question, since we are rounding to the nearest hundredth, we need to look at the thousandths place

0.082

Then, remember this important rule:

• If that number is smaller than 5 (meaning 0, 1, 2, 3, or 4), round down.

• If that number is 5 or greater (meaning 5, 6, 7 ,8, or 9), round up.

For this example, since 2 is less than 5, we round down.

0.080

3.) Bring this rounded part back to the original number

49.682 49.680

4.) Write it in correct decimal format

Answer: 49.68

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Examples

Example 1

Round 49.682 to the nearest tenth

1.) First, find the tenths

49.682

Now let's leave off everything bigger than the tenths

0.682

2.) Now we need to decide which is the nearest tenth. Since 0.682 is between 0.600 and 0.700, our choices are to:

• round down to 0.600

• round up to 0.700

Look at the place value just smaller than the one we're rounding to. In this question, since we are rounding to the nearest tenth, we need to look at the hundredths place

0.682

For this example, since 8 is greater than 5, we round up.

0.700

3.) Bring this rounded part back to the original number

49.682 49.700

4.) Write it in correct decimal format

Answer: 49.7

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Example 2

Round 49.682 to the nearest whole number

1.) First, find the whole number.

49.682

9.682

Since 9.682 is between 9.000 and 10.000 , our choices are to:

• round down to 9.000

• round up to 10.000

In this question, since we are rounding to the nearest whole number, we need to look at the tenths place

9.682

6 is greater than 5, we round up.

10.000

3.) Bring this rounded part back to the original number

49.682 50.000

(Notice that since we rounded to 10 and 10 has 2 digits, we need to carry the 1)

4.) Write it in correct decimal format

Answer: 50

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Example 3

Round 49.682 to the nearest ten

1.) 49.682

1.) 49.682

9 is greater than 5, we round up.

50.000

3.) Bring this rounded part back to the original number

49.682 50.000

4.) Write it in correct decimal format

Answer: 50

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Example 4

Round 0.382 to the nearest whole number

1.) First, find the whole number.

0.382

Since 0.382 is between 0.000 and 1.000, our choices are to:

• round down to 0.000

• round up to 1.000

In this question, since we are rounding to the nearest whole number, we need to look at the tenths place

0.382

3 is less than 5, we round down.

0.000

3.) Bring this rounded part back to the original number

0.382 0.000

4.) Write it in correct decimal format

Answer: 0

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Practice your skills