5.07 Rounding decimals

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Do you remember how to round whole numbers?

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When we round a number to a particular place value, we look at the digit one place to the right to determine whether we round up or down. If that digit is lower than $5$5, we round down, and if it is $5$5 or more we round up.

This is true whether we are rounding whole numbers or decimal values. For example, to round $6.318$6.318 to the nearest tenth, we look at the value of the hundredths digit:

Ones	$\cdot$·	Tenths	Hundredths	Thousandths
$6$6	$\cdot$·	$3$3	$1$1	$8$8

In this case, the hundredths digit is $1$1. This is less than $5$5, so we round down and leave the digit in the tenths place as a $3$3. The rounded value is therefore $6.3$6.3.

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Question 1

 

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In the above example, notice that no digits after the tenths place value are left - we don't fill them in with zeros in the same way as we do when rounding whole numbers. We only keep zeros when they are within the digits that are included in the rounding.

For example, let's round $3.5972$3.5972 to the nearest hundredth. To do so, we look at the value of the thousandth digit:

Ones	$\cdot$·	Tenths	Hundredths	Thousandths	Ten Thousandths
$3$3	$\cdot$·	$5$5	$9$9	$7$7	$2$2

In this case, the hundredths digit is $7$7. This is at least $5$5, so we round up. This means that the $9$9 in the hundredths place becomes $10$10. To represent this, we leave the $0$0 and carry the $1$1 to the left, into the tenths place. So the result is $3.60$3.60. It is important to keep the $0$0 in the hundredths place this time because we were rounding to the nearest hundredth.

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Question 2