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Decimal numbers


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Numeracy Basics

Decimal Numbers

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This topic will cover how to:

  • identify and interpret decimal numbers;
  • round decimal numbers to a specified accuracy;
  • truncate decimal numbers to a specified number of digits; and
  • convert decimal measures of time to whole number measures in different forms (i.e. years to years and months).
  • identify and interpret decimal numbers;
  • round decimal numbers to a specified accuracy;
  • truncate decimal numbers to a specified number of digits; and
  • convert decimal measures of time to whole number measures in different forms (i.e. years
    to years and months).

Decimal Numbers

A decimal number is a number that contains both a whole number part and a fractional part, separated by a decimal point.

The whole number part of a decimal number is the part to the left of the decimal point, while the fractional part is the part to the right:

2.35

If the whole number part of a decimal number is 0, we usually put a zero in front of the decimal
point to avoid confusion. For example 0.35.

If the fractional part of a decimal number is 0, we usually omit the decimal point and write
the number as a whole number. For example we write 2.0 simply as 2.

Rounding Decimal Numbers

It can be useful to round decimal numbers, so that they are easier to read and understand and so that we can make estimates.
For example if we say that Steve jumped 3.5m in his school's long-jump competition, we have rounded this distance to one decimal place.

The number of digits to round to depends on the context- you might round to the nearest whole number, or to one or two (or even more) decimal places.

Something to watch out for when rounding is that you don't round too early in your working.

In fact ideally, when using a calculator you should retain all accurate answers in your calculator as you work and not round at all until your final answer

Rounding to a Specified Accuracy

When rounding a decimal number to a certain number of decimal places, or to the nearest whole number, you should follow these steps:

1) Find the relevant 'round-off place' in your number.

  • For example, when rounding 4.576 to 2 decimal places the round off place is the 2nd decimal place; 4.576

2) Determine the number which is one place to the right of your round-off place.

  • For example, when rounding 4.576 to 2 decimal places this number is 6; 4.576

If this number is greater than or equal to 5 you should increase the number in the round-off place by 1, and remove all digits to the right of it. In other words, you should round up.

If this number is less than 5, you should keep the number in the round-off place the same, and again remove all digits to the right of it. In other words, you should round down.

  • For example, when rounding 4.576 to 2 decimal places you should round up (since 6 is greater than 5), so you should increase the 7 to 8 and remove all digits to the right of it; 4.58

1) Find the relevant 'round-off place' in your number.

  • For example, when rounding 4.576 to 2 decimal places the round off place is the 2nd decimal
    place; 4.576

2) Determine the number which is one place to the right of your round-off place.

  • For example, when rounding 4.576 to 2 decimal places this number is 6; 4.576

3.) If this number is greater than or equal to 5 you should increase the number in the round-off place by 1, and remove all digits to the right of it. In other words, you should round up.

If this number is less than 5, you should keep the number in the round-off place the same, and again remove all digits to the right of it. In other words, you should round down.

For example, when rounding 4.576 to 2 decimal places you should round up (since 6 is greater than 5), so you should increase the 7 to 8 and remove all digits to the right of it; 4.58

Examples: Rounding to a Specified Accuracy

Tom has just started swimming, and manages to swim seven laps of his local swimming pool. He times that it takes him 300 seconds to do this. Assuming that Tom swims at the same speed for each lap, calculate how many seconds it takes him to swim each lap, rounded to:

a. the nearest whole number,

Calculating 300 ÷ 7 gives 42.857142857…

So rounded to the nearest whole number this is 43 (round up)

b. one decimal place,

42.9 (round up)

c. two decimal places, and

42.86 (round up)

d. three decimal places.

42.857 (round down)

Calculating 300 ÷ 7 gives 42.857142857…

So rounded to the nearest whole number this is 43 (round up)

42.9 (round up)

42.86 (round up)

42.857 (round down)

Activity 1: Practice Questions

Truncation

Although rounding is the most common way of reducing the number of digits in a solution, in some cases it is not appropriate. Consider, for example, that you have $9 to buy popcorn, which costs $2.50 a bucket. A simple division calculation gives:

9 ÷ 2.5 = 3.6

However to say that this means we can buy 3.6 or 4 (when rounded to the nearest whole number) buckets of popcorn is neither practical nor correct.


Instead, we should say that we can buy 3.

This example is an application of truncation. In this case it is not reasonable to have any digits after the decimal point, so we truncate our original solution of 3.6 to 3. In other cases, you may be asked to truncate a figure to a particular number of decimal places. In general, truncation should only be used when rounding does not make sense (as in our popcorn example), or where specified. In all other cases, you should round numbers using the method described previously.

9 ÷ 2.5 = 3.6

Examples: Truncation

1) Truncate 6.35912356 to:

  • a. A whole number
  • b. 1 decimal place
  • c. 3 decimal places
  • d. 5 decimal places

2) Truncate -42.5392643 to:

  • a. A whole number
  • b. 1 decimal place
  • c. 3 decimal places
  • d. 5 decimal places

= 6
= 6.3
= 6.359
= 6.35912
= -42
= -42.5
= -42.539
= -42.53926

Activity 2: Practice Questions

Converting Decimals to More Practical Forms

Sometimes when you perform a calculation you might end up with a decimal number that would be easier to interpret in another form.

For example, consider that you need to pay back an interest-free loan of $33 000, and that you
will repay $12 000 per year.

If you wish to determine the number of years it will take you to repay this loan, you can simply divide $33 000 by $12 000:

$33 000/$12 000 = 2.75 years

To state this in terms of years and months, consider that the ‘.75’ part of our decimal number refers to 0.75 of 12 months (i.e. 0.75 x 12 months = 9 months),
and hence our final answer is 2 years and 9 months.

Examples: Converting Decimals to
More Practical Forms

Convert 2.33 years into years and months (rounded to the nearest month)

0.33 x 12 = 3.96 ≈ 4

So solution is 2 years and 4 months

Convert 3.75 days into days and hours

There are 24 hours in a day, and 0.75 x 24 = 18

So solution is 3 days and 18 hours

Convert 7.33 hours into hours and minutes (rounded to the nearest minute)

There are 60 minutes in an hour, and 0.33 x 60 = 19.8 ≈ 20

So solution is 7 hours and 20 minutes

Convert 18.25 minutes into minutes and seconds

There are 60 seconds in a minute, and 0.25 x 60 = 15

So solution is 18 minutes and 15 seconds

0.33 x 12 = 3.96 ≈ 4

So solution is 2 years and 4 months

There are 24 hours in a day, and 0.75 x 24 = 18

So solution is 3 days and 18 hours

There are 60 minutes in an hour, and 0.33 x 60 = 19.8 ≈ 20

So solution is 7 hours and 20 minutes

There are 60 seconds in a minute, and 0.25 x 60 = 15

So solution is 18 minutes and 15 seconds

Activity 3: Practice Questions

End of Topic

Congratulations, you have completed this topic.

You should now have a better understanding of Decimal Numbers.

 


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