Lesson 4 — Activity 1: Place Value Recap!
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Lesson 4 — Activity 1:
Place Value Recap!
Of course, you are very familiar with decimals because Canada's money is based on the decimal system.
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When you worked with place value in Lesson 1, you worked only with whole numbers. That means you worked only with numbers that are to the left of the decimal point. All numbers after a decimal point have a value less than 1.
When you work with money, there are often numbers before and after the decimal point. The numbers after the decimal point are called decimals. They have place value names based on their position away from the decimal point (e.g., tenths, hundredths, thousandths) just like whole numbers (e.g., tens, hundreds, thousands). When you read a decimal number such as $3.15, you read "three dollars and fifteen cents." The decimal point is always read as "and."
$3 |
. |
15
|
← |
. |
→ |
Left |
. |
Right |
$3 is GREATER than 1 |
. |
15 cents is LESS than 1 |
Look at the following numbers:
0.5
0.05
0.005
These numbers all have the number 5, but because of their distance from the decimal point, they are all different numbers. Think about them in terms of money. The closer a number is to the decimal point, the larger the number — or the more
money it is worth!
Would you rather have five tenths of a dollar or five hundredths of a dollar?
0.5 is five tenths
(That's half a dollar, or 50 cents!)
0.05 is five hundredths
(That's a nickel — 5 cents!)
0.005 is five thousandths
(Forget it! That's only half a cent!)
I think you'd rather have five tenths!
The place
value
names of decimal fractions are based on their position in relation to the decimal point — just as they are with whole numbers. Look at the number below to review the different place values both before and after the decimal.
Now let's look at an example. The table below, shows the difference in the value of each of the 7 digits in the number 7,777.777.
Thousands |
Hundreds |
Tens |
Ones |
. |
Tenths |
Hundredths |
Thousandths |
7 |
7 |
7 |
7 |
. |
7 |
7 |
7
|
7,000 |
700 |
70 |
7 |
. |
7/10 |
7/100 |
7/1,000 |
Be sure to look closely at the second
row
to see the
value
of each of the 7s depending on where it is in the number. For example, the first 7 is actually 7,000 because it is in the thousands position. The last 7 after the decimal is actually the decimal fraction 7/1,000 because it is in
the thousandths position.
Follow these basic rules when reading decimal numbers.
-
The number 67.54 is read as sixty-seven and fifty-four hundredths, or more commonly as sixty-seven point five four.
-
If this number was money, it would be read as sixty-seven dollars and fifty-four cents.
-
If the number is less than 1 and has a 0 in the ones place, read it as a whole number, but add the name of the last
column
in the number. For example, 0.54 is read as fifty-four hundredths because the last digit, 4, is in the hundredths place.
Why is it important to write the number 0 before a decimal fraction? Think about how small a decimal point is, and how easy it would be to miss it when reading a number. This is especially important when taking medication. If a label on a prescription suggested a dose of .5 ml, it would be very easy for a person to miss the decimal point and take 5 ml instead. This would result in an overdose. If the number is written as 0.5 ml, it is more obvious.
Click here to read more important information on zeros in decimals!
Follow these basic rules when writing decimal numbers with zeros.
-
If there is no whole number, insert 0 before the decimal point. For example, 0.54 is the correct way to write fifty-four hundredths.
-
Any empty places between the actual number and the decimal point must be filled with a zero. When writing 7/10, as a decimal, the 7 is in the first place after the decimal point: 0.7. When 7 hundredths (7/100) is written as a decimal, a 0 must fill the
tenths place because the hundredths place is the second place after the decimal point. Example: 0.07 is seven hundredths.
-
Always note the word “and” when writing numbers. The example below shows clearly how important this is.
Remember:
Three hundred four thousandths is written as 0.304.
Three hundred and four thousandths is written as 300.004.
There is a huge difference!
Self-check!
Try this!
Answer these questions on your own first.
When you are finished, click on the tab below to check your answers!
