Multiplying decimals by 10 or 100
The purpose of this activity is to support students anticipate the result of multiplying a decimal number by 10 or 100.
About this resource
New Zealand Curriculum: Level 3-4
Learning Progression Frameworks: Multiplicative thinking, Signpost 6 to Signpost 7
These activities are intended for students who understand multiplication and division of whole numbers and who know most, if not all, of the basic multiplication facts. It is also expected that students have an existing understanding of whole number place value to at least six places.
Multiplying decimals by 10 or 100
Achievement objectives
NA4-6: Know the relative size and place value structure of positive and negative integers and decimals to three places.
Required materials
- decimats found in Multiplying by decimals MM
- A3 photocopies of Multiplying place value mat
- scissors
- calculators
See Materials that come with this resource to download:
- Multiplying by decimals MM (.pdf)
- Multiplying place value mat (.pdf)
1.
Make the number 0.6 with decimats and a place value mat.
- What number have I made?
- What does six represent in this number? (six tenths)
- What would happen if I made 0.6 ten times greater if I multiplied it by ten?
Establish that each tenth would become ten times greater and become a one. Ten times 0.6 is therefore 6 ones.
Match the decimat model with a written expression. Although you might initially do this using a horizontal expression like 0.6 x 1, you should progress towards using vertical written algorithms, as shown below. Confirm the result with a calculator.
2.
Extend the number multiplied by ten to include decimals with two and three places. Make models with decimats, and discuss what each place value part becomes as it is multiplied by ten. Tenths become ones, hundredths become tenths, and thousandths become hundredths.
For example, 10 x 0.256 = 2.56. For each number you multiply, create a written expression, and use a calculator to confirm the answer.
3.
Extend the problems to include decimals multiplied by 100. Begin with a decimal like 0.43 (100 x 0.43 = 43). If each part becomes 100 times larger, then four tenths become four tens, and three hundredths become three ones.
4.
Use the calculator to establish a symbolic pattern for multiplying decimals by one, ten, 100, and 1000. Organise the results in a table, like the one shown below for 0.678:
Hundreds |
Tens |
Ones |
Tenths |
Hundredths |
Thousandths |
|---|---|---|---|---|---|
|
|
0 |
6 |
7 |
8 |
|
|
6 |
7 |
8 |
|
|
6 |
7 |
8 |
|
|
6 |
7 |
8 |
|
|
|
- What patterns do you notice in the table?
Students should notice that each multiplication by ten shifts the digits one place to the left from their original position. This pattern allows anticipation of what a decimal becomes when made 10, 100, or 1000 times larger.
Students may notice that the calculator does not show the decimal point when 0.678 is multiplied by 1000.
- Why is the decimal point no longer needed?
5.
Provide practice examples, using physical modelling with decimats only if needed. This could be done in pairs or small groups. As you work, you might introduce relevant te reo Māori kupu, such as the words for numbers and words related to decimals, for example, tau ā-ira (decimal number). Examples might be:
- 10 x 1.05 =
- 100 x 2.93 =
- 10 x 0.602 =
- 100 x 5.067 =
1.
Apply tens times and 100 times greater to multiplication problems. For example, if 4 x 6 = 24, then 400 x 6 = ? Calculators can be used to confirm predictions.
2.
Consider what happens when a decimal is divided by 10 or 100. For example, if 10 x 2.9 = 29 what is 2.9 ÷ 10 = ? If 100 x 8.4 = 840 what is 8.4 ÷ 100 = ?
Calculators can be used to confirm predictions.
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