Minds On

One tenth of a dollar

One dime, or 10¢, is a tenth of a dollar.

We can express one tenth of a dollar like this: $0.10.

10¢ equals $0.10 because 10 dimes make 1 dollar.

10 dimes with addition symbols in between them equal 1 dollar.

Repeated addition can also be expressed as multiplication.

Brainstorm

Brainstorm

Can you express the repeated addition of the 10 dimes as a multiplication statement?

If possible, share your thinking with a partner.

Press ’Answer’ to access the multiplication statement.

$0.10 + $0.10 + $0.10 + $0.10 + $0.10 + $0.10 + $0.10 + $0.10 + $0.10 + $0.10 = $1.00

is the same as:

10 × $0.10 = $1.00

In this learning activity, we are learning to multiply a whole number with 0.1 or tenths, and 0.01 or hundredths.

Action

Multiplying with dimes

Multiplication is repeated addition.

Can you multiply with dimes?

Figuring out dimes in tenths

Five dimes with addition symbols in between them.

For each number of dimes, figure out how many tenths they equal.

Then, write an addition statement and a multiplication statement for the equivalent value.

Complete Dimes in Tenths in your notebook or using the following fillable and printable document. To help guide you, the first three and final dime rows have been completed.

Dimes in Tenths

Press the Activity button to access Dimes in Tenths.

Activity (Open PDF in a new tab)

Did You Know?

Zeros at the end of a decimal

Zeros added to the end of a decimal do not change the value of the decimal.

Examine the following base ten model that shows that 0.2 = 0.20 = 0.200.

Three base ten models. The first model displays tenths and has 2 tenths coloured in. Under it is the numerical zero point two and “2 tenths” in words. The second model displays hundredths and has 20 tenths coloured in. Under it is the numerical zero point two zero and “2 hundredths” in words. The third model displays thousandths and has 200 thousandths coloured in. Under it is the numerical zero point two zero zero and “200 thousandths” in words.

This fact also applies when we add a decimal with zeros after a whole number.

For example, the number 6, can be written as a decimal like this:

6 = 6.0 = 6.00

Doing this does not change the value of 6. We can express six dollars as $6 or $6.00.

Adding zeros after the last digit in a decimal is often helpful when working with different place values of decimals.

Multiplying whole numbers by 0.1

We can use mental math strategies to multiply whole numbers by 0.1.

Examine the following multiplication statements. Do you notice a pattern?

2 × 0.1 = 0.2

4 × 0.1 = 0.4

13 × 0.1 = 1.3

25 × 0.1 = 2.5

146 × 0.1 = 14.6

Multiplying a whole number by 0.1 is the same as dividing by 10!

The digits shift one place value to the left.

Examine the following place value chart that shows how to multiply 4, 60, and 62 by 0.1.

A place value chart with eight columns. The columns are named, in order, Ten Thousands, One Thousands, Hundreds, Tens, Ones, Decimal Point, Tenths, and Hundredths.

In the first row there is a four in the Ones column, followed by a decimal point, and a zero in the Tenths column. This number is multiplied by 0.1, and an arrow shows the decimal point moving to the left of the four in the Ones column.

In the second row, there is the answer represented as a zero in the Ones column followed by a decimal point, and a four in the tenths column.

In the third row there is a six in the Tens column, a zero in the Ones column, followed by a decimal point, and a zero in the tenths and hundredths column. This number is multiplied by 0.1, and an arrow shows the decimal point moving to the left of the zero in the Ones column.

In the fourth row, there is the answer represented as a six in the Ones column followed by a decimal point, and a zero in the Tenths and Hundredths column.

In the fifth row there is a six in the Tens column, a two in the Ones column, followed by a decimal point, and a zero in the tenths and hundredths column. This number is multiplied by 0.1, and an arrow shows the decimal point moving to the left of the zero in the Ones column.

In the sixth row there is the answer represented as a six in the Ones column followed by a decimal point, a two in the Tenths and a zero Hundredths column.

Student Success

Think

What do you think will happen when we multiply whole numbers by 0.01? What pattern might we notice?

Multiply the following numbers to help uncover the pattern:

2 × 0.01

4 × 0.01

13 × 0.01

25 × 0.01

146 × 0.01

Record your thinking in print, digitally, or with an audio recording.

When you’re ready, press ’Answer’ to access a list of the answers and a possible pattern.

2 × 0.01 = 0.02

4 × 0.01 = 0.04

13 × 0.01 = 0.13

25 × 0.01 = 0.25

146 × 0.01 = 1.46

Multiplying by 0.01 is the same as dividing by 100!

The digits shift two place values to the left.

Consolidation

Popsicle fund raiser

Two friends are running a popsicle sale to raise funds for a local charity.

On the first day, they sell 103 mini-popsicles for $0.10 each.

On the second day, they sell 54 mini-popsicles for $0.10 each.

Test Your Skills

Test your skills

Using the information provided, complete the following tasks in print, digitally or with an audio recording:

  1. Create a multiplication sentence to show how many mini-popsicles were sold on the first day.
  2. Create a multiplication sentence to show how many mini-popsicles were sold on the second day.
  3. How many popsicles were sold in total?
  4. How much money was raised in total for the local charity?

The cost of popsicle sticks

If each individual popsicle stick costs one cent, or $0.01, then…

  • how much did 103 popsicle sticks cost?
  • how much did 54 popsicle sticks cost?
  • how much did all the popsicle sticks cost?

Use a method of your choice to express a math sentence with the answer.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel...

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.