B. Number · Operations: Numbers to 100 000, Decimals, Fractions, Ratios and RatesMental Math: Multiplying by 0.1 and 0.01
B2.3About 35 minutes
Learning goals- I can multiply a whole number by 0.1 in my head.
- I can multiply a whole number by 0.01 in my head.
- I can explain how the digits move in a place value chart.
- I can use multiplying by 0.1 and 0.01 with dimes, cents and centimetres.
Words to know
tenth (0.1)
One of 10 equal parts of a whole. A dime is one tenth of a dollar.
hundredth (0.01)
One of 100 equal parts of a whole. A cent is one hundredth of a dollar, and a centimetre is one hundredth of a metre.
place value
The value of a digit because of where it is in a number.
Remember from Grade 4
In Grade 4 you learned that when you multiply by 10, 100 or 1000, each digit moves to a bigger place, and when you divide by 10, each digit moves one place to the right (smaller). For example, 37 ÷ 10 = 3.7.
In Grade 5 you'll multiply by 0.1 and 0.01. These numbers are less than 1, so the product gets smaller.
Let's start with money
A dime is worth $0.10, or one tenth of a dollar. What are 37 dimes worth?
10 dimes make $1. So 37 dimes make $3 and 7 dimes more, which is $3.70.
In math: 37 × 0.1 = 3.7.
Now think of cents. One cent is $0.01, one hundredth of a dollar. 37 cents is 37 × 0.01 = 0.37 of a dollar, or $0.37.
What does × 0.1 mean?
× 0.1 means "one tenth of". To find one tenth of a number, you split it into 10 equal parts. So:
Multiplying by 0.1 is the same as dividing by 10. Each digit moves one place to the right.
× 0.01 means "one hundredth of". So:
Multiplying by 0.01 is the same as dividing by 100. Each digit moves two places to the right.
| Number | Hundreds | Tens | Ones | Tenths | Hundredths |
|---|
| 450 | 4 | 5 | 0 | | |
| 450 × 0.1 = 45 | | 4 | 5 | 0 | |
| 450 × 0.01 = 4.5 | | | 4 | 5 | 0 |
Worked exampleExample 1: Multiply by 0.1
- × 0.1 means one tenth of 23, the same as 23 ÷ 10.
- Move each digit one place to the right: the 2 tens become 2 ones, and the 3 ones become 3 tenths.
- That gives 2.3.
7 jumps of one tenth land on 0.7. So 7 × 0.1 = 0.7.Worked exampleExample 2: Multiply by 0.01
- × 0.01 means one hundredth of 125, the same as 125 ÷ 100.
- Move each digit two places to the right: 1 hundred becomes 1 one, 2 tens become 2 tenths, 5 ones become 5 hundredths.
- That gives 1.25.
Worked exampleExample 3: Centimetres to metres
Maya is 136 cm tall. How tall is she in metres?
- 1 cm is one hundredth of a metre, or 0.01 m.
- 136 cm = 136 × 0.01 m.
- Move each digit two places right: 1.36.
Check if your answer makes sense
- × 0.1 makes a number 10 times smaller. 60 × 0.1 = 6, and 6 is ten times smaller than 60. ✓
- × 0.01 makes a number 100 times smaller. 600 × 0.01 = 6. ✓
If your answer got bigger, you moved the digits the wrong way!
A handy shortcut
When a whole number ends in 0, multiplying by 0.1 just takes that 0 away: 340 × 0.1 = 34. If it ends in 00, multiplying by 0.01 takes both zeros away: 1200 × 0.01 = 12.
Just for funFunny but true: a Canadian dime is smaller than a penny and a nickel, but it is worth more than both of them. Small coin, big attitude!
Hands-on activityDimes, cents and centimetres
You need: some dimes and other coins (or paper ones you draw), a metre stick or measuring tape, and a pencil.
- Count out a handful of dimes. Write how many, then multiply by 0.1 to find their value in dollars. Check by making groups of 10 dimes (each group is $1).
- Measure three things in centimetres, like a book, a table and your arm span. Change each to metres by multiplying by 0.01. Write it like this: 75 cm = 75 × 0.01 m = 0.75 m.
- Measure your height in cm and change it to metres.
Math talk: "Why does the number get smaller when we change cm to m?"
Your turn
4.7. Each digit moves one place right.
0.63. Each digit moves two places right.
20. One tenth of 200 is 20.
3.5. 350 ÷ 100 = 3.50 = 3.5.
$1.80. 18 × 0.1 = 1.8, so $1.80.
More practice: warm-up
1. Ten tenths make one whole.
1. One hundred hundredths make one whole.
More practice: on your own
3A pencil is 15 cm long. How long is it in metres?
0.15 m. 15 × 0.01 = 0.15.
5Which is bigger: 60 × 0.1 or 600 × 0.01?
They are equal. 60 × 0.1 = 6 and 600 × 0.01 = 6.
Challenge
1Find the missing number: □ × 0.1 = 3.5.
35. 35 × 0.1 = 3.5. (Think: 3.5 is one tenth of what number? 3.5 × 10 = 35.)
2How many times bigger is 4 × 0.1 than 4 × 0.01? Explain.
10 times bigger. 4 × 0.1 = 0.4 and 4 × 0.01 = 0.04. 0.4 is 4 tenths, which is 40 hundredths, and 40 hundredths is 10 times 4 hundredths.
3A class collected 345 dimes for a food drive. How much money is that? How many more dimes do they need to reach $40?
$34.50. 345 × 0.1 = 34.5. $40 is 400 dimes, so they need 400 − 345 = 55 more dimes.
Quiz
3. Multiplying by 0.1 is the same as ...
5. How much are 40 dimes worth?
6. A ribbon is 72 cm long. How long is it in metres?
Big idea: The Grade 5 curriculum (B2.3) asks students to use mental math to multiply whole numbers by 0.1 and 0.01. The key understanding is that × 0.1 means "one tenth of" (the same as ÷ 10) and × 0.01 means "one hundredth of" (the same as ÷ 100), so the digits shift to the right and the number gets smaller.
Common difficulties:
- Expecting multiplication to always make a number bigger. Show with dimes: 37 dimes is only $3.70.
- Moving digits the wrong way, or the wrong number of places (63 × 0.01 = 6.3). Use a place value chart.
- "Adding a zero" rules. Avoid rules like "just move the decimal point" without understanding; ask your child to say what each digit becomes.
How to help: Use money and measuring. Ask "How many dollars is 26 dimes?" or "How many metres is 85 cm?" while shopping or measuring furniture.