Hello, Super Mathematicians!
Welcome to the amazing world of Decimal Multiplication! Don't worry if that sounds a bit tricky. It's actually a super useful skill that you use in real life all the time, like when you're shopping or measuring things for a fun project.
In these notes, we'll learn how to multiply numbers with those little dots called decimal points. We'll break it down into easy steps, share some cool tricks, and show you why it's so important. Let's get started!
Part 1: The Magic of 10, 100, and 1000!
Multiplying a decimal by 10, 100, or 1000 is like a magic trick! The digits stay the same, but the decimal point goes on an adventure. When we multiply by these numbers, our answer gets bigger.
How it Works: Move the Point to the RIGHT!
The trick is to move the decimal point to the right. How many places do you move it? Just count the zeros!
- To multiply by 10 (one zero), move the decimal point 1 place to the right.
- To multiply by 100 (two zeros), move the decimal point 2 places to the right.
- To multiply by 1000 (three zeros), move the decimal point 3 places to the right.
Let's see some examples!
Example 1: Multiply 4.56 by 10
There is one zero in 10, so we move the decimal point one place to the right.
$$4.56 \times 10 = 45.6$$Example 2: Multiply 1.234 by 100
There are two zeros in 100, so we move the decimal point two places to the right.
$$1.234 \times 100 = 123.4$$What if we run out of numbers?
Great question! If you need to move the point but there are no more digits, just add a zero as a placeholder.
Example: Multiply 5.8 by 100
We need to move the point 2 places, but there's only one digit after it. So, we add a zero!
$$5.8 \times 100 = 580$$Key Takeaway
To multiply a decimal by 10, 100, or 1000, count the zeros and move the decimal point that many places to the right. The number gets bigger!
Part 2: The Shrinking Power of 0.1, 0.01, and 0.001!
Now for something really cool! When you multiply a number by a tiny decimal like 0.1, the answer actually gets smaller. It's like finding a small piece of the original number.
How it Works: Move the Point to the LEFT!
This time, the decimal point's adventure goes in the other direction. You move the decimal point to the left.
- To multiply by 0.1 (one decimal place), move the decimal point 1 place to the left.
- To multiply by 0.01 (two decimal places), move the decimal point 2 places to the left.
- To multiply by 0.001 (three decimal places), move the decimal point 3 places to the left.
Let's try it!
Example 1: Multiply 78.9 by 0.1
There is one decimal place in 0.1, so we move the decimal point one place to the left.
$$78.9 \times 0.1 = 7.89$$Example 2: Multiply 56 by 0.01
Remember, a whole number has an invisible decimal point at the end (56 is the same as 56.0). There are two decimal places in 0.01, so we move the point two places to the left.
$$56 \times 0.01 = 0.56$$Key Takeaway
To multiply a number by 0.1, 0.01, or 0.001, count the decimal places in the tiny number and move the decimal point that many places to the left. The number gets smaller!
Part 3: The Main Event - Multiplying Decimals!
You're ready for the main event! Multiplying a decimal by a whole number or another decimal is easy if you remember this simple three-step trick. Don't worry if this seems tricky at first, we'll go through it step-by-step.
The Three-Step Trick
Step 1: Ignore the Dots!
First, pretend the decimal points aren't there. Write down the problem as if they were whole numbers.
Step 2: Multiply, Multiply, Multiply!
Solve the multiplication problem just like you normally would.
Step 3: Count and Place the Dot!
Now, go back to the original numbers. Count the total number of digits after the decimal points in BOTH numbers. Your answer must have that same total number of decimal places.
Let's do an example together! Multiply 3.2 by 1.5
Step 1: Ignore the Dots!
We'll multiply 32 by 15.
Step 2: Multiply!
$$ \begin{array}{@{}c@{\,}c@{}c} & & 32 \\ & \times & 15 \\ \hline & 1 & 60 \\ & 3 & 20 \\ \hline & 4 & 80 \\ \end{array} $$So, 32 x 15 = 480.
Step 3: Count and Place the Dot!
Let's look at the original numbers:
3.2 has 1 digit after the decimal point.
1.5 has 1 digit after the decimal point.
In total, that's 1 + 1 = 2 decimal places.
So, our answer must have 2 decimal places. We take our result (480) and place the decimal point so there are 2 digits after it.
$$4.80$$So, $$3.2 \times 1.5 = 4.80$$ (which is the same as 4.8!)
Did you know?
When you multiply a number by a decimal that is less than 1 (like 0.5 or 0.25), your answer will be smaller than the number you started with! It's because you are finding a "part" of that number. For example, 10 x 0.5 is the same as finding half of 10, which is 5!
Key Takeaway
To multiply any decimals: 1. Ignore the dots and multiply. 2. Count the total decimal places in the question. 3. Give the answer the same total number of decimal places.
Part 4: Estimation and Rounding - Your Maths Superpowers!
Sometimes, you don't need an exact answer. You just need a "close enough" answer. This is where estimating and rounding come in handy! The syllabus asks us to use this symbol: ≈, which means "approximately equal to".
Estimating Your Answer
Estimating before you multiply helps you check if your final answer makes sense. It's like being a detective and looking for clues!
How to Estimate:
Just round the numbers in your question to the nearest whole number and then multiply.
Example: Let's estimate the answer to $$5.9 \times 3.2$$
- 5.9 is very close to 6.
- 3.2 is close to 3.
So, we can estimate by calculating $$6 \times 3 = 18$$.
Our final answer should be somewhere around 18. (The real answer is 18.88, so our estimate was great!)
Rounding Off Your Answer
Sometimes, an answer has too many decimal places. We can make it simpler by "rounding it off".
Memory Aid: The Rounding Rhyme!
Five or more, raise the score. Four or less, let it rest.
Example: Let's say we get an answer of 18.88 and we need to round it to the nearest tenth.
- Find the tenths place. It's the first 8. (18.88)
- Look at the digit to its right. It's another 8.
- Is it 5 or more? Yes! So, we "raise the score" of the tenths digit. The 8 becomes a 9.
So, $$18.88 \approx 18.9$$
Key Takeaway
Estimate before you solve to check your work. Round off long answers to make them simpler, using the ≈ symbol.
Part 5: Let's Solve Some Real-World Problems!
Now, let's use our new skills to solve some problems you might see every day.
Problem 1: Shopping Trip!
A bag of yummy chocolates costs $3.50. You decide to buy 4 bags to share with your friends. How much will it cost in total?
Thinking it through: We need to find the total cost, so we multiply the price of one bag by the number of bags.
Calculation: $$3.50 \times 4$$
- Ignore the dots: $$350 \times 4 = 1400$$
- Count the places: 3.50 has 2 decimal places. 4 has 0 decimal places. Total = 2.
- Place the dot: Our answer 1400 needs 2 decimal places. So it becomes 14.00.
Answer: It will cost $14.00 in total.
Problem 2: Craft Time!
A long piece of colourful ribbon is 2.8 metres long. For your art project, you only need 0.5 of the ribbon. How long is the piece of ribbon you will use?
Thinking it through: We need to find a "part" of the ribbon, so we multiply. Remember, multiplying by 0.5 is the same as finding half!
Calculation: $$2.8 \times 0.5$$
- Ignore the dots: $$28 \times 5 = 140$$
- Count the places: 2.8 has 1 decimal place. 0.5 has 1 decimal place. Total = 1 + 1 = 2 decimal places.
- Place the dot: Our answer 140 needs 2 decimal places. So it becomes 1.40.
Answer: The piece of ribbon you will use is 1.4 metres long. (1.40 is the same as 1.4)
You did it! You've learned the secrets of decimal multiplication. Keep practising, and soon it will be second nature. Great work!