Grade 4
Course ContentDecimals
Habari Mwanafunzi! Let's Talk About the Mighty Dot: Decimals!
Ever been sent to the duka and seen a price like Ksh 45.50? Or maybe you've seen an M-PESA message with an amount like Ksh 200.75? That little dot is not just there for decoration! It's called a decimal point, and it's a super powerful tool in mathematics. Today, we're going to become masters of decimals, and you'll see how you already use them every single day!
What Exactly IS a Decimal?
Think of a whole number, like 100 shillings. Easy, right? A decimal is a way to write a number that is not whole. It's a piece, a part, or a fraction of a whole number.
The magic is in the place value. You remember the place value for whole numbers: Ones, Tens, Hundreds... Well, the decimal point creates a whole new world to its right!
+-----------+------+------+-------+--------------+-------------+--------------+
| HUNDREDS | TENS | ONES | . | TENTHS | HUNDREDTHS | THOUSANDTHS |
| (100) | (10) | (1) | Decimal | (1/10 or 0.1)| (1/100 or 0.01)|(1/1000 or 0.001)|
+-----------+------+------+-------+--------------+-------------+--------------+
| 1 | 5 | 9 | . | 2 | 5 | 0 |
+-----------+------+------+-------+--------------+-------------+--------------+
So, the number 159.25 means we have 1 Hundred, 5 Tens, 9 Ones, 2 Tenths, and 5 Hundredths. It's like saying "one hundred fifty-nine and a quarter." In Kenya, you might see this as the distance between two towns in kilometres!
Real-World Example: Think about our money! One shilling is made of 100 cents. So, one cent is 1/100 of a shilling. We can write 50 cents as Ksh 0.50. It's not a full shilling, it's a part of it!
Reading and Writing Decimals
Reading decimals is easy once you get the hang of it. There are two main ways:
- The "Point" Method: Simply read the number, say "point", and then read the digits after the point. For 12.75, you say "Twelve point seven five." This is the most common way.
- The "Place Value" Method: You read the whole number, say "and", then read the number after the decimal and say its place value. For 12.75, you say "Twelve and seventy-five hundredths."
Comparing Decimals: Who is Bigger?
Imagine you are at the shop. One brand of biscuits costs Ksh 60.50 and another costs Ksh 60.75. Which one is more expensive? To compare decimals, you follow these simple steps:
- Line up the numbers by their decimal points.
- Start from the left and compare the digits in each place value.
- The first place where the digits are different tells you which number is bigger.
Step 1: Line them up
60.50
60.75
Step 2: Compare from the left
- Tens place: Both are 6. (Same)
- Ones place: Both are 0. (Same)
- Tenths place: One is 5, the other is 7. Aha!
Step 3: Conclude
Since 7 is bigger than 5, 60.75 is bigger than 60.50.
The second packet of biscuits is more expensive! Sawa?
Image Suggestion: A vibrant, colourful photo of a Kenyan market stall (duka). There are shelves with various items like packets of sugar, flour, and sodas. Two different brands of biscuits are placed side-by-side with clear, handwritten price tags showing 'Ksh 60.50' and 'Ksh 60.75'. A student's hand is pointing, comparing the two prices.
Let's Do Some Maths! Operations with Decimals
1. Addition and Subtraction
This is the most important rule: ALWAYS line up the decimal points! If you do that, it's just like adding or subtracting whole numbers.
Shopping Trip! You go to a kiosk to buy a soda for Ksh 35.50 and a chapati for Ksh 20.00. How much do you pay?
Step 1: Line up the decimal points.
35.50
+ 20.00
-------
Step 2: Add column by column, from right to left.
35.50
+ 20.00
-------
55.50
You will pay Ksh 55.50 in total. Easy!
2. Multiplication
Multiplying decimals has a little trick. Forget the decimal point for a moment, then bring it back at the end!
- Step 1: Multiply the numbers as if they were whole numbers.
- Step 2: Count the total number of decimal places in the original numbers.
- Step 3: In your answer, place the decimal point so it has the same number of decimal places you counted.
Example: A tailor needs 2.5 metres of kitenge fabric to make a dress. If the fabric costs Ksh 400.50 per metre, what is the total cost?
Step 1: Multiply 40050 by 25 (ignoring decimals)
40050
x 25
-------
200250 (40050 * 5)
801000 (40050 * 2)
-------
1001250
Step 2: Count decimal places in the original numbers.
400.50 (2 decimal places)
2.5 (1 decimal place)
Total = 2 + 1 = 3 decimal places.
Step 3: Place the decimal point in the answer.
Start from the right and move 3 places to the left.
1001.250
The total cost is Ksh 1,001.25.
3. Division
Division is the big boss, but we can handle it! The main goal is to make the number you are dividing by (the divisor) a whole number.
- Step 1: If the divisor is a decimal, move its decimal point to the right until it's a whole number.
- Step 2: Move the decimal point in the number being divided (the dividend) the same number of places to the right.
- Step 3: Divide as you normally would, placing the decimal point in the answer directly above its new position in the dividend.
Example: Four friends share a lunch bill of Ksh 950.50 equally. How much does each person pay?
Here, the divisor is 4, which is already a whole number. So we just divide!
237.625
_______
4 | 950.500 <- We add zeros as needed
-8
---
15
-12
----
30
-28
---
25
-24
---
10
-8
--
20
-20
---
0
Each person pays Ksh 237.625. Since we don't have a coin smaller than 50 cents, in real life, you would round this. Some would pay Ksh 237.50 and others Ksh 238!
You've Got This!
Well done for making it this far! Decimals are not scary; they are just a way of being more precise. From the fuel pump to the supermarket, from a carpenter's measuring tape to an athlete's stopwatch, decimals are everywhere. Keep practicing, stay curious, and you'll be a mathematics champion. Kazi nzuri!
Habari Mwanafunzi! Let's Unlock the Magic of Decimals!
Have you ever been to the supermarket or your local duka and seen prices like KSh 45.50 for bread or KSh 120.75 for milk? That small dot between the numbers is not just a speck of ink! It's a powerful mathematical tool called a decimal point, and today, we are going to become masters of it. Decimals are everywhere – in prices, in measurements when the tailor is making your school uniform, and even in sports results! So, let's get ready to explore this exciting part of numbers.
Image Suggestion: A vibrant, colourful image of a Kenyan market scene. A stall is visible with neatly arranged fruits and vegetables. Price tags are clearly displayed showing decimal prices, for example: "Mangoes: KSh 35.50", "Sukuma Wiki (bunch): KSh 10.00", "Tomatoes (kg): KSh 90.50". A smiling student is looking at the prices with curiosity.
Part 1: What Exactly is a Decimal?
Think of a whole number, like the 100 Shillings your auntie gave you. A decimal represents a part of a whole number, just like 50 cents is a part of 100 Shillings.
A decimal is simply another way of writing a fraction. The decimal point separates the whole number part from the fraction part.
- Numbers to the left of the dot are whole numbers (like 1, 10, 25 Shillings).
- Numbers to the right of the dot are the parts or fractions (like 50 cents, which is half a shilling).
Imagine a number line. Decimals live in the spaces between the whole numbers!
<---!---!---!---!---!---!---!---!---!---!---!--->
0 0.1 0.2 ... 0.5 ... 0.8 0.9 1 1.1 1.2 ... 2
^ ^
| |
A small part A whole number
of 1 (1/10) and a small
part (1 and 1/10)
Part 2: Place Value - A Home for Every Digit
Just like every house in your estate has an address, every digit in a number has a place. This is very important for understanding decimals. The decimal point is the main landmark!
Let's look at the number 345.789
+-----------+-----------+----------+---+----------+------------+-------------+
| HUNDREDS | TENS | ONES | . | TENTHS | HUNDREDTHS | THOUSANDTHS |
| (100) | (10) | (1) | . | (1/10) | (1/100) | (1/1000) |
+-----------+-----------+----------+---+----------+------------+-------------+
| 3 | 4 | 5 | . | 7 | 8 | 9 |
+-----------+-----------+----------+---+----------+------------+-------------+
- 345 is the whole number part.
- The . is the decimal point.
- 789 is the decimal part.
- 7 is in the Tenths place (it means 7/10).
- 8 is in the Hundredths place (it means 8/100).
- 9 is in the Thousandths place (it means 9/1000).
Notice the "-ths" at the end of the decimal place values? That's the secret to remembering they are parts of a whole!
Part 3: Doing Maths with Decimals (The Fun Part!)
Now that we understand what decimals are, let's use them. Here is the most important rule, especially for adding and subtracting:
The Golden Rule: Always, always, ALWAYS line up the decimal points! Keep them in a straight, neat column, like soldiers on parade.
A. Addition and Subtraction
Imagine you go to the kiosk. You buy a bottle of soda for KSh 35.50 and a chapati for KSh 20.00. How much do you spend?
Step 1: Write down the numbers, lining up the decimal points.
KSh 35.50
+ KSh 20.00
----------
Step 2: Add the columns from right to left, just like with whole numbers.
Bring the decimal point straight down into your answer.
KSh 35.50
+ KSh 20.00
----------
KSh 55.50 <-- Your total cost!
Now, you pay with a KSh 100 note. What is your change? That's subtraction!
Step 1: Line up the decimal points. Wait, 100 has no decimal point!
No problem, we can add one. 100 is the same as 100.00.
KSh 100.00
- KSh 55.50
-----------
Step 2: Subtract from right to left, borrowing where needed.
Bring the decimal point straight down.
9 9 10
/ / /
KSh 100.00
- KSh 55.50
-----------
KSh 44.50 <-- This is your change!
B. Multiplication
Multiplying decimals has a different trick. Let's say you need to buy 2.5 kg of sugar, and one kilogram costs KSh 160.
- Step 1: Ignore the decimals and multiply the numbers: 25 x 160.
- Step 2: Count the total number of decimal places in the original numbers. (2.5 has one decimal place. 160 has zero). Total = 1.
- Step 3: Place the decimal point in your answer so it has that many places.
160
x 25
-----
800 (5 x 160)
+3200 (20 x 160)
-----
4000
Now, we need 1 decimal place in our answer.
So, 4000 becomes 400.0.
The cost is KSh 400.00.
Image Suggestion: A split-panel image. On the left, a student is carefully weighing 2.5kg of sugar on a digital scale in a shop. On the right, the same student is at a desk, writing out the multiplication problem (160 x 2.5) in their exercise book, looking focused.
Part 4: Tusuluhishe Shida! (Let's Solve a Problem!)
Time to be a real mathematician! Let's solve a story problem.
Amina is travelling by matatu from Nairobi to Nakuru, a distance of 159.2 kilometres. The matatu driver says they have already covered 85.7 kilometres. How many more kilometres are left to reach Nakuru?
What kind of maths do we need here? We have the total distance and the part covered. To find the remaining part, we need to subtract!
Step 1: Write the numbers down, lining up the decimal points.
159.2 km
- 85.7 km
-------
Step 2: Subtract from right to left. We need to borrow.
8 12
/ /
159.2 km
- 85.7 km
-------
73.5 km
Answer: Amina has 73.5 kilometres left to reach Nakuru. See? You just used decimals to solve a real-life Kenyan problem!
You've Done It! Hongera!
Wow! You have learned so much today. We discovered that decimals are just parts of a whole number, we learned how to use the place value chart, and we even did addition, subtraction, and multiplication with them.
Remember the golden rule for adding and subtracting: Line up the decimal points!
Keep practicing. The more you use decimals, the easier they will become. You will see them everywhere now! Wewe ni mwerevu sana! (You are very smart!)
Habari Mwanafunzi! Unlocking the Power of Decimals!
Hello there, future mathematician! Ever been to the duka or supermarket and seen prices like KSh 50.50 for a packet of milk or KSh 125.75 for sugar? Or maybe you've measured your height and found you are 1.5 metres tall? That little dot is called a decimal point, and it's a super important part of numbers. Today, we're going on an adventure to understand decimals. By the end of this lesson, you'll see them not as tricky dots, but as helpful friends in your daily life. Let's begin!
Image Suggestion: A vibrant, colourful illustration of a Kenyan market stall (duka). A friendly shopkeeper is handing a packet of milk to a smiling student. The price tag clearly visible says "Milk: KSh 55.50". The style should be cheerful and educational, like a modern textbook illustration.
What Exactly IS a Decimal?
Think about our Kenyan Shillings. We have shillings and we have cents. It takes 100 cents to make 1 shilling. A decimal point helps us write an amount that has both shillings and cents together in a neat way.
For example, KSh 50 and 50 cents is written as KSh 50.50. The decimal point separates the whole shillings from the part of a shilling (the cents).
So, a decimal number has two parts:
- A whole number part (to the left of the dot).
- A decimal part (to the right of the dot), which represents a fraction or a piece of a whole.
Let's look at this with a Place Value Chart. It helps us see the value of each digit.
+-----------+------+------+---+--------------+------------+-------------+
| Thousands | Hundreds | Tens | Ones | . (Decimal) | Tenths | Hundredths | Thousandths |
+-----------+------+------+---+--------------+------------+-------------+-------------+
| | | 1 | 2 | . | 3 | 5 | 8 |
+-----------+------+------+---+--------------+------------+-------------+-------------+
In the number 12.358:
- 12 is the whole number part.
- The dot . is the decimal point.
- 3 is in the tenths place (3/10).
- 5 is in the hundredths place (5/100).
- 8 is in the thousandths place (8/1000).
We read this number as "Twelve and three hundred fifty-eight thousandths". But in everyday life, you will hear people say "Twelve point three five eight". Both are correct, but understanding the first way helps you know what it really means!
Operations with Decimals: The Fun Part!
Now let's see how we can use decimals in calculations. This is where you'll feel like a real math wizard!
1. Addition (+) and Subtraction (-)
There is ONE golden rule for adding and subtracting decimals: Line up the decimal points! Imagine the points are buttons on a shirt, and you have to line them up perfectly.
Scenario: You go to the shop with KSh 150. You buy a loaf of bread for KSh 60.00 and a packet of biscuits for KSh 35.50. How much do you spend in total?
Let's add KSh 60.00 and KSh 35.50.
Step 1: Write the numbers, aligning the decimal points.
60.00
+ 35.50
-------
Step 2: Add the columns from right to left, just like with whole numbers.
60.00
+ 35.50
-------
95.50
You spent KSh 95.50!
Now, how much change do you get from your KSh 150? We subtract!
Step 1: Align the decimal points. Note that 150 can be written as 150.00.
150.00
- 95.50
--------
Step 2: Subtract, borrowing where needed.
150.00
- 95.50
--------
54.50
You will get KSh 54.50 back. Vizuri sana!
Image Suggestion: A simple, clear diagram showing two numbers (e.g., 12.34 and 5.6) being added. A bright red dashed vertical line should run through the decimal points to emphasize the alignment. The numbers should look like they are on a grid paper.
2. Multiplication (×)
Multiplying decimals is a bit different. Here's the secret trick:
- Forget the decimals for a moment and multiply the numbers as if they were whole numbers.
- Count the total number of digits after the decimal point in BOTH numbers you multiplied.
- Put the decimal point back in your answer. The answer must have the same number of decimal places you counted in step 2.
Scenario: The price of one kilogram of sukuma wiki is KSh 45.50. You want to buy 2.5 kilograms for your family. How much will it cost?
We need to calculate 45.50 × 2.5.
Step 1: Multiply 4550 by 25 (ignoring the decimals).
4550
x 25
------
22750 (5 x 4550)
+ 91000 (20 x 4550)
------
113750
Step 2: Count the decimal places in the original numbers.
- 45.50 has 2 decimal places.
- 2.5 has 1 decimal place.
- Total decimal places = 2 + 1 = 3.
Step 3: Place the decimal point in the answer. We need 3 decimal places.
Starting from the right of 113750, we move 3 places to the left.
The answer is 113.750.
So, it will cost KSh 113.75.
3. Division (÷)
Division can seem tricky, but we have a rule to make it easy. The goal is to make the number you are dividing by (the divisor) a whole number.
Scenario: Four friends went for lunch and the total bill was KSh 1820.40. They want to share the cost equally. How much should each person pay?
We need to calculate 1820.40 ÷ 4. Here, the divisor (4) is already a whole number, so it's straightforward!
Step 1: Place the decimal point in the answer directly above the decimal point in the number being divided.
______
4|1820.40
Step 2: Divide as you normally would.
455.10
_______
4|1820.40
-16
---
22
-20
---
20
-20
---
04
-4
--
00
Each friend should pay KSh 455.10. Sawa?
Your Turn to Be the Expert!
Decimals are everywhere: in recipes (1.5 cups of flour), in sports (a race won by 0.2 seconds), and in construction (a plank of wood 2.5 metres long). Now that you know how to work with them, you have a new mathematical superpower! Keep practicing, look for decimals in the world around you, and you'll be a master in no time.
Remember, just like learning to ride a bike, practice makes perfect. Hongera for learning something new today!
Pro Tip
Take your own short notes while going through the topics.
