Understanding place value
🎯 In this topic you will
- Explain the value of a digit in a decimal number (tenths and hundredths)
- Multiply and divide whole numbers by 1000
- Multiply and divide decimals by 10 and 100
Correct Medicine Dosage
I t is very important for a doctor to give the correct amount of medicine. A dose of 10 ml is ten times greater than a dose of 1 ml and ten times smaller than a dose of 100 ml.
🧠 Key Words
- compose
- decimal
- decimal place
- decimal point
- decompose
- hundredth
- place value
- tenth
Show Definitions
- compose: To build a number by joining its parts together.
- decimal: A number that includes a decimal point to show parts that are less than one whole.
- decimal place: The position of a digit to the right of the decimal point.
- decimal point: The symbol used to separate the whole number part from the fractional part of a number.
- decompose: To break a number into its parts based on place value.
- hundredth: One part when a whole is divided into 100 equal pieces.
- place value: The value of a digit depending on its position in a number.
- tenth: One part when a whole is divided into 10 equal pieces.
📌 The Value of a Digit
T he value of a digit depends on its position in the number. Think about what the digit 5 is worth in these numbers.
💡 Quick Math Tip
Digit Value Depends on Position: The same digit can represent different amounts depending on where it appears in the number — for example, the digit 5 is worth more in the tens place than in the ones or tenths place.
❓ EXERCISES
1. Write these numbers in digits.
a. One thousand and one point zero one
b. Five hundred thousand and five point nine
c. Four hundred and three thousand, and thirty-four point six six
👀 Show answer
b) $500005.9$
c) $403034.66$
2. Write these numbers in words.
a. $345.09$
b. $5378.12$
c. $158\,035.4$
d. $3030.03$
👀 Show answer
b) five thousand three hundred and seventy-eight point one two
c) one hundred and fifty-eight thousand and thirty-five point four
d) three thousand and thirty point zero three
3. What is the value of the digit 7 in these numbers?
a. $6703.46$
b. $70\,213.8$
c. $606\,456.7$
d. $234\,560.07$
👀 Show answer
b) $70\,000$
c) $0.7$
d) $0.07$
4. Write these numbers in words and digits.
a. $200\,000 + 6\,000 + 300 + 2 + 0.1$
b. $900\,000 + 90\,000 + 900 + 9 + 0.9$
c. $100\,000 + 20\,000 + 5\,000 + 600 + 20 + 5 + 0.4 + 0.03$
👀 Show answer
b) $990909.9$ — nine hundred and ninety thousand nine hundred and nine point nine
c) $125625.43$ — one hundred and twenty-five thousand six hundred and twenty-five point four three
5. Write the missing numbers.
a. $358 \times 100 =$ □
b. $2700 \div$ □ $= 27$
c. $5600 \div 1000 =$ □
d. $456 \times 1000 =$ □
👀 Show answer
b) $100$
c) $5.6$
d) $456000$
6. Sofia multiplies a number by 10, then again by 10 and then again by 10.
Her answer is $20\,000$. What number did she start with?
👀 Show answer
7. Write the missing numbers.
a. $3.45 \times 100 =$ □
b. $16.8 \div 10 =$ □
c. $6.5 \times 10 =$ □
👀 Show answer
b) $1.68$
c) $65$
8. Find and correct the mistakes in this diagram.
• $58 \times 100 = 5800$ (the diagram wrongly shows $0.58$)
• $58 \times 1000 = 58000$ (not $5800$)
• $58 \div 1000 = 0.058$ (not $5800$)
• $58 \div 10 = 5.8$ is correct
👀 Show answer
9. Which missing number is the odd one out?
A $33 \div 10 =$ □ B □ $\times 100 = 330$
C □ $\times 10 = 30.3$ D $3300 \div 1000 =$ □
Explain your answer.
👀 Show answer
B = $3.3$
C = $3.03$
D = $3.3$
The odd one out is **C** because its value ($3.03$) is different — all others equal $3.3$.
🧠 Think Like a Mathematician
Zara is thinking of a decimal number less than 1.
Your task:
- Work out what number Zara is thinking of.
- Create a similar clue-based number puzzle of your own.
- Show you are specialising by giving examples that fit the criteria.
👀 show answer
- The tenths digit is $3$ because if the hundredths digit is four more, it becomes $7$.
- $3 + 7 = 10$ — this satisfies the clue.
- Therefore, the decimal number is $0.37$.
- Example of a similar puzzle you could write:
“I am thinking of a decimal number less than 1. The hundredths digit is double the tenths digit. The sum of the digits is 9.” (Answer: $0.36$)