Place vaule
🎯 In this topic you will
- Explain the value of each digit in numbers with up to three decimal places.
- Multiply and divide whole numbers and decimals by 10, 100, and 1000.
- Compose, decompose, and regroup numbers with up to three decimal places.
🧠 Key Words
- compose
- decompose
- decimal point
- digit
- hundredths
- place value
- regroup
- tenths
- thousandths
Show Definitions
- compose: To build a number by combining smaller place value parts together.
- decompose: To break a number into smaller parts based on its place values.
- decimal point: The dot in a number that separates the whole number part from the decimal part.
- digit: Any of the ten symbols (0–9) used to write numbers.
- hundredths: The place value representing one part out of one hundred, two places to the right of the decimal point.
- place value: The value of a digit based on its position in a number.
- regroup: To rearrange numbers by trading between place values when calculating.
- tenths: The place value representing one part out of ten, immediately to the right of the decimal point.
- thousandths: The place value representing one part out of one thousand, three places to the right of the decimal point.
🔢 Reading and Writing Decimals
You already know how to read and write decimal numbers with $1$ or $2$ decimal places.
🧮 Working with Numbers
You can compose, decompose and regroup numbers, and you can multiply and divide by $10$, $100$ and $1000$.
🦋 A Real-World Example
The Western Pygmy Blue Butterfly is very small. Some have a wingspan of only $0.375$ inches, which is between $9$ and $10$ millimetres.
❓ EXERCISES
1. What is the value of the digit $7$ in these numbers?
a. $6703.46$
b. $213.807$
c. $456.702$
d. $60.078$
👀 Show answer
b. $0.007$
c. $0.7$
d. $0.07$
2. Sonia has these five cards.
What is the smallest number, greater than $1$, she can make using all her cards?
👀 Show answer
3. Find the odd one out.
$1.234$
$1234$ thousandths
$12.34$
$123.4$ hundredths
$123$ hundredths and $4$ thousandths
Explain your answer.
👀 Show answer
4. Add these numbers together and write the total number in words and digits.
a. $2 + 0.1 + 0.03 + 0.009$
b. $-900 - 9 - 0.9 - 0.009$
c. $20 + 5 + 0.4 + 0.03 + 0.001$
d. $-3 - 0.4 - 0.08 - 0.001$
Swap books with your partner and check their answer. Read the numbers to each other.
👀 Show answer
b. $-909.909$
c. $25.431$
d. $-3.481$
5. Copy and complete.
$37.844 = 30 + 7 + \square + 0.04 + \square$
👀 Show answer
6. Petra is regrouping decimal numbers. She spills ink on her work. What number is under each ink blot?
a. $0.546 = 0.4 + \square + 0.006$
b. $0.789 = 0.7 + 0.07 + \square$
👀 Show answer
b. $0.019$
7. Find the missing numbers.
a. $7.2 \times 1000 = \square$
b. $0.85 \times 100 = \square$
c. $4.28 \times 10 = \square$
d. $670 \div 100 = \square$
e. $151 \div 1000 = \square$
f. $5.5 \div 10 = \square$
Check your answers with your partner.
👀 Show answer
b. $85$
c. $42.8$
d. $6.7$
e. $0.151$
f. $0.55$
8. Look at these number cards.
Write the letter of the card that is:
a. one thousand times bigger than $12$
b. one hundredth of $12$
c. one thousandth of $120\,000$
👀 Show answer
b. $\text{D}$
c. $\text{E}$
9. Mira divides a number by $10$, then by $10$ again and then by $10$ again. Her answer is $0.005$. What number did she start with?
👀 Show answer
🧠 Think like a Mathematician
There are $10$ trees in the Numberland Woods.
Each tree has $10$ branches. Each branch has $10$ twigs.
Each twig has $10$ flowers. Each flower has $10$ petals.
Sofia went into the woods.
She took $1$ petal, $1$ flower, $1$ twig and $1$ branch.
Question: How many petals are left in the woods?
Show Answers
- Total petals originally: $10 \times 10 \times 10 \times 10 \times 10 = 100\,000$.
- Petals removed:
- $1$ petal
- $1$ flower = $10$ petals
- $1$ twig = $10 \times 10 = 100$ petals
- $1$ branch = $10 \times 10 \times 10 = 1000$ petals
- Total removed: $1 + 10 + 100 + 1000 = 1111$.
- Petals left: $100\,000 - 1111 = 98\,889$.