➗ Divide Decimals by Powers of Ten
Grade 5 Complete Notes & Formulae
Key Concepts
- Dividing by powers of ten (10, 100, 1000, ...) moves the decimal point to the left.
- The number of zeros in the power of ten is the number of places the decimal moves.
- Dividing by exponents: \(10^n\) means move the decimal \(n\) places to the left.
1️⃣ Steps: Dividing by Powers of Ten (\(10, 100, 1000, ...\))
The Rule:
- Each zero (or exponent) means move the decimal one place left.
- \(a.bcd \div 10 = 0.abcd\) (move 1 place left)
- \(a.bcd \div 100 = 0.0abcd\) (2 places)
- \(a.bcd \div 1000 = 0.00abcd\) (3 places)
Examples:
- \(7.1 \div 10 = 0.71\)
- \(4.8 \div 100 = 0.048\)
- \(32 \div 1000 = 0.032\)
- \(6.39 \div 10^2 = 0.0639\)
Main Formula
\(x.yz \div 10^n = 0.0...xyz\)
(move decimal \(n\) places left)
2️⃣ Decimal Division Patterns & Place Value
- Every time you divide by 10, the number becomes 10 times smaller (move decimal 1 left).
- Repeated division by powers of ten shrinks numbers to tenths, hundredths, thousandths, etc.
- Pattern: Numbers get smaller on the place value chart with each division by 10.
| Divide By | Movement | Example | Result |
|---|---|---|---|
| 10 | 1 place left | 36.92 ÷ 10 | 3.692 |
| 100 | 2 places left | 36.92 ÷ 100 | 0.3692 |
| 1000 | 3 places left | 36.92 ÷ 1000 | 0.03692 |
3️⃣ Dividing with Exponents
- \(a.bcd \div 10^n\): Move the decimal \(n\) places to the left.
- \(\text{If not enough digits, add zeros to the left}\).
Examples:
\(7.45 \div 10^2 = 0.0745\)
\(18.2 \div 10^3 = 0.0182\)
\(0.5 \div 10^1 = 0.05\)
\(7.45 \div 10^2 = 0.0745\)
\(18.2 \div 10^3 = 0.0182\)
\(0.5 \div 10^1 = 0.05\)
Exponent Rule
\(x.yz \div 10^n =\) shift decimal \(n\) left
4️⃣ Dividing by 0.1, 0.01 and Fractional Powers
Key Rule:
Dividing by 0.1 or 0.01 makes the number bigger!
Dividing by 0.1 or 0.01 makes the number bigger!
- \(a.bc \div 0.1 = a.bc \times 10\) (move decimal right once)
- \(a.bc \div 0.01 = a.bc \times 100\) (move decimal right twice)
- \(a.bc \div 0.001 = a.bc \times 1000\)
Examples:
\(4.2 \div 0.1 = 42\)
\(0.13 \div 0.01 = 13\)
\(4.2 \div 0.1 = 42\)
\(0.13 \div 0.01 = 13\)
Dividing by Small Decimals Formula
\(x.yz \div 0.1^n = x.yz \times 10^n\)
(move decimal \(n\) places right)
5️⃣ Find the Missing Number
- If \(x \div 100 = 0.42\), what is \(x\)?
Move decimal two right: \(x = 42\) - If \(y \div 0.1 = 7.8\), what is \(y\)?
Divide by 0.1 = multiply by 10: \(y = 0.78\)
6️⃣ Decimal Place Value Chart (Visual)
| Thousands | Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 1,000 | 100 | 10 | 1 | . | 0.1 | 0.01 | 0.001 |
7️⃣ Practice Problems
- \(24.75 \div 10 =\) _____
- \(6.12 \div 100 =\) _____
- \(2.9 \div 0.1 =\) _____
- \(5.17 \div 1000 =\) _____
- \(0.28 \div 0.01 =\) _____
- If \(x \div 100 = 5.73\), what is \(x\)?
Answers:
1) 2.475
2) 0.0612
3) 29
4) 0.00517
5) 28
6) 573
1) 2.475
2) 0.0612
3) 29
4) 0.00517
5) 28
6) 573