Place Value Patterns
What happens to the decimal point when you multiply a decimal by 10? Give an example using 3.47
34.7 It moves to the right
3.2 × 10
= 32 Decimal moves 1 right.
Estimate 786 ÷ 3:
780 ÷ 3 = 260 (good estimate)
10³
1000
$0.85 × 3
$2.55
Write 4,072.359 in expanded form using place value (include thousandths).
4,000 + 70 + 2 + 0.3 + 0.05 + 0.009
4.25 × 0.1
= 0.425
Multiplying by 0.1 is the same as dividing by 10 → move decimal 1 left.
1,024 ÷ 8 (place value split)
1,024 = 800 + 200 + 24
800 ÷ 8 = 100
200 ÷ 8 = 25
24 ÷ 8 = 3
Total = 128
54 × 10³
54 × 10³ = 54 × 1000 = 54,000
2.45 + 3.6 = 2.45 + 3.60 =
6.05 miles
Compare 5.406 and 5.46:
5.406 < 5.46
0.75 cups/batch × 8 batches
= 6.00 cups
Because 75 hundredths × 8 = 600 hundredths → 6 cups.
3,456 ÷ 12 (partial quotients)
12×200 = 2400 → remainder 1056
12×80 = 960 → remainder 96
12×8 = 96 → remainder 0
Total = 288
5.47 × 10²
= 5.47 × 100 = 547
1.25 × 0.4
1.25 × 4 = 5.00, then divide by 10 (because 0.4 is 4 tenths): 0.5 cups
Round 12.678
Nearest tenth: look at the hundredths (7) → round up: 12.7
Nearest whole: look at the tenths (6) → round up: 13
24.6 ÷ 0.3
Multiply both by 10 to clear decimals:
246 ÷ 3 = 82
So 24.6 ÷ 0.3 = 82
2,500 ÷ 24 (full boxes + remainder meaning)
24×100 = 2400 → remainder 100
24×4 = 96 → remainder 4
So 104 full boxes, 4 toys left over.
0.805 ÷ 10¹
= 0.805 ÷ 10 = 0.0805
$47.50 ÷ 5 =
= $9.50
If a number × 100 = 7,204.5, the original is ÷100 (move decimal 2 left):
7,204.5 ÷ 100 = 72.045
12.03 × 4.2
Do 1203 × 42, then place decimals (2 decimal places in 12.03 and 1 in 4.2 → total 3).
1203 × 42 = 1203×40 + 1203×2 = 48,120 + 2,406 = 50,526
Put 3 decimals: 50.526
4,812 ÷ 36 (build quotient by place value)
36×100 = 3600 → remainder 1212
36×30 = 1080 → remainder 132
36×3 = 108 → remainder 24
So quotient is 133 remainder 24
(That’s 133 24/36 = 133 2/3 ≈ 133.666…)
6.302 ÷ 10²
0.06302
4.5 × 2.75
12.375