Estimate each of the following products by rounding off each number to nearest tens:
(a) 87 × 32
(b) 311 × 113
(c) 3239 × 28
(d) 1385 × 789
(a) 90 × 30 = 2700
(b) 310 × 110 = 34100
(c) 3240 × 30 = 97200
(d) 1390 × 790 = 1098100
Goal: estimate by rounding each number to the nearest 10, then multiply.
Rounding rule: Ones digit 0–4 → round down. Ones digit 5–9 → round up.
(a) 87 × 32
Round:
\(87 \approx 90\)
\(32 \approx 30\)
Multiply:
\(90 \times 30 = 9 \times 3 \times 100 = 27 \times 100 = 2700\)
(b) 311 × 113
Round:
\(311 \approx 310\)
\(113 \approx 110\)
Multiply:
\(310 \times 110 = 31 \times 11 \times 100\)
\(31 \times 11 = 341\)
So, \(341 \times 100 = 34100\)
(c) 3239 × 28
Round:
\(3239 \approx 3240\)
\(28 \approx 30\)
Multiply:
\(3240 \times 30 = 324 \times 3 \times 100\)
\(324 \times 3 = 972\)
So, \(972 \times 100 = 97200\)
(d) 1385 × 789
Round:
\(1385 \approx 1390\)
\(789 \approx 790\)
Multiply:
\(1390 \times 790 = (139 \times 79) \times 100\)
\(139 \times 79 = 139 \times (80 - 1)\)
\(= 139 \times 80 - 139 \times 1\)
\(= 11120 - 139 = 10981\)
So, \(10981 \times 100 = 1098100\)
Note: These are estimates, so answers are close to the exact products.