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Place value and estimating: cheat sheet

Number Foundations · The words and methods from the lessons, with an example of each.

power of 10

Each place value column is a power of 10. The exponent counts the zeros, and the ones column is 100=110^0 = 1.

103=10×10×10=100010^3 = 10 \times 10 \times 10 = 1000

decimal places

The number of digits after the decimal point. To 2 decimal places means to the nearest hundredth.

3.746 has 3 decimal places3.746 \text{ has 3 decimal places}

estimate

A quick, close answer from rounded numbers. Round to the first digit and keep the size; then compare with the exact answer.

38×52≈40×50=200038 \times 52 \approx 40 \times 50 = 2000
38 × 52 ≈ 40 × 50 = 2000; the exact answer is 1976
38 × 52 ≈ 40 × 50 = 2000; the exact answer is 1976

estimating

Round each number to its first digit, keep its size, calculate, then compare with the exact answer.

19.6×4.1≈20×4=8019.6 \times 4.1 \approx 20 \times 4 = 80

expanded notation

A number as the sum of each digit times its place value. A column holding 0 adds nothing, so leave it out.

4052=4×103+5×101+2×1004052 = 4 \times 10^3 + 5 \times 10^1 + 2 \times 10^0
4052 on the columns: 4 × 10³ + 5 × 10¹ + 2 × 10⁰
4052 on the columns: 4 × 10³ + 5 × 10¹ + 2 × 10⁰

round to decimal places

Look at the digit straight after the place. 5 or more rounds up; 4 or less leaves the digit. Halfway rounds up.

3.746→3.75 (2 d.p.)3.746 \to 3.75 \ (2 \text{ d.p.})
3.746 is past the halfway mark 3.745, so it rounds to 3.75
3.746 is past the halfway mark 3.745, so it rounds to 3.75